Preface

**Section 3 Spinel-Based Ferrofluids 137**

**VI** Contents

**Ferrofluids 139**

**Magnetic Fluids 161** Tomohiro Iwasaki

**Section 4 Synthesis and Applications 183**

**Applications 253**

Oscar F. Odio and Edilso Reguera

Chapter 10 **CVD‐Made Spinels: Synthesis, Characterization and Applications for Clean Energy 217**

Chapter 7 **Manganese-Zinc Spinel Ferrite Nanoparticles and**

Rajender Singh and Gadipelly Thirupathi

Chapter 8 **Mechanochemical Synthesis of Water-Based Magnetite**

Chapter 9 **Nanostructured Spinel Ferrites: Synthesis, Functionalization, Nanomagnetism and Environmental Applications 185**

Chapter 11 **Spinel‐Structured Nanoparticles for Magnetic and Mechanical**

Chapter 12 **Photothermal Conversion Applications of the Transition Metal**

Pengjun Ma, Qingfen Geng and Gang Liu

Chapter 13 **Anti‐Corrosive Properties and Physical Resistance of Alkyd**

Patrick Mountapmbeme Kouotou, Guan‐Fu Pan and Zhen‐Yu Tian

Malik Anjelh Baqiya, Ahmad Taufiq, Sunaryono, Khuroti Ayun, Mochamad Zainuri, Suminar Pratapa, Triwikantoro and Darminto

**(Cu, Mn, Co, Cr, and Fe) Oxides with Spinel Structure 273**

**Resin–Based Coatings Containing Mg‐Zn‐Fe Spinels 285** Kateřina Nechvílová, Andrea Kalendová and Miroslav Kohl

The magnetism of lodestone (Fe3O4), now known to be a room temperature ferrimagnet with the spinel structure, was discovered many centuries ago. However, it was likely the research work of Snoek and others in the mid-twentieth century [1–3] that really kindled the research interest of the scientific community to this new class of magnetic materials whose structure is based on nonmagnetic mineral called spinel with the chemical formula MgAl2O4. These materials are magnetic spinels with the formula AB2X4 = [A][B2]X4, where A and B are gener‐ ally divalent and trivalent cations, respectively, and X is usually oxygen although spinels with X = S, Se, Te, etc. have also been investigated. This spinel structure is cubic with cell length of about 0.84 nm, and it normally contains 8 formula units of the spinel. Ferrites are a special class of spinels with the general formula MFe2O4, M being a divalent metal ion.

The continued worldwide interest in these materials stems from two primary factors: (i) A variety of magnetic and nonmagnetic ions can be accommodated on the eight tetrahedral A sites and 16 octahedral B sites leading to new materials and a wealth of new physics and phenomena resulting from their fundamental investigations, and (ii) unlike metallic room temperature ferromagnets such as Fe, Co, and Ni, the magnetic spinels generally have very low electrical conductivity which leads to many applications of these spinels particularly in microwave communication devices and where reducing the eddy current losses is an impor‐ tant consideration. Recent developments in the use of magnetic spinels for microwave com‐ munication devices have been reviewed by Harris et al. [4]. The ferromagnetic-like magnetic moment observed in many of these spinels at room temperature is due to ferrimagnetism resulting from overall noncancelation of the magnetic moments aligned usually antiferro‐ magnetically on the A and B sites. The theory of this ferrimagnetism was first advanced by Néel [5], and it is described in detail in the book by Morrish [6] where some of the other basic properties of ferrimagnets and magnetic spinels are also given.

The diversity of the properties of the magnetic spinels is best illustrated by comparing the nature of magnetism in the three simple spinels: Mn3O4 = [Mn2+][2Mn3+]O4, Fe3O4 = [Fe3+] [Fe2+Fe3+]O4, and Co3O4 = [Co2+][2Co3+]O4. It is noted that for Mn3O4 and Co3O4, the A site is occupied by divalent cations as expected in *normal* spinels. However, Fe3O4 is an example of an *inverse* spinel because the positions of half of the Fe3+ ions on the A sites and Fe2+ ions on the B site are inverted between the A and B sites. This degree of inversion can vary between 0 and 1 in more complex spinels. Magnetically, Mn3O4 is a ferrimagnet with an ordering temperature TC = 43 K [7], Co3O4 is an antiferromagnet with Néel temperature TN = 30 K [8], and Fe3O4 is a room temperature ferrimagnet with ordering temperature TC = 800 K [9]. Such large differences in their magnetism illustrate how changes in magnetic ions lead to enor‐ mous differences in the magnetic properties of the spinels. The physics behind these differ‐ ences is explained in the original papers listed above and references quoted in these publications.

There are certain topics of fundamental interest related to magnetic spinels which unfortu‐ nately did not get included in this book as separate chapters. Since these topics are consid‐ ered to be quite important, a brief description of these topics is given here for the benefit of the readers of this book. The first such topic is the nature of magnetism in the group of nor‐ mal spinels such as ZnFe2O4 and CdFe2O4 in which the A sites are occupied by nonmagnetic ions only, such as Zn2+ and Cd2+ in the above cases. A 1956 paper by Anderson [10] showed that in such a case where only the B sites are occupied by cations with magnetic moments, in the above case by Fe3+, magnetic ordering is not possible at any nonzero temperature be‐ cause of magnetic frustration. This indeed is observed in the above cases [6, 11]. Another recent example of such magnetic frustration is the defect spinel MgMnO3 = (¾){Mg2+} {Mg2+1/3Mn4+4/3 V1/3}O4 with V as vacancy on the octahedral sites; this material showed the presence of some short-range magnetic ordering but without a magnetic transition associat‐ ed with long-range ordering [12].

Another topic of considerable importance but not covered in any of the chapters included here is the special area of defect spinels, the prime example of which is the mineral maghe‐ mite with the chemical formula γ-Fe2O3. For γ-Fe2O3, not all the usual octahedral B sites are occupied, and the unit cell contains (32/3) formula units arranged as (32/3) (γ-Fe2O3) = [8 Fe3+][(40/3)Fe3+.(8/3) V]O32. Just like Fe3O4, γ-Fe2O3 is also a ferrimagnet at room temperature [6, 13]. However, in γ-Fe2O3, ferrimagnetism results from the difference in the number of antiferromagnetically aligned Fe3+ ions on the A and B sites, 8 and (40/3) in this case. In con‐ trast, in magnetite with ionic distribution as 8Fe3O4 = 8[Fe3+][Fe2+Fe3+]O4, ferrimagnetism re‐ sults from the magnetic moments of 8 Fe2+ ions on the B sites since the magnetic moment on the antiferromagnetically aligned 8 Fe3+ ions each on A and B sites cancels out. For many applications, γ-Fe2O3 is sometimes preferred over Fe3O4 since Fe3+ ions are in the S-state in which spin-orbit coupling does not make any meaningful contribution to its magnetic mo‐ ment. Among other known examples of defect spinels is MgMnO3 which has already been mentioned in the previous paragraph, nanoparticles of ZnMnO3 with the ionic arrangement as 4ZnMnO3-δ = 3 [Zn1/32+ Mn2/33+Mn2/3 4+ V1/3]O11/3 with δ =0.25 [14] and nanoparticles of Li0.5Mg0.5MnO3 [15]. The nature of magnetic ordering in the latter two cases is not yet certain since the reported measurements were done only on nanoparticles of about 20 nm size, and so the observations were likely dominated by finite size and surface effects. The magnetic properties of bulk system may indeed be different.

Another area which deserves mention and is the focus of major current interest involves the biomedical applications of magnetic nanoparticles, particularly nanoparticles of maghemite (γ-Fe2O3) and magnetite (Fe3O4) as drug delivery agents, because of their apparent biocom‐ patibility and biodegradability [16–19]. For such applications, surfaces of the nanoparticles are functionalized and attached with appropriate therapeutic molecules. The room tempera‐ ture super-paramagnetism of magnetic nanoparticles such as γ-Fe2O3 [13] and Fe3O4 [20] also allows their use for enhancing contrast in magnetic resonance imaging (MRI) [16–19].

This book on magnetic spinels contains 13 chapters written by different groups from around the world. These chapters deal with both the fundamental properties of the spinels as well as some of their applications. These chapters, each dealing with specific properties and ap‐

plications, are intended to serve not only as a review of the specific research area but also present recent developments in that specific area. As editor, I have reviewed each chapter and made recommendations for changes which were generally accepted by the authors, and I thank these authors for their diligence and contributions to this project. Nevertheless, a uniform style of writing was not possible under this scenario, and therefore the individual style of each author will be evident in these chapters. Also, there is obvious lack of linking between different chapters unlike in a text book written by one or two authors. Neverthe‐ less, the 13 chapters are loosely grouped into four parts based on the overall similarities of the topics in each part. Part 1 has three chapters dealing with the synthesis and properties of spinel ferrites and their nanoparticles, Part 2 contains three chapters on the electronic and magnetic properties of the spinels, Part 3 has two chapters on spinel-based ferrofluids, and Part 4 has five chapters dealing with the synthesis of various spinels and their applications. In each chapter, the authors have endeavored to bring out the current status of research in that particular area so that these chapters are good starting points for those readers who wish to pursue further research in that area. As noted above, although not all aspects of the magnetic spinels could be covered in these chapters, the topics that are covered have suffi‐ cient diversity to allow the readers to have good appreciation of the very interesting proper‐ ties of the magnetic spinels and their many current and potential future applications. Different experimental techniques for the synthesis of specific spinels along with their struc‐ tural and fundamental magnetic properties are covered in these chapters. Also, some of the basic properties of magnetic nanoparticles and how and why these properties differ from those of their bulk counterparts are covered. Therefore, it is my hope that the material pre‐ sented in these chapters would be of interest to both new graduate students just starting research in spinels as well as to more seasoned researchers.

#### **References**

ences is explained in the original papers listed above and references quoted in these

There are certain topics of fundamental interest related to magnetic spinels which unfortu‐ nately did not get included in this book as separate chapters. Since these topics are consid‐ ered to be quite important, a brief description of these topics is given here for the benefit of the readers of this book. The first such topic is the nature of magnetism in the group of nor‐ mal spinels such as ZnFe2O4 and CdFe2O4 in which the A sites are occupied by nonmagnetic ions only, such as Zn2+ and Cd2+ in the above cases. A 1956 paper by Anderson [10] showed that in such a case where only the B sites are occupied by cations with magnetic moments, in the above case by Fe3+, magnetic ordering is not possible at any nonzero temperature be‐ cause of magnetic frustration. This indeed is observed in the above cases [6, 11]. Another recent example of such magnetic frustration is the defect spinel MgMnO3 = (¾){Mg2+} {Mg2+1/3Mn4+4/3 V1/3}O4 with V as vacancy on the octahedral sites; this material showed the presence of some short-range magnetic ordering but without a magnetic transition associat‐

Another topic of considerable importance but not covered in any of the chapters included here is the special area of defect spinels, the prime example of which is the mineral maghe‐ mite with the chemical formula γ-Fe2O3. For γ-Fe2O3, not all the usual octahedral B sites are occupied, and the unit cell contains (32/3) formula units arranged as (32/3) (γ-Fe2O3) = [8 Fe3+][(40/3)Fe3+.(8/3) V]O32. Just like Fe3O4, γ-Fe2O3 is also a ferrimagnet at room temperature [6, 13]. However, in γ-Fe2O3, ferrimagnetism results from the difference in the number of antiferromagnetically aligned Fe3+ ions on the A and B sites, 8 and (40/3) in this case. In con‐ trast, in magnetite with ionic distribution as 8Fe3O4 = 8[Fe3+][Fe2+Fe3+]O4, ferrimagnetism re‐ sults from the magnetic moments of 8 Fe2+ ions on the B sites since the magnetic moment on the antiferromagnetically aligned 8 Fe3+ ions each on A and B sites cancels out. For many applications, γ-Fe2O3 is sometimes preferred over Fe3O4 since Fe3+ ions are in the S-state in which spin-orbit coupling does not make any meaningful contribution to its magnetic mo‐ ment. Among other known examples of defect spinels is MgMnO3 which has already been mentioned in the previous paragraph, nanoparticles of ZnMnO3 with the ionic arrangement as 4ZnMnO3-δ = 3 [Zn1/32+ Mn2/33+Mn2/3 4+ V1/3]O11/3 with δ =0.25 [14] and nanoparticles of Li0.5Mg0.5MnO3 [15]. The nature of magnetic ordering in the latter two cases is not yet certain since the reported measurements were done only on nanoparticles of about 20 nm size, and so the observations were likely dominated by finite size and surface effects. The magnetic

Another area which deserves mention and is the focus of major current interest involves the biomedical applications of magnetic nanoparticles, particularly nanoparticles of maghemite (γ-Fe2O3) and magnetite (Fe3O4) as drug delivery agents, because of their apparent biocom‐ patibility and biodegradability [16–19]. For such applications, surfaces of the nanoparticles are functionalized and attached with appropriate therapeutic molecules. The room tempera‐ ture super-paramagnetism of magnetic nanoparticles such as γ-Fe2O3 [13] and Fe3O4 [20] also allows their use for enhancing contrast in magnetic resonance imaging (MRI) [16–19].

This book on magnetic spinels contains 13 chapters written by different groups from around the world. These chapters deal with both the fundamental properties of the spinels as well as some of their applications. These chapters, each dealing with specific properties and ap‐

publications.

VIII Preface

ed with long-range ordering [12].

properties of bulk system may indeed be different.


**Mohindar Singh Seehra** Department of Physics and Astronomy West Virginia University Morgantown, USA **Synthesis, Properties and Applications**

[14] Rall, J. D., Thota, S. Kumar, J. and Seehra, M. S. Appl. Phys. Lett. 100, 252407

[15] Singh, V., Seehra, M. S., Manivannan, A. and Kumta, P. N., J. Appl. Phys. 111,

[16] Thanh, N. T. K.(editor)," Magnetic Nanoparticles: From Fabrication to Clinical

[18] Pankhurst, Q. A. , Thanh, N. K. T., Jones, S. K. and Dobson, J., J. Phys. D.: Appl.

[20] Dutta, C., Pal. S., Seehra, M. S., Shah N. and Huffman, G. P., J. Appl. Phys.105,

**Mohindar Singh Seehra**

West Virginia University Morgantown, USA

Department of Physics and Astronomy

Applications" (CRC Press, Boca Raton, FL, USA, 2012). [17] Revia, R. A. and Zhang, M. Materials Today, 19, 157 (2016).

[19] Wang C. et al. J. Control. Release. 136, 82 (2012).

(2012).

X Preface

07E302. (2012).

07B501 (2009).

Phys. 42, 224001 (2009).

#### **Spinel Ferrite Nanoparticles: Correlation of Structure and Magnetism Spinel Ferrite Nanoparticles: Correlation of Structure and Magnetism**

Barbara Pacakova, Simona Kubickova, Alice Reznickova, Daniel Niznansky and Jana Vejpravova Barbara Pacakova, Simona Kubickova, Alice Reznickova, Daniel Niznansky and Jana Vejpravova

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66074

#### **Abstract**

This chapter focuses on the relationship between structural and magnetic properties of cubic spinel ferrite *M*Fe2O4 (*M* = Mg, Mn, Fe, Co, Ni, Cu and Zn) nanoparticles (NPs). First, a brief overview of the preparation methods yielding well‐developed NPs is given. Then, key parameters of magnetic NPs representing their structural and magnetic properties are summarized with link to the relevant methods of characterization. Peculiar features of magnetism in real systems of the NPs at atomic, single‐particle, and mesoscopic level, respectively, are also discussed. Finally, the significant part of the chapter is devoted to the discussion of the structural and magnetic properties of the NPs in the context of the relevant preparation routes. Future outlooks in the field profiting from tailoring of the NP properties by doping or design of core‐shell spinel‐only particles are given.

**Keywords:** cubic spinel ferrite nanoparticles, magnetic properties, core‐shell struc‐ ture, particle size, spin canting, Mössbauer spectroscopy, magnetic susceptibility, size effect, superparamagnetism, magnetic anisotropy

## **1. Introduction**

Spinel ferrite nanoparticles (NPs) are in the spotlight of current nanoscience due to immense application potential. Very interesting aspects of the spinel ferrite NPs are their excellent magnetic properties often accompanied with other functional properties, such as catalytic activity. Moreover, the magnetic response of the NPs can be tuned by particle size and shape

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

up to some extent. Consequently, various spinel ferrite NPs are suggested as universal and multifunctional materials for exploitation in biomedicine [1–4], magnetic recording, catalysis [5–8] including magnetically separable catalysts [9–12], sensing [13–16] and beyond (MgFe2O4 in Li ion batteries [17, 18], or investigation of dopamine [19]). Thus it is of ultimate interest to get control over their functional properties, which requires in‐depth understanding of the correlation between their structural and magnetic order. For example, the particle size and shape are extremely important both in biomedical imaging using Magnetic Resonance Imaging (MRI) [20] and therapies by means of magnetic field‐assisted hyperthermia [21].

The chapter aims to summarize the most important aspects of magnetism of cubic spinel ferrite nanoparticles (*M*Fe2O4, *M* = Mg, Mn, Fe, Co, Ni, Cu, and Zn) in context of their crystal and magnetic structure. The factors that drive magnetic performance of the spinel ferrite NPs can be recognized on three levels: on the atomic level (degree of inversion and the presence of defects), at single‐particle level as balance between the crystallographically and magnetically ordered fractions of the NP (single‐domain and multi‐domain NPs, core‐shell structure, and beyond), and at mesoscopic level by means of mutual interparticle interactions and size distribution phenomena. All these effects are strongly linked to the preparation routes of the NPs. In general, each preparation method provides rather similar NPs by means of morphol‐ ogy and crystalline order. Thus the "three‐level" concept, which is the focal motif of the chapter, can be applied to all cubic spinel ferrite NPs.

## **2. Brief overview of preparation methods of spinel ferrite nanoparticles**

In this section, selected methods of the NP preparation are summarized. Explicitly, the wet methods yielding well‐defined NPs, either isolated or embedded in a matrix, are accented. The reason is that only such samples can be sufficiently characterized and the factors defined within the "three level" concept can be disentangled. Outstanding reviews on the specific method(s) with further details and references are also included [22–25].

Coprecipitation method is the archetype route, which can be used for preparation of all cubic spinel ferrite NPs: Fe3O4/γ‐Fe2O3 [24, 26], MgFe2O4 [27], etc. In general, two water‐soluble metallic salts are coprecipitated by a base. The reaction can be partly controlled in order to improve characteristics of the NPs [26, 28, 29]; however, it is generally reported as a facile method yielding polydispersed NPs with lower crystallinity and consequently less significant magnetic properties.

The family of decomposition routes includes wet approaches based on decomposition of metal organic precursors in high‐boiling solvents, typically in the presence of coating agents (all [30], Fe3O4/γ‐Fe2O3 [24, 31], CoFe2O4 [32, 33], NiFe2O4 [34], ZnFe2O4 [35]). The most common organic complexes used for decomposition are metal oleates and acetylacetonates. The decomposition methods yield highly crystalline particles close to monodisperse limit with very good magnetic properties. However, the reaction conditions must be controlled in corre‐ spondence of the growth model suggested by Cheng et al. [22]. They can be also tailored to produce NPs of different shapes (CoFe2O4 [36, 37], Fe3O4/γ‐Fe2O3 [38, 39]). Higher‐order assemblies of the NPs can be also achieved by varying the ratio of the precursor and reaction temperature (CoFe2O4 [40]). Alternatively, the decomposition takes place in high‐pressure vessel (autoclave) [41, 42].

up to some extent. Consequently, various spinel ferrite NPs are suggested as universal and multifunctional materials for exploitation in biomedicine [1–4], magnetic recording, catalysis [5–8] including magnetically separable catalysts [9–12], sensing [13–16] and beyond (MgFe2O4 in Li ion batteries [17, 18], or investigation of dopamine [19]). Thus it is of ultimate interest to get control over their functional properties, which requires in‐depth understanding of the correlation between their structural and magnetic order. For example, the particle size and shape are extremely important both in biomedical imaging using Magnetic Resonance Imaging (MRI) [20] and therapies by means of magnetic field‐assisted hyperthermia [21].

The chapter aims to summarize the most important aspects of magnetism of cubic spinel ferrite nanoparticles (*M*Fe2O4, *M* = Mg, Mn, Fe, Co, Ni, Cu, and Zn) in context of their crystal and magnetic structure. The factors that drive magnetic performance of the spinel ferrite NPs can be recognized on three levels: on the atomic level (degree of inversion and the presence of defects), at single‐particle level as balance between the crystallographically and magnetically ordered fractions of the NP (single‐domain and multi‐domain NPs, core‐shell structure, and beyond), and at mesoscopic level by means of mutual interparticle interactions and size distribution phenomena. All these effects are strongly linked to the preparation routes of the NPs. In general, each preparation method provides rather similar NPs by means of morphol‐ ogy and crystalline order. Thus the "three‐level" concept, which is the focal motif of the chapter,

**2. Brief overview of preparation methods of spinel ferrite nanoparticles**

In this section, selected methods of the NP preparation are summarized. Explicitly, the wet methods yielding well‐defined NPs, either isolated or embedded in a matrix, are accented. The reason is that only such samples can be sufficiently characterized and the factors defined within the "three level" concept can be disentangled. Outstanding reviews on the specific method(s)

Coprecipitation method is the archetype route, which can be used for preparation of all cubic spinel ferrite NPs: Fe3O4/γ‐Fe2O3 [24, 26], MgFe2O4 [27], etc. In general, two water‐soluble metallic salts are coprecipitated by a base. The reaction can be partly controlled in order to improve characteristics of the NPs [26, 28, 29]; however, it is generally reported as a facile method yielding polydispersed NPs with lower crystallinity and consequently less significant

The family of decomposition routes includes wet approaches based on decomposition of metal organic precursors in high‐boiling solvents, typically in the presence of coating agents (all [30], Fe3O4/γ‐Fe2O3 [24, 31], CoFe2O4 [32, 33], NiFe2O4 [34], ZnFe2O4 [35]). The most common organic complexes used for decomposition are metal oleates and acetylacetonates. The decomposition methods yield highly crystalline particles close to monodisperse limit with very good magnetic properties. However, the reaction conditions must be controlled in corre‐ spondence of the growth model suggested by Cheng et al. [22]. They can be also tailored to produce NPs of different shapes (CoFe2O4 [36, 37], Fe3O4/γ‐Fe2O3 [38, 39]). Higher‐order

can be applied to all cubic spinel ferrite NPs.

4 Magnetic Spinels- Synthesis, Properties and Applications

magnetic properties.

with further details and references are also included [22–25].

A large group of preparation protocols is based on solvothermal treatments, in aqueous conditions termed as hydrothermal. The preparation can be carried out either in a simple single‐solvent system (MgFe2O4 [43], NiFe2O4 [44, 45]), mixture of solvents (MnFe2O4 [46], ZnFe2O4 [47]), surfactant‐assisted routes (ZnFe2O4 [48]), or in multicomponent systems, such as water‐alcohol‐fatty acid (Fe3O4/γ‐Fe2O3 [49], CoFe2O4 [50]). The solvothermal routes are often carried out at elevated pressure and can be also maintained in supercritical conditions (MgFe2O4 [51]). The NPs prepared by this class of methods are in general of very good crystallinity, in some cases competitive to the NPs obtained by the decomposition routes.

Spinel ferrite NPs can be also obtained with the help of normal or reverse micelle methods, often referred as microemulsion routes (all [52, 53], Fe3O4/γ‐Fe2O3 [54], MgFe2O4 [55–57], CoFe2O4 [58], NiFe2O4 [59], CoFe2O4 and MnFe2O4 [60], ZnFe2O4 [61]). This approach takes advantage of the defined size of the micelle given by the ratio of the microemulsion components (water‐organic phase‐surfactant) according to the equilibrium phase diagram [62]. The micelles serve as nano‐reactors, which exchange the constituents dissolved in the water phase during the reaction and self‐limit the maximum size of the NPs. The as‐prepared NPs are often subjected to thermal posttreatment, which improves the NP crystallinity and enhances magnetic properties. However, such NPs are no more dispersible in liquid phase and their applications are thus limited. On the other hand, the microemulsion technique can be used for preparation of the NPs of a defined shape [63] and mixed ferrites [64].

A modified polyol method is also used for preparation of spinel ferrite NPs [22, 24, 65–67]. While in the standard route the polyol acts as a solvent and sometimes reducing or complexing agent for metal ions, for preparation of the ferrite NPs, the reaction of 1,2‐alkanediols and metal acetylacetonates in high‐boiling solvents is the most common variant.

Sol‐gel chemistry is a handy approach to produce spinel ferrite NPs. The common tactic is the growth of the NPs in porous silica matrix yielding well‐developed NPs embedded in the transparent matrix. The route requires annealing of the gel; however, the particle size can be sufficiently varied by the annealing temperature. Different spinel ferrites can be prepared (Fe3O4/γ‐Fe2O3 [68], CoFe2O4 [69–71], MnFe2O4 [72], NiFe2O4 [73–75]).

NPs of spinel ferrites are also prepared with assistance of microwaves [76, 77], ultrasound (CoFe2O4 [78], MgFe2O4 [79]), combustion routes (MgFe2O4 [80]), or mechanical treatments (MgFe2O4 [81], MnFe2O4 [82], NiFe2O4 [83]); however, the as‐prepared NPs often require heat treatment, and the resulting samples with sufficient crystallinity are better classified as fine powders. Less common methods such as the use of electrochemical synthesis for the γ‐Fe2O3 NPs [84] or NiFe2O4 [85] and synthesis employing ionic liquids for cubic magnetite NPs [86] were recently reported. NPs with size in the multicore limit were obtained by disaccharide‐ assisted seed growth [87]. Recently, combination of stop‐flow lithography and coprecipitation was reported [88]. Typical TEM images of spinel ferrite NPs prepared by the most common routes are shown in **Figure 1**.

**Figure 1.** TEM images of the spinel NPs prepared by different methods, with distributions of particle diameters in the inset. (a) γ‐Fe2O3 NPs prepared by coprecipitation technique. (b) CoFe2O4 NPs prepared by decomposition of oleic pre‐ cursor. (c) ZnFe2O4 NPs prepared by sol‐gel method.

The preparation methods described above can be successfully applied to preparation of core‐ shell NPs: CoFe2O4@*M*Fe2O4; *M* = Ni, Cu, Zn or γ‐Fe2O3 [89], and MnFe2O4@γ‐Fe2O3 [90]; CoFe2O4@ZnFe2O4 [91]; CuFe2O4@MgFe2O4 [92]; or other mixed ferrites NPs [93, 94]. A natural core‐shell structure is obtained for magnetite NPs due to topotactic oxidation to maghemite, which is mirrored, for example, in varying heating efficiency [95]. As a final remark, the selection of a particular preparation route yielding either a single core or multicore NPs is crucial and must be considered in the context of a specific application [96].

## **3. Characterization of magnetic nanoparticles: parameters and methods**

In this section, the most important parameters characterizing structural and magnetic prop‐ erties of NPs are introduced. Overview of the key experimental methods used for their evaluation is also included. For straightforwardness, details on the theoretical models and related formalism are not given, but relevant references are included. More details on the topic can be found in a comprehensive work by Koksharov [97].

#### **3.1. Basic structural and magnetic characterization**

The most important parameter is the particle size itself, usually attributed to the diameter of a single NP. The first‐choice technique for determination of the particle size is the transmission electron microscopy (TEM), which gives the real (or physical) particle size, *d*TEM. As the NPs of spinel ferrites are usually spherical, cubic, octahedral, or symmetric star‐like objects, the value is a reasonable measure of the NP dimension as it gives information on the principal dimensions of those objects. Analysis of the TEM images also provides particle‐size distribu‐ tion, sometimes expressed as polydispersity index (PDI = *σ*(*d*TEM)/<*d*TEM>). The direct TEM observation gives information on aggregation, chaining of particles, and other morphological specifics. Using high‐resolution TEM (HR TEM), internal structure of the NPs can be inspected, for example, the thickness of disordered surface layer and defects can be identified.

Particle size can be also determined using powder X‐ray diffraction (XRD). The profile of the diffraction peak contains information about the so‐called crystallite size, *D*hkl, and the micro‐ strain (arise from the presence of vacancies, dislocation, stacking faults, or poor crystallinity of the material). Generally, the experimental profile is the convolution of the instrumental profile caused by the experimental setup and the physical profile caused by the intrinsic properties of the measured material [98].

The physical profile is the convolution of the two dominant contributions caused by the small *D*hkl and by the microstrain. The *D*hkl is defined as a coherently diffracting length in a crystal‐ lographic direction [hkl] that is parallel to the diffraction vector (surface normal) [98]. Assum‐ ing the spherical NPs with random orientation of individual [hkl] directions, the *D*hkl determines the diameter of the coherently diffracting domain; in other words it is the diameter of the crystalline part of the NP, the *d*XRD. For highly symmetric shapes expected for spinel ferrite NPs, the coherently diffracting domain can be sufficiently described by a sphere or an ellipsoid in the case of flat crystallites.

**Figure 1.** TEM images of the spinel NPs prepared by different methods, with distributions of particle diameters in the inset. (a) γ‐Fe2O3 NPs prepared by coprecipitation technique. (b) CoFe2O4 NPs prepared by decomposition of oleic pre‐

The preparation methods described above can be successfully applied to preparation of core‐ shell NPs: CoFe2O4@*M*Fe2O4; *M* = Ni, Cu, Zn or γ‐Fe2O3 [89], and MnFe2O4@γ‐Fe2O3 [90]; CoFe2O4@ZnFe2O4 [91]; CuFe2O4@MgFe2O4 [92]; or other mixed ferrites NPs [93, 94]. A natural core‐shell structure is obtained for magnetite NPs due to topotactic oxidation to maghemite, which is mirrored, for example, in varying heating efficiency [95]. As a final remark, the selection of a particular preparation route yielding either a single core or multicore NPs is

**3. Characterization of magnetic nanoparticles: parameters and methods**

In this section, the most important parameters characterizing structural and magnetic prop‐ erties of NPs are introduced. Overview of the key experimental methods used for their evaluation is also included. For straightforwardness, details on the theoretical models and related formalism are not given, but relevant references are included. More details on the topic

The most important parameter is the particle size itself, usually attributed to the diameter of a single NP. The first‐choice technique for determination of the particle size is the transmission electron microscopy (TEM), which gives the real (or physical) particle size, *d*TEM. As the NPs of spinel ferrites are usually spherical, cubic, octahedral, or symmetric star‐like objects, the value is a reasonable measure of the NP dimension as it gives information on the principal dimensions of those objects. Analysis of the TEM images also provides particle‐size distribu‐ tion, sometimes expressed as polydispersity index (PDI = *σ*(*d*TEM)/<*d*TEM>). The direct TEM observation gives information on aggregation, chaining of particles, and other morphological specifics. Using high‐resolution TEM (HR TEM), internal structure of the NPs can be inspected,

for example, the thickness of disordered surface layer and defects can be identified.

crucial and must be considered in the context of a specific application [96].

can be found in a comprehensive work by Koksharov [97].

**3.1. Basic structural and magnetic characterization**

cursor. (c) ZnFe2O4 NPs prepared by sol‐gel method.

6 Magnetic Spinels- Synthesis, Properties and Applications

Other important parameters characterizing magnetic NPs are related to formation of a single‐ domain state. In order to decrease the magnetostatic energy that is associated with the dipolar fields, the ferromagnetic (or ferrimagnetic)‐ordered crystal is divided into the magnetic domains. Within each of the domain, the magnetization, *M* reaches the saturation. The domain creation depends on the competition between the reduction of the magnetostatic energy and the energy required to form the domain walls separating the adjacent domains. The size of the domain wall is a balance between the exchange energy that tries to unwind the domain wall and the magnetocrystalline anisotropy with the opposite effect.

In the magnetic NPs, the typical dimensions are comparable with the thickness of the domain; thus, at some critical size, it is energetically favorable for the NP to become single domain. The critical dimension ranging from 10‐7 to 10‐8 m is strictly specific to each magnetic spinel ferrite [99].

In small magnetic NPs reaching the single‐domain regime, the paramagnetic‐like behavior can be observed even below the Curie temperature, *T*c. The state is therefore called the superpar‐ amagnetism (SPM) as the whole particle behaves as one giant spin (superspin) consisting of the atomic magnetic moments; thus, the magnetic moment of the whole NP is 102 to 105 times larger than the atomic moment. The magnetization follows the behavior of the Langevin function. The theory of SPM and superspin relaxation of the NPs was treated by C. P. Bean, J.D. Livingston and M. Knobel. et al. [100, 101]. The key parameters representing the magnetic properties of single‐domain NPs are blocking temperature, *T*B, and superspin or NP magnetic moment, *μ*m. The *T*B is related to the particle size through its volume, *V* as:

$$T\_\mathrm{B} = K\_\mathrm{eff} V \; (a k\_\mathrm{B}) \tag{1}$$

where *K*eff is the effective anisotropy constant. Parameter *a* is given by the measurement time, *τ*m as *a* = ln(*τ*m / *τ*0), *a* = 25 for the SPM systems with relaxation time *τ*0 = 10‐12 s (see the following paragraphs) and *τ*m = 100 s [101, 102].

The *μ*m is related to the saturation magnetization, *M*s, which is defined as the maximum allowed magnetization at given temperature (all spins are aligned along the field direction) and often deviates from a theoretical bulk value. For ideal NPs (physical volume is identical with the volume where the magnetic structure is like in the bulk spinel), the dependence of *μ*m on *M*<sup>s</sup> can be written as *μ*m = *Ms V*.

Another important parameter is the relaxation time, *τ* of the NP superspin. For a particle with uniaxial anisotropy, the superspin relaxation corresponds to the flip between two equilibrium states separated by an energy barrier *K*effV, which can be overcome by the thermal fluctuations at the *T*B. The superspin relaxation in the SPM systems is described by the Néel‐Arrhenius law as [103, 104]:

$$\mathfrak{r} = \mathfrak{r}\_0 \exp(E\_\Lambda \,/ \, k\_\mathcal{B} T) \tag{2}$$

where *E*A is the anisotropy energy and other variables and constants have usual meaning.

Below the *T*B, the NPs are in the so‐called blocked state analogous to the ordered state (such as ferromagnetic or ferrimagnetic), and the magnetic moments are fixed into the direction of the easy axis and can only fluctuate around these directions. The *T*B also depends on the time window of the measurements, *τ*m. If the *τ*m > *τ*, the NPs have enough time to fluctuate and the SPM state can be observed. On the other hand, if *τ*m < *τ*, the blocked regime is observed. Thus, determination of the *T*B is dependent on the used experimental technique (10‐8 s for Mössbauer spectroscopy (MS), 1 s for magnetic measurements, 10–10‐3 s for a.c. susceptibility measure‐ ments).

A very important parameter characterizing the blocked state is the coercivity, *H*c (or coercive field) as it gives information on opening of the hysteresis loop. Depending on the dominant anisotropy term, the *H*<sup>c</sup> value reaches values in fractions of 2*K*eff/*M*s [101, 105]. In general, the coercivity (and also remanence) of NPs with nonspherical shapes shows complex angular dependence due to the shape anisotropy [106]. In very small particles, the coercivity is an interplay between the surface disorder and surface anisotropy [107].

The typical magnetic measurements of the NP magnetic parameters yielding the above‐ described parameters can be summarized as follows: temperature dependence of the magnet‐ ization in low external applied field, the so‐called zero field cooled curve (ZFC) and field cooled curve (FC); field dependence of the magnetization at fixed temperatures, the so‐called magnetization isotherm (or hysteresis loop in the blocked state); and the a.c. susceptibility measurement. The ZFC‐FC protocol reveals the value of the *T*B, while the analysis of the magnetization isotherms in the SPM state serves for determination of the *μ*m. From this value, the so‐called magnetic size of a NP, *d*mag (size of the magnetically ordered part), can be determined.

A unique tool used in characterization of spinel ferrite NPs is the Mössbauer spectroscopy. It is a dual probe both for structure and magnetism at local level based on recoilless resonant absorption of γ radiation. In general, information on coordination surroundings of the iron cations, their valence, degree of inversion of the spinel structure, and orientation of spins on the cubic spinel sub‐lattices can be obtained [108, 109].

The small spinel ferrite NPs exhibit relaxation time in order of 10‐9 s that is close to the time window of the MS (10‐8 s) allowing the study of relaxation of the NPs by means of MS [109, 110]. Furthermore, the big advantage of the MS is that it is not restricted to the well crystalline samples; thus, a non‐well crystalline NP can be also investigated using MS. Finally, the so‐ called spin canting angle, usually attributed to the presence of the surface spins, can be estimated [111].

#### **3.2. Real effects in magnetic nanoparticles**

#### *3.2.1. Size distribution*

The *μ*m is related to the saturation magnetization, *M*s, which is defined as the maximum allowed magnetization at given temperature (all spins are aligned along the field direction) and often deviates from a theoretical bulk value. For ideal NPs (physical volume is identical with the volume where the magnetic structure is like in the bulk spinel), the dependence of *μ*m on *M*<sup>s</sup>

Another important parameter is the relaxation time, *τ* of the NP superspin. For a particle with uniaxial anisotropy, the superspin relaxation corresponds to the flip between two equilibrium states separated by an energy barrier *K*effV, which can be overcome by the thermal fluctuations at the *T*B. The superspin relaxation in the SPM systems is described by the Néel‐Arrhenius law

where *E*A is the anisotropy energy and other variables and constants have usual meaning.

Below the *T*B, the NPs are in the so‐called blocked state analogous to the ordered state (such as ferromagnetic or ferrimagnetic), and the magnetic moments are fixed into the direction of the easy axis and can only fluctuate around these directions. The *T*B also depends on the time window of the measurements, *τ*m. If the *τ*m > *τ*, the NPs have enough time to fluctuate and the SPM state can be observed. On the other hand, if *τ*m < *τ*, the blocked regime is observed. Thus, determination of the *T*B is dependent on the used experimental technique (10‐8 s for Mössbauer spectroscopy (MS), 1 s for magnetic measurements, 10–10‐3 s for a.c. susceptibility measure‐

A very important parameter characterizing the blocked state is the coercivity, *H*c (or coercive field) as it gives information on opening of the hysteresis loop. Depending on the dominant anisotropy term, the *H*<sup>c</sup> value reaches values in fractions of 2*K*eff/*M*s [101, 105]. In general, the coercivity (and also remanence) of NPs with nonspherical shapes shows complex angular dependence due to the shape anisotropy [106]. In very small particles, the coercivity is an

The typical magnetic measurements of the NP magnetic parameters yielding the above‐ described parameters can be summarized as follows: temperature dependence of the magnet‐ ization in low external applied field, the so‐called zero field cooled curve (ZFC) and field cooled curve (FC); field dependence of the magnetization at fixed temperatures, the so‐called magnetization isotherm (or hysteresis loop in the blocked state); and the a.c. susceptibility measurement. The ZFC‐FC protocol reveals the value of the *T*B, while the analysis of the magnetization isotherms in the SPM state serves for determination of the *μ*m. From this value, the so‐called magnetic size of a NP, *d*mag (size of the magnetically ordered part), can be

A unique tool used in characterization of spinel ferrite NPs is the Mössbauer spectroscopy. It is a dual probe both for structure and magnetism at local level based on recoilless resonant absorption of γ radiation. In general, information on coordination surroundings of the iron

interplay between the surface disorder and surface anisotropy [107].

0 AB *τ = τ (E k T)* exp / (2)

can be written as *μ*m = *Ms V*.

8 Magnetic Spinels- Synthesis, Properties and Applications

as [103, 104]:

ments).

determined.

All real systems of the NPs exhibit an intrinsic size distribution, which must be considered in evaluation and interpretation of structural and magnetic data. The most common is the log‐ normal distribution (see **Figure 1**); however, Gaussian distribution has been also reported [112–114]. In the case of the TEM observation for the *d*TEM, the NPs can be termed depending on the value of the PDI as monodisperse (PDI < 0.05–0.1), highly uniform (PDI < 0.2), and polydisperse (PDI > 0.2). Similar classification might be applied to the distribution of *d*XRD; however, such in‐depth analysis is usually not included in common Rietveld treatment of the XRD data. On the other hand, the role of size distribution by means of magnetic size, *d*mag, and superspin values is extremely important for evaluation of magnetic properties. The mean magnetic moment per single NP, *μ*m, and distribution width, *σ*, can be derived from the experimental data, *μ*m = *μ*0exp(*σ*<sup>2</sup> / 2), as the magnetization as a function of the applied field, *H*, and temperature, *T*, in SPM state can be described as a weighted sum of Langevin functions [69, 115, 116]:

$$M\_{\mathbf{A}}(H\_{\mathbf{A}},T) = \int\_{0}^{\pi} \mu \, L\left(\frac{\mu H}{k\_{\mathbf{B}}T}\right) f\_{\mathbf{L}}\left(\mu\right) \mathrm{d}\,\mu\tag{3}$$

where *L*(*x*) represents the Langevin function and *f*L(*μ*) is the log‐normal distribution of magnetic moments *μ*. The NP size distribution also affects the character of ZFC and FC curves as it is mirrored in distribution of the *T*B and *K*eff, and suited models must be applied to obtain median values, *T*Bm and distribution width *σ* as relevant parameters [117–120].

One of the possible approaches evaluating the *T*B distribution is based on refinement of the ZFC temperature dependence of magnetization, *M*ZFC(*T*) which is given by equation [101, 121, 122]:

$$M\_{\rm ZFC}(T) \propto \frac{M\_{\rm s}^2 H}{3K\_{\rm eff}} \left[ \frac{2\mathcal{S}}{t} \int t\_{\rm B} f(t\_{\rm B}) dt\_{\rm B} + \int f(t\_{\rm B}) dt\_{\rm B} \right] \tag{4}$$

where *t*B = *T*B/*T*Bm is the reduced blocking temperature of individual NPs and *f*(*t*B) is the log‐ normal distribution function of reduced blocking temperatures. The first term in Eq. (4) represents contribution of the NPs in the SPM state, whereas the second term belongs to the NPs in blocked state.

Typical examples of magnetization isotherms and ZFC‐FC curves influenced by the particle‐ size distribution are shown in **Figure 2**, presenting unhysteretic magnetization isotherms (Langevin curves) for different values of *μ* and *σ* and ZFC‐FC curves for different values of *T*<sup>B</sup> and *σ*.

**Figure 2.** Model Langevin and ZFC‐FC curves for selected NP magnetic moments and blocking temperature. (a) Lan‐ gevin curves for magnetic moments with different orders of magnitude and *σ* = 0.5. (b) Evolution of Langevin curve for different magnetic moment distributions visualized in (c). (d) Ideal ZFC‐FC curves for NP without size distribution. (e) Evolution of the ZFC‐FC curve for fixed *T*B and different distribution widths (f).

#### *3.2.2. Spin canting phenomenon and surface effects*

Decreasing the NP size, the number of atoms located at the surface dramatically increases. Thus the surface spins become dominant in the magnetic properties of the whole NP. The atoms at the surface exhibit lower coordination numbers originating from breaking of symmetry of the lattice at the surface.

Moreover, the exchange bonds are broken resulting in the spin disorder and frustration at the surface leading to the undesirable effects such as low saturation magnetization of the NP and the unsaturation of the magnetization in the high magnetic applied field [123]. To explain these effects, J. M. D. Coey proposed the so‐called core‐shell model in which the NP consists of a core with the normal spin arrangement and the disordered shell, where the spins are inclined at random angles to the surface, the so‐called spin canting angle [123] (see **Figure 3**). The spin canting angle in general depends on the number of the magnetic nearest neighbors connecting with the reduced symmetry and dangling bonds. Other effects such as the interparticle interactions play role [124]. The spin canting angle can be determined with the help of in‐field Mössbauer spectroscopy (IFMS); an example is given in **Figure 4**.

where *t*B = *T*B/*T*Bm is the reduced blocking temperature of individual NPs and *f*(*t*B) is the log‐ normal distribution function of reduced blocking temperatures. The first term in Eq. (4) represents contribution of the NPs in the SPM state, whereas the second term belongs to the

Typical examples of magnetization isotherms and ZFC‐FC curves influenced by the particle‐ size distribution are shown in **Figure 2**, presenting unhysteretic magnetization isotherms (Langevin curves) for different values of *μ* and *σ* and ZFC‐FC curves for different values of *T*<sup>B</sup>

**Figure 2.** Model Langevin and ZFC‐FC curves for selected NP magnetic moments and blocking temperature. (a) Lan‐ gevin curves for magnetic moments with different orders of magnitude and *σ* = 0.5. (b) Evolution of Langevin curve for different magnetic moment distributions visualized in (c). (d) Ideal ZFC‐FC curves for NP without size distribution. (e)

Decreasing the NP size, the number of atoms located at the surface dramatically increases. Thus the surface spins become dominant in the magnetic properties of the whole NP. The atoms at the surface exhibit lower coordination numbers originating from breaking of symmetry of

Moreover, the exchange bonds are broken resulting in the spin disorder and frustration at the surface leading to the undesirable effects such as low saturation magnetization of the NP and the unsaturation of the magnetization in the high magnetic applied field [123]. To explain these effects, J. M. D. Coey proposed the so‐called core‐shell model in which the NP consists of a core with the normal spin arrangement and the disordered shell, where the spins are inclined

Evolution of the ZFC‐FC curve for fixed *T*B and different distribution widths (f).

*3.2.2. Spin canting phenomenon and surface effects*

the lattice at the surface.

NPs in blocked state.

10 Magnetic Spinels- Synthesis, Properties and Applications

and *σ*.

**Figure 3.** Scheme of the internal structure of ideal (a) and magnetic core‐shell (b) structure of NP. (c) Scheme of the ideal and core‐shell NP with the model of NP diameters determined by TEM, X‐ray diffraction, and magnetic measure‐ ments. (d and e) Model Langevin curves for the ideal and core‐shell NP with paramagnetic contribution due to the disordered spins in the NP shell.

**Figure 4.** Schematic representation of the typical zero field cooled curve (ZFC) and field cooled curves (FC) for differ‐ ent types of NP ensembles. a) uniform NPs with negligible interparticle interactions, b) uniform NPs with "intermedi‐ ate" interparticle interactions, c) NPs with non‐negligible particle size distribution and strong interparticle interactions. The blocking temperature, *T*B and the irreversibility temperature, *T*DIFF typical for strongly interacting regime are shown.

However, the spin canting is not a unique property of the surface spins, and several works point to the volume nature of the effect [125–127]. Thus the surface effects in the NPs together with the origin of the spin canting angle are still discussed within the scientific community [109, 128–130].

Another consequence of the increased number of the surface atoms is the dominance of surface term to the anisotropy energy, usually expressed as a sum: *K*v + (6/*d*)*K*s, where *K*<sup>v</sup> is the bulk value of the *K*eff and *K*s describes the contribution from the surface spins originated by structural deviations and spin frustration on the surface. Depending on the NP shape, the surface anisotropy may contain non‐negligible admixture of higher‐order Néel terms [130]. In real systems, the *K*eff is additionally modified by the presence of other effects, mainly interparticle interactions described below.

#### *3.2.3. Interparticle interactions*

The interparticle interactions play a very important role in the magnetic response of the NPs, because they are usually not enough spatially separated to follow the behavior of an ideal SPM system. In general, two types of interaction can be observed: 1) the exchange interaction that affects mainly the surface spins of the NPs in close proximity thus can be neglected in most cases and 2) the long‐range order dipolar interaction that is the dominant due to the high magnetic moment of the NPs [131].

The NP systems can be tentatively divided into the weakly interacting systems (the represen‐ tatives are much diluted ferrofluids or NPs embedded in matrix in small concentration) and strongly interacting system with the powder samples as representatives. The strength of the interparticle interactions is given by the magnitude of the superspins and interparticle distance, in reality by the concentration of the NPs in ferrofluids, thickness of the NP coating, or matrix‐to‐NP ratio. The interparticle interactions affect all parameters characterizing the single‐domain state. Furthermore, the strong interparticle interactions can result in the collective magnetic state at low temperature that resembles the typical physical properties of spin glasses [104], termed as superspin glasses in the case of strongly interacting SPM species [132–134].

In weakly interacting system, the dipolar interaction is treated as a perturbation to the SPM model within the Vogel‐Fulcher law [104], the NP relaxation time is then written as:

$$
\pi = \pi\_0 \exp\left(E\_\mathsf{A} \,/\, k\_\mathsf{B} \left(T - T\_\mathrm{o}\right)\right). \tag{5}
$$

The effect on the *T*<sup>B</sup> is described by two models giving contradictory results on the relaxation times—the Hansen‐Morup model (HM) [135] and the Dormann‐Bessais‐Fiorani model (DBF) [129]. The decrease of the *T*B is predicted by the HM model, while its increase was obtained by the DBF model. So far, there have been no clear experimental evidences for a preference of one of these models. Some authors suggested that a phenomenological correction to the *T*B in the weakly interacting systems could be used in the same way as it is done fore the relaxation time by adding the phenomenological constant *T*0 to the *T*B of the SPM system [102, 136, 137]. A different approach treats weak interparticle interactions as additional magnetic field acting on a single NP, when correction to the external magnetic field, (1‐*H*/*H*K) <sup>a</sup> is added to Eq. (1) [101].

However, the spin canting is not a unique property of the surface spins, and several works point to the volume nature of the effect [125–127]. Thus the surface effects in the NPs together with the origin of the spin canting angle are still discussed within the scientific community

Another consequence of the increased number of the surface atoms is the dominance of surface term to the anisotropy energy, usually expressed as a sum: *K*v + (6/*d*)*K*s, where *K*<sup>v</sup> is the bulk value of the *K*eff and *K*s describes the contribution from the surface spins originated by structural deviations and spin frustration on the surface. Depending on the NP shape, the surface anisotropy may contain non‐negligible admixture of higher‐order Néel terms [130]. In real systems, the *K*eff is additionally modified by the presence of other effects, mainly interparticle

The interparticle interactions play a very important role in the magnetic response of the NPs, because they are usually not enough spatially separated to follow the behavior of an ideal SPM system. In general, two types of interaction can be observed: 1) the exchange interaction that affects mainly the surface spins of the NPs in close proximity thus can be neglected in most cases and 2) the long‐range order dipolar interaction that is the dominant due to the high

The NP systems can be tentatively divided into the weakly interacting systems (the represen‐ tatives are much diluted ferrofluids or NPs embedded in matrix in small concentration) and strongly interacting system with the powder samples as representatives. The strength of the interparticle interactions is given by the magnitude of the superspins and interparticle distance, in reality by the concentration of the NPs in ferrofluids, thickness of the NP coating, or matrix‐to‐NP ratio. The interparticle interactions affect all parameters characterizing the single‐domain state. Furthermore, the strong interparticle interactions can result in the collective magnetic state at low temperature that resembles the typical physical properties of spin glasses [104], termed as superspin glasses in the case of strongly interacting SPM species

In weakly interacting system, the dipolar interaction is treated as a perturbation to the SPM

The effect on the *T*<sup>B</sup> is described by two models giving contradictory results on the relaxation times—the Hansen‐Morup model (HM) [135] and the Dormann‐Bessais‐Fiorani model (DBF) [129]. The decrease of the *T*B is predicted by the HM model, while its increase was obtained by the DBF model. So far, there have been no clear experimental evidences for a preference of one of these models. Some authors suggested that a phenomenological correction to the *T*B in the weakly interacting systems could be used in the same way as it is done fore the relaxation time by adding the phenomenological constant *T*0 to the *T*B of the SPM system [102, 136, 137]. A

*τ=τ E k T T* 0 AB 0 exp / . ( ( - )) (5)

model within the Vogel‐Fulcher law [104], the NP relaxation time is then written as:

[109, 128–130].

[132–134].

interactions described below.

12 Magnetic Spinels- Synthesis, Properties and Applications

*3.2.3. Interparticle interactions*

magnetic moment of the NPs [131].

In the case of strong interactions, the collective state of the NP condensates below a charac‐ teristic temperature—the so‐called glass‐transition temperature, *T*g—and the equation for the relaxation time is usually given by scaling law for critical spin dynamics [131, 132]:

$$\mathfrak{r} = \mathfrak{r}\_0 \left( T\_\mathrm{m} \,/ \, T\_\mathrm{g} - 1 \right)^{\mathfrak{r}\mathfrak{r}} \tag{6}$$

where *T*m is the temperature of the maximum at the a.c. susceptibility curve and *zv* is the dynamical critical component. However; strongly interacting systems do not necessarily fulfill criteria for the so‐called superspin‐glass systems obeying Eq. (6). Then, one of the approaches dealing with the effect of strong interactions on shift of the *T*B is treated within the random anisotropy model (RAM) [101, 138–140]. RAM predicts the increase of interparticle interactions with decreasing correlation length, *L* which is a measure of average distance at which the magnetization fluctuations within the NP system are correlated. Then the *K*eff and particle volume *V* are averaged to the number *N* of the NP involved in the interactions, introducing new *K*L and *V*L variables, and consequently, the formula for the *T*B is modified to:

$$T\_\mathbf{B} = K\_\mathbf{L} V\_\mathbf{L} N^{1/2} \tag{7}$$

The heart of the problem of calculating the *T*<sup>B</sup> for interacting systems within the RAM model is the correct evaluation of the *K*L and *V*L of NP system.

**Figure 5.** Typical MS spectra of almost ideal and core‐shell NPs. The first column shows comparison of room‐tempera‐ ture MS spectra for the perfectly crystalline and ordered 7nm ‐Fe2O3 NPs (a) and core‐shell 15 nm with 7 nm crystal‐ line cores (d). The pink line is the fit of the spectra attributed to the fraction of NPs in SPM state. The middle and right column shows evolution of MS at low temperatures (4 K) in 0 T (b and e) and 6 T(c and f), respectively. Splitting of the lines attributed to the octahedral and tetrahedral positions can be disentangled after application of external magnetic field (c and f). Peak widening due to the disordered magnetic spins in the NP shell (d) is observable on the 4 K spectra (e and f), especially for the 1st and 6th lines.

The presence of interparticle interactions (as well as the particle‐size distribution) is usually evidenced on the ZFC‐FC curves; typical examples of medium and strongly interacting ensembles of NPs in comparison to the ideal noninteracting case are given in **Figure 5**. In real samples, all effects are present with variable contribution, and in some cases, both the size distribution and interparticle interactions must be addressed to describe the magnetic response of the samples properly [141, 142] (**Figure 5**).

## **4. Synergy of structural and magnetic probes**

In order to provide complete insight into properties of magnetic NPs, synergy of structural and magnetic probes is essential. Atthe atomic and single‐particle level,the complementarity ofthe (HR) TEM and XRD provides information on phase composition, the presence and type of defects, and particle sizes: *d*XRD and *d*TEM. The analysis of MS gives important knowledge on the degree of inversion and spin canting, which is then considered for interpretation of the magnetization data. Moreover, the particle‐size distribution obtained from the TEM should be confronted with the superspindistributionobtainedby the analysis oftheLangevincurves;this analysis also yields the magnetic size, *d*mag. Using the three different particle‐size parameters (*d*mag, *d*XRD, *d*TEM), the concept of the core‐shell model of NP can be extended as the core‐shell structureofthespins isoftennotidenticalwiththecrystallographicallyordered‐disorderedpart of the NP. The reason is that the spin frustration and disorder usually occur at volume larger than the size of the crystalline part. Comparing the *d*mag, *d*XRD, and *d*TEM values, a very good estimate of the particle crystallinity and degree of spin order is obtained. A schematic repre‐ sentation ofthe crystallographic (structural) and magnetic core‐shell model structures together with typical magnetization isotherms in the SPM state are shown in **Figure 3**.

At the mesoscopic level, the influence of interparticle interactions should not be neglected. For that purpose, morphology of the NP ensembles observed by the TEM gives estimate of mutual interparticle distance. The relevance of the interaction regime can be corroborated by a.c. susceptibility experiments, which yields characteristic relaxation times of the superspins, τ. As discussed above, those are strongly reformed because of the interactions. Finally, the effect of the *μ*, *T*B, and *K*eff distribution must be then carefully disentangled in order to estimate the pure contribution of the interaction.

## **5. Impact of preparation and strategies of tuning magnetic properties**

The intrinsic NP parameters at all levels are imprinted during the preparation process. In this section, a brief discussion of this issue is given in the view of the "three‐level" concept considering the structural and spin order in the unit cell and coordination polyhedra, single‐ particle, and NP ensemble level. Strategies profiting from the control over the imprint of the real effects by substitution or formation of artificial core‐shell structures are also mentioned.

The degree of inversion, *δ* of the spinel structure is found to be significantly influenced by the preparation of the spinel ferrite NPs. In bulk, the normal or inverse spinel structure usually dominates. However, the degree of inversion in the NPs is often close to 0.5 and the mixed spinel structure is the most common. For example, the NiFe2O4 is a typical inverse spinel, while in NPs obtained by the sol‐gel method, the *δ* value of 0.6 was reported [143]. A very similar values were observed for sol‐gel‐prepared NPs of CoFe2O4 [69] (inverse spinel in bulk) and of ZnFe2O4 with normal spinel bulk structure [144]. The cation distribution in NPs prepared by coprecipitation method also often corresponds to mixed spinel structure as was demonstrated for ZnFe2O4 [145] and MnFe2O4 [146]. Moreover, the *δ* value can be controlled in the NPs prepared by the polyol method [65] and using tailored solvothermal protocols [147]. In addition, the stoichiometry of the NPs is not always matching the expected M2+/M3+/O2‐ ratio (1:2:4), e.g., as reported for NPs prepared by hydrothermal method [50].

The presence of interparticle interactions (as well as the particle‐size distribution) is usually evidenced on the ZFC‐FC curves; typical examples of medium and strongly interacting ensembles of NPs in comparison to the ideal noninteracting case are given in **Figure 5**. In real samples, all effects are present with variable contribution, and in some cases, both the size distribution and interparticle interactions must be addressed to describe the magnetic response

In order to provide complete insight into properties of magnetic NPs, synergy of structural and magnetic probes is essential. Atthe atomic and single‐particle level,the complementarity ofthe (HR) TEM and XRD provides information on phase composition, the presence and type of defects, and particle sizes: *d*XRD and *d*TEM. The analysis of MS gives important knowledge on the degree of inversion and spin canting, which is then considered for interpretation of the magnetization data. Moreover, the particle‐size distribution obtained from the TEM should be confronted with the superspindistributionobtainedby the analysis oftheLangevincurves;this analysis also yields the magnetic size, *d*mag. Using the three different particle‐size parameters (*d*mag, *d*XRD, *d*TEM), the concept of the core‐shell model of NP can be extended as the core‐shell structureofthespins isoftennotidenticalwiththecrystallographicallyordered‐disorderedpart of the NP. The reason is that the spin frustration and disorder usually occur at volume larger than the size of the crystalline part. Comparing the *d*mag, *d*XRD, and *d*TEM values, a very good estimate of the particle crystallinity and degree of spin order is obtained. A schematic repre‐ sentation ofthe crystallographic (structural) and magnetic core‐shell model structures together

with typical magnetization isotherms in the SPM state are shown in **Figure 3**.

At the mesoscopic level, the influence of interparticle interactions should not be neglected. For that purpose, morphology of the NP ensembles observed by the TEM gives estimate of mutual interparticle distance. The relevance of the interaction regime can be corroborated by a.c. susceptibility experiments, which yields characteristic relaxation times of the superspins, τ. As discussed above, those are strongly reformed because of the interactions. Finally, the effect of the *μ*, *T*B, and *K*eff distribution must be then carefully disentangled in order to estimate the

**5. Impact of preparation and strategies of tuning magnetic properties**

The intrinsic NP parameters at all levels are imprinted during the preparation process. In this section, a brief discussion of this issue is given in the view of the "three‐level" concept considering the structural and spin order in the unit cell and coordination polyhedra, single‐ particle, and NP ensemble level. Strategies profiting from the control over the imprint of the real effects by substitution or formation of artificial core‐shell structures are also mentioned. The degree of inversion, *δ* of the spinel structure is found to be significantly influenced by the preparation of the spinel ferrite NPs. In bulk, the normal or inverse spinel structure usually

of the samples properly [141, 142] (**Figure 5**).

14 Magnetic Spinels- Synthesis, Properties and Applications

pure contribution of the interaction.

**4. Synergy of structural and magnetic probes**

The presence of defects, mainly by means of oxygen vacancies, is believed to be another important factor driving magnetic properties of the NPs. It was shown that they dominate the properties of the NPs obtained by mechanochemical processes [148], and it was also demon‐ strated that the level of defects can be influenced by vacuum annealing [149–151]. A specific issue is related to the presence of the Verwey transition in the Fe3O4 NPs [152] as the topotactic oxidation from magnetite to maghemite is a rapid process in common environments. Conse‐ quently,experimentalinvestigationsoftheironoxideNPswithsizebelow20nmdonotevidence the transition [26, 153]. Recently, the Verwey transition was observed in the NPs with a size of 6 nm, which were kept under inert atmosphere, and thus their oxidation was prevented [154].

The most significant and discussed issue is the spin order at single‐particle level and its sur‐ face to volume nature. Most works report the dominance of surface spin frustration and suggest the presence of the magnetically dead layer. The increased contribution of the frus‐ trated spins is attributed mainly to size effect, low crystallinity, and surface roughness, dom‐ inating in the NPs obtained by coprecipitation method [26, 155–165]. The spin canting in the surface layer was also observed in diluted ferrofluids, which confirms the nature of the ef‐ fect on single‐particle level [166]. However, the surface spin structure can be reformed when the NPs are in close proximity [131]. Significant increase of the amount of disordered spins was reported for hollow NPs of NiFe2O4 thanks to the additional inner surface [167]. On the other hand, the spin canting was also considered as volume effect, which occurs due to ion order‐disorder in the spinel structure [127, 168] or pinning of the spins on internal defects in single NPs [125].

Focusing on the mesoscopic effects, the NP size distribution and interparticle interactions will be addressed. The particle‐size distribution is found to be very sensitive to the preparation method used. The NPs with almost monodisperse character are obtained by the decomposition route; however, the parameters of the reaction must be carefully controlled. For example, the prolongation of the reaction time leads both to larger NPs but also increased size distribution [33, 169]. Similar effect was observedforincreasing concentration ofthe oleic acidor oleylamine [33]. Other techniques provide NPs with PDI over 0.2, and the size distribution must be then considered in analysis of the magnetic measurements [69, 116, 142]. However, it is worth mentioning that the narrow‐size distribution of the *d*TEM does not automatically imply the same value of the *d*XRD or *d*mag, as shown, e.g., for maghemite NPs [125]. In majority of real samples, interparticle interactions contribute to the magnetic properties. In most cases, the samples are studiedinformofpowders,whichcontainNPs inveryclosecontact.Consequently,theresponse of suchsystems isalways inthe limitofthemediumtostronginteractionsandisalmostinvariant to the preparation route used, and the interaction strength for a given NP size is given by minimum distance between the NPs, in other words by the thickness of the surface coating [42, 170–172]. Upon specific conditions, well‐defined aggregates are formed [173], as reported, e.g., for preparations in microemulsion [174], by decomposition method [175] and by controlled encapsulationintophospholipides [176]. Suchassemblies attractedinterestdue to considerably enhanced heating properties in hyperthermia [177], which is associated with the enhancement ofthe single‐object(aggregate) anisotropy.Indense ensembles ofthe NPs,the onset of collective relaxationisalsocorroboratedbysignificantincreaseoftherelaxationtime[178–184];analogous consequence was observed in the aggregates [185]. However, the influence of the intra‐ and inter‐aggregate interactions is not explicitly decoupled. Recent studies also suggest a strong influence of the reformed particle energy barrier on the details of the aging dynamics, memory behavior, and apparent superspin dimensionality of the particles [132].

In spite of the fact that the surface effects, defects, and interparticle interactions are believed to be contra‐productive factors as they in general decrease the value of saturation magnetiza‐ tion [26], they were recognized as potential enhancers of effective magnetocrystalline aniso‐ tropy, reflected, for example, in increase of the hysteresis losses [186]. Consequently, attempts to prepare smart NPs based on artificial core‐shell structure, e.g., NiFe2O4@γ‐Fe2O3 [187], ZnFe2O4@γ‐Fe2O3 [188], and Co,Fe2/Ni,Fe2O4 [189], appeared recently. Tri‐magnetic multi‐shell structures prepared by high‐temperature decomposition of the metal oleates were also reported [190].

Alternative strategy is the tuning of magnetic properties of the spinel ferrite NPs via site‐ specific occupation of the spinel lattice. This is a straightforward approach as the relevant metal ions can substitute each other in the spinel structure easily. In this case, however, the site occupation must be carefully evaluated and controlled. Successful preparation and basic investigation of structure and magnetic properties of the NPs of Mn‐doped CuFe2O4 ferrite [191], Zn‐doped MnFe2O4 [192] and NiFe2O4 [193, 194], Co‐doped NiFe2O4 [195] and ZnFe2O4 [196], and Cr‐doped CoFe2O4 [197] were reported. Recently, doping of spinel fer‐ rites by large cations was suggested as a promising way to increase the effective magnetic anisotropy. La‐doped CoFe2O4 [198], Sr‐doped MgFe2O4 [199], and Ce‐doped NiFe2O4 [200] or ZnFe2O4 [201] were prepared. For the doped samples, the most promising are the pol‐ yol, sol‐gel, or microemulsion methods as they do not require identical decomposition temperatures of metal precursors like the organic‐based routes, allow rather good control over homogeneity of doping, and yield samples with sufficiently low particle‐size distri‐ bution.

## **6. Conclusions and outlooks**

The core message of the chapter is to emphasize the importance of structural and spin order mirrored in magnetic properties of well‐defined spinel ferrite nanoparticles (NPs). The correlation between the specific preparation route to the typical structural and magnetic parameters of the particles is given, and the suitability of the resulting NPs in the context of possible applications is evaluated. Explicitly the meaning of different particle sizes obtained by different characterization methods, related to the degree of structural and spin order, is emphasized in the context of the magnetic properties. In order to wrap up the given subject, let's outline future outlooks in the field. The research of fine magnetic particles is progressively developing thanks to high demand on their practical exploitation, mainly in biomedicine. The forthcoming trend in customization of the magnetic NPs is obviously converging to control of the required magnetic properties at single‐particle level by adjustment of the synthetic protocols, which lead to fine tuning of the particle size, shape, and degree of order [169, 202]. For example, enhancement of the specific absorption rate in NPs can be achieved in natural or arbitrary core‐shell structures [203], via coupling of magnetically soft and hard ferrites for maximization of hysteresis losses [204] or by doping‐driven enhancement of heat generation [205]. Finally, smart self‐assembling strategies leading to superstructures [206], which can be even induced by magnetic field [207], seem to be a powerful tool for managing the magnetic response of the NPs at mesoscopic level.

## **Acknowledgements**

studiedinformofpowders,whichcontainNPs inveryclosecontact.Consequently,theresponse of suchsystems isalways inthe limitofthemediumtostronginteractionsandisalmostinvariant to the preparation route used, and the interaction strength for a given NP size is given by minimum distance between the NPs, in other words by the thickness of the surface coating [42, 170–172]. Upon specific conditions, well‐defined aggregates are formed [173], as reported, e.g., for preparations in microemulsion [174], by decomposition method [175] and by controlled encapsulationintophospholipides [176]. Suchassemblies attractedinterestdue to considerably enhanced heating properties in hyperthermia [177], which is associated with the enhancement ofthe single‐object(aggregate) anisotropy.Indense ensembles ofthe NPs,the onset of collective relaxationisalsocorroboratedbysignificantincreaseoftherelaxationtime[178–184];analogous consequence was observed in the aggregates [185]. However, the influence of the intra‐ and inter‐aggregate interactions is not explicitly decoupled. Recent studies also suggest a strong influence of the reformed particle energy barrier on the details of the aging dynamics, memory

In spite of the fact that the surface effects, defects, and interparticle interactions are believed to be contra‐productive factors as they in general decrease the value of saturation magnetiza‐ tion [26], they were recognized as potential enhancers of effective magnetocrystalline aniso‐ tropy, reflected, for example, in increase of the hysteresis losses [186]. Consequently, attempts to prepare smart NPs based on artificial core‐shell structure, e.g., NiFe2O4@γ‐Fe2O3 [187], ZnFe2O4@γ‐Fe2O3 [188], and Co,Fe2/Ni,Fe2O4 [189], appeared recently. Tri‐magnetic multi‐shell structures prepared by high‐temperature decomposition of the metal oleates were also

Alternative strategy is the tuning of magnetic properties of the spinel ferrite NPs via site‐ specific occupation of the spinel lattice. This is a straightforward approach as the relevant metal ions can substitute each other in the spinel structure easily. In this case, however, the site occupation must be carefully evaluated and controlled. Successful preparation and basic investigation of structure and magnetic properties of the NPs of Mn‐doped CuFe2O4 ferrite [191], Zn‐doped MnFe2O4 [192] and NiFe2O4 [193, 194], Co‐doped NiFe2O4 [195] and ZnFe2O4 [196], and Cr‐doped CoFe2O4 [197] were reported. Recently, doping of spinel fer‐ rites by large cations was suggested as a promising way to increase the effective magnetic anisotropy. La‐doped CoFe2O4 [198], Sr‐doped MgFe2O4 [199], and Ce‐doped NiFe2O4 [200] or ZnFe2O4 [201] were prepared. For the doped samples, the most promising are the pol‐ yol, sol‐gel, or microemulsion methods as they do not require identical decomposition temperatures of metal precursors like the organic‐based routes, allow rather good control over homogeneity of doping, and yield samples with sufficiently low particle‐size distri‐

The core message of the chapter is to emphasize the importance of structural and spin order mirrored in magnetic properties of well‐defined spinel ferrite nanoparticles (NPs). The

behavior, and apparent superspin dimensionality of the particles [132].

16 Magnetic Spinels- Synthesis, Properties and Applications

reported [190].

bution.

**6. Conclusions and outlooks**

The authors gratefully acknowledge Dr. Puerto Morales from the Instituto de Ciencia de Materiales de Madrid for her generous support and for sharing his expertise in synthesis of uniform iron oxide nanoparticles and Prof. Carla Cannas from the Università degli studi di Cagliari for sharing her knowledge in synthesis of core‐shell spinel ferrite nanoparticles. The research was carried out thanks to the support of the Czech Science Foundation, project no. 15‐01953S, and 7FP program project MULTIFUN (no. 262,943), cofinanced by the Ministry of Education, Youth, and Sports (project no. 7E12057). Magnetic measurements were performed in MLTL (http://mltl.eu/), which is supported within the program of Czech Research Infra‐ structures (project no. LM2011025).

## **Author details**

Barbara Pacakova1 , Simona Kubickova1 , Alice Reznickova1 , Daniel Niznansky2 and Jana Vejpravova1,2\*

\*Address all correspondence to: vejpravo@fzu.cz

1 Department of Magnetic Nanosystems, Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

2 Department of Inorganic Chemistry, Faculty of Science, Charles University in Prague, Pra‐ gue, Czech Republic

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## **Lithium Ferrite: Synthesis, Structural Characterization and Electromagnetic Properties Lithium Ferrite: Synthesis, Structural Characterization and Electromagnetic Properties**

Sílvia Soreto, Manuel Graça, Manuel Valente and Luís Costa Sílvia Soreto, Manuel Graça, Manuel Valente and Luís Costa Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/110790

#### **Abstract**

Lithium ferrite (LiFe5 O8 ) is a cubic ferrite, belongs to the group of soft ferrite materials with a square hysteresis loop, with high Curie temperature and magnetization. The spinel structure of LiFe5 O8 has two crystalline forms: ordered, β-LiFe<sup>5</sup> O8 (*Fd3m* space group) and disordered, α-LiFe<sup>5</sup> O8 (*P41 32/P43 32* space group). It has numerous technological applications in microwave devices, computer memory chip, magnetic recording, radio frequency coil fabrication, transformer cores, rod antennas, magnetic liquids among others. It is also a promising candidate for cathode in rechargeable lithium batteries. In this work, the dc electrical conductivity, the impedance spectroscopy and the magnetization of Li2 O-Fe2 O3 powders, with [Li]/[Fe]=1/5 (mol), heat-treated at several temperatures, are studied and related to their structure and morphology. The structural data were obtained by X-ray diffraction and Raman spectroscopy, and the morphology by scanning electron microscopy. The impedance spectroscopy was analysed in function of temperature and frequency, and it was observed that the dielectric properties are highly dependent on the microstructure of the samples. The dc magnetic susceptibility was recorded with a vibrating sample magnetometer, under zero field cooled and field cooled sequences, between 5-300 K. Typical hysteresis curves were obtained and the saturation magnetization increases with increase in heat-treatment temperature.

**Keywords:** lithium ferrite, electric and dielectric properties, magnetic properties

## **1. Introduction**

Technologically, ferrites are very important due to their interesting magnetic and electrical properties which can be exploited for applications in high-capacity batteries, electrochromic displays, wastewater cleaning, low magnetization ferrofluids, intercalation electrodes in

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

rechargeable batteries and as strong oxidizing agents [1–5]. Ferrites crystallize in three structure: (i) cubic spinel structure with the general formula MO.Fe2 O3 (M = Mn2+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+, Mg2+); (ii) hexagonal ferrites with the formula MO.6Fe2 O3 (M = Ba2+, Ca2+, Sr2+); and (iii) and garnets with the formula 2M2 O3 .5Fe2 O3 where M is a cation with (3+) charge such as Y or another rare earth [6].

The cubic lithium ferrite (**Figure 1**), spinel LiFe5 O8 [7] , is one of the most important ferrites, and it belongs to the soft ferrite materials group, with high Curie temperature (620°C) [8], square hysteresis loop and high magnetization. The spinel lithium ferrite has been widely studied and confirmed to have two crystalline forms: β-LiFe<sup>5</sup> O8 (*Fd3m* space group), known as the disordered LiFe5 O8 , and the α-LiFe<sup>5</sup> O8 (space group *P41 32/P43 32*), called ordered spinel phase. The first one is obtained by the rapid quenching of the samples from temperatures above 800°C to room temperature. Upon slow cooling and below 750°C, an ordered phase is obtained [9]. In the ordered form, α-LiFe<sup>5</sup> O8 , the octahedral *12d* and tetrahedral *8c* sites are occupied by iron ions, *Fe3+*, and the octahedral *4b* positions are occupied by lithium ions, *Li+* , in the cubic primitive cell. The disordered structure, β-LiFe<sup>5</sup> O8 , has an inverse spinel structure, where the tetrahedral *8a* positions are occupied by *Fe3+* ions and the ions *Li+* and *Fe3+* are randomly distributed over the *16d* octahedral positions [10, 11].

**Figure 1.** Cubic crystal of LiFe5 O8 with space group P4132 (213).

To prepare LiFe5 O8 by solid-state reaction method, high temperatures (>1200°C) are needed, which is a major issue due to the volatility of lithium above 1000°C. Therefore, the prepared material has a low quality because the sintering process normally leads to low specific surface areas [12], affecting its electrical and magnetic properties. Several chemical methods have been used for synthesis, such as co-precipitation, glass crystallization, hydrothermal, mechanical alloying and sol-gel methods. Therefore, the preparation of LiFe5 O8 at low temperatures is a subject of interest.

In order to improve the material properties, in this work lithium ferrite was prepared at a low temperature, by the solid-state reaction method using iron and lithium nitrates as precursors. First, the use of nitrates as base materials and, second, the use of the high-energy planetary ball milling to prepare the base material for further heat treatments are not conventional route and denote improvements which have not been reported in the literature. The electric and magnetic properties of the ferrite prepared by this method have been already published [5, 13, 14]. With the main aim to enhance the electric and magnetic properties of LiFe5 O8 and determine the best temperature for the thermal treatment, the powders after the ball milling are heat-treated at different temperatures.

The dependence of the particle size with the sintering temperature was also studied, and these studies were correlated with the measured electrical, dielectric and magnetic properties. The obtained results were analysed and compared with those presented in the literature.

## **2. Methods and procedures**

rechargeable batteries and as strong oxidizing agents [1–5]. Ferrites crystallize in three struc-

O8 [7] ,

(space group *P41*

and it belongs to the soft ferrite materials group, with high Curie temperature (620°C) [8], square hysteresis loop and high magnetization. The spinel lithium ferrite has been widely

phase. The first one is obtained by the rapid quenching of the samples from temperatures above 800°C to room temperature. Upon slow cooling and below 750°C, an ordered phase is

O8

O8

where the tetrahedral *8a* positions are occupied by *Fe3+* ions and the ions *Li+*

occupied by iron ions, *Fe3+*, and the octahedral *4b* positions are occupied by lithium ions, *Li+*

O3

O8

O8

by solid-state reaction method, high temperatures (>1200°C) are needed,

O8

at low temperatures is a

which is a major issue due to the volatility of lithium above 1000°C. Therefore, the prepared material has a low quality because the sintering process normally leads to low specific surface areas [12], affecting its electrical and magnetic properties. Several chemical methods have been used for synthesis, such as co-precipitation, glass crystallization, hydrothermal, mechanical

alloying and sol-gel methods. Therefore, the preparation of LiFe5

with space group P4132 (213).

*32/P43*

, the octahedral *12d* and tetrahedral *8c* sites are

O3

where M is a cation with (3+) charge such as

is one of the most important ferrites,

(M = Mn2+, Fe2+, Co2+, Ni2+,

(*Fd3m* space group), known

, has an inverse spinel structure,

*32*), called ordered spinel

and *Fe3+* are ran-

, in

(M = Ba2+, Ca2+, Sr2+); and

ture: (i) cubic spinel structure with the general formula MO.Fe2

studied and confirmed to have two crystalline forms: β-LiFe<sup>5</sup>

the cubic primitive cell. The disordered structure, β-LiFe<sup>5</sup>

domly distributed over the *16d* octahedral positions [10, 11].

, and the α-LiFe<sup>5</sup>

(iii) and garnets with the formula 2M2

32 Magnetic Spinels- Synthesis, Properties and Applications

The cubic lithium ferrite (**Figure 1**), spinel LiFe5

O8

obtained [9]. In the ordered form, α-LiFe<sup>5</sup>

Y or another rare earth [6].

as the disordered LiFe5

To prepare LiFe5

**Figure 1.** Cubic crystal of LiFe5

subject of interest.

O8

O8

Cu2+, Zn2+, Mg2+); (ii) hexagonal ferrites with the formula MO.6Fe2

O3 .5Fe2 O3

> As described in detail in our recent papers [5, 12, 13], the solid-state method was used to prepare lithium ferrite (LiFe5 O8 ) powders starting with iron (III) nitrate (Fe(NO3 )3 .9H2 O) and lithium nitrate (LiNO3 (Merck KGaA, Darmstadt, Germany). Considering the 1:5 required stoichiometry of Li:Fe, appropriate amounts of the two starting materials were mixed and homogenized in a planetary ball mill system (Fritsch Pulverisette 7.0) at 250 rpm for 1 h using equal volumes of balls to powders. Following this, 10 mL of ethanol was added to the mixture followed by additional ball milling at 500 rpm for 3 h, stopping the system for 5 min every hour to reduce over-heating. Next, in order to evaporate the ethanol, the vessel with the mixture was placed in a furnace at 80°C for 24 h.

> The next step in the synthesis procedure was heat treatment of the powder at nine temperatures between 200 and 1400°C (see **Figure 2**) at 10°C/min in two steps: first at 100°C for 1 h and the second at desired temperature for 4 h. After this heat treatment, the samples were structurally characterized using the techniques of X-ray diffraction (XRD), micro-Raman spectroscopy and scanning electron microscopy (SEM). The equipment used for the structural characterization was X'Pert MPD Philips diffractometer (CuKα radiation, λ = 1.54060 Å) for X-ray diffraction, an HR-800-UV Jobin Yvon Horiba spectrometer (532 nm laser line) for micro-Raman spectroscopy using a microscope objective (50×) and a Hitachi S4100-1 SEM system for SEM images with the samples covered with carbon before microscopic observation. Further details on these procedures are given in Refs. [5, 12, 13]. Electrical and magnetic measurements on the samples were performed following the structural characterization.

> For the measurements of electrical conductivity and impedance, the samples were pressed into 2-mm-thick discs with the opposite sides of the discs painted with silver paste for electrical contacts. The measurements were performed in helium atmosphere in order to improve the heat transfer and eliminate the moisture. The dc conductivity (σdc) was measured from 100 to 360 K employing a Keithley Model 617 electrometer using applied voltage of 100 V. Employing an Agilent 4294A precision impedance analyser in the Cp-Rp configuration, the measurements of impedance in the frequency range of 100 Hz–2 MHz were performed from 200 to 360 K.

**Figure 2.** XRD patterns of the powders heat-treated between 400 and 1400°C: (\*) Fe<sup>2</sup> O3 ; (o) LiFe5 O8 ; (+) Li2 FeO3 ; (#) LiNO3. Adapted from Refs. [13, 14].

The magnetic properties of the samples were measured using a vibrating sample magnetometer (VSM). The dc magnetic susceptibility was measured from 5 to 300 K under two protocols: (i) cooling the sample in zero field (ZFC) and (ii) cooling the sample with the magnetic field applied (FC). Typical hysteresis curves were obtained at several temperatures.

### **3. Results and discussion**

#### **3.1. Structural and morphological measurements**

**Figure 2** shows the XRD patterns of the samples after each heat treatment. The XRD spectra of the sample treated at 200°C shows the presence of lithium nitrate crystal phase. This phase disappears with the increase in the heat-treatment temperature. The samples heat-treated at 200 and 400°C present the α-Fe<sup>2</sup> O3 as the major crystalline phase. The non-detection by the XRD of the lithium nitrate phase in the sample treated at 400°C suggests the existence of an amorphous phase containing mainly lithium ions. This result also revealed that the planetary ball milling process did not induce the formation of new crystalline phases before the heat treatments.

A low amount of lithium ferrite is found in the sample with heat treatment at 600°C, but the main diffraction peaks are attributed to the α-Fe<sup>2</sup> O3 phase. The formation of LiFe5 O8 crystal phase can be attributed to the reaction between α-Fe<sup>2</sup> O3 and free Li+ ions. In samples with heat treatments at 1050, 1100 and 1150°C, all diffraction peaks can be assigned to the lithium ferrite crystal phase as described in Eq. (1) with loses of *NOx* .

$$\text{5Fe} \left( \text{NO}\_3 \right)\_3 + \text{LiNO}\_3 \xrightarrow{\Delta} \text{LiFe}\_5\text{O}\_8 + y\text{NO}\_x \tag{1}$$

In the sample treated at 1200°C besides lithium ferrite peaks, the lithium ferrate (Li2 FeO3 ) phase is also detected. The presence of this phase can be explained through the chemical reaction, Eq. (2), where the peak characteristics of Fe3 O4 are also present.

$$\text{15 Fe (NO}\_3\text{)}\_3 + \text{3 LiNO}\_3 \xrightarrow{\Delta} \text{LiFe}\_5\text{O}\_8 + \text{Li}\_2\text{FeO}\_3 + \text{3Fe}\_3\text{O}\_4 + y\text{ NO}\_x \tag{2}$$

In the sample heat-treated at 1400°C, besides the peak characteristics of magnetite, lithium ferrite and lithium ferrate crystal phases also present peak characteristics of hematite, Eq. (3). In this sample, the major phase is attributed to lithium ferrate crystal phase showing broad diffraction peaks.

$$\text{15 Fe (NO}\_3\text{)}\_3 + \text{3 LiNO}\_3 \xrightarrow{\Delta} \text{LiFe}\_5\text{O}\_8 + \text{Li}\_2\text{FeO}\_3 + \text{Fe}\_3\text{O}\_4 + \text{3Fe}\_2\text{O}\_3 + y\text{ NO}\_x \tag{3}$$

According to Wolska et al. [7] results, for heat treatment above 1000°C the disordered LiFe5 O8 phase can be formed. However, in our results, the LiFe5 O8 phase detected was only the ordered one (α-LiFe<sup>5</sup> O8 ) with the space group *P41 32/*P43 32.

To determine the crystallite size, Lc , of lithium ferrite crystal phase, the Debye-Scherrer equation was used:

$$L\_c = \frac{N\lambda}{\beta \cos \theta} \tag{4}$$

Here, *β* is full width half maximum of the diffracted peaks, *λ* is the wavelength of X-ray radiation, *θ* is the angle of diffraction and *N* is a numerical factor frequently referred to as

The magnetic properties of the samples were measured using a vibrating sample magnetometer (VSM). The dc magnetic susceptibility was measured from 5 to 300 K under two protocols: (i) cooling the sample in zero field (ZFC) and (ii) cooling the sample with the magnetic field applied

**Figure 2** shows the XRD patterns of the samples after each heat treatment. The XRD spectra of the sample treated at 200°C shows the presence of lithium nitrate crystal phase. This phase disappears with the increase in the heat-treatment temperature. The samples heat-treated at 200

the lithium nitrate phase in the sample treated at 400°C suggests the existence of an amorphous phase containing mainly lithium ions. This result also revealed that the planetary ball milling process did not induce the formation of new crystalline phases before the heat treatments.

A low amount of lithium ferrite is found in the sample with heat treatment at 600°C, but the

O3

O3

as the major crystalline phase. The non-detection by the XRD of

O3 ; (o) LiFe5 O8 ; (+) Li2 FeO3

and free Li+

phase. The formation of LiFe5

O8

ions. In samples with heat

crystal

; (#) LiNO3.

(FC). Typical hysteresis curves were obtained at several temperatures.

**Figure 2.** XRD patterns of the powders heat-treated between 400 and 1400°C: (\*) Fe<sup>2</sup>

**3. Results and discussion**

Adapted from Refs. [13, 14].

34 Magnetic Spinels- Synthesis, Properties and Applications

and 400°C present the α-Fe<sup>2</sup>

**3.1. Structural and morphological measurements**

main diffraction peaks are attributed to the α-Fe<sup>2</sup>

phase can be attributed to the reaction between α-Fe<sup>2</sup>

O3

**Figure 3.** Crystallite size of LiFe5 O8 phase in samples heat-treated at 1000, 1050, 1100, 1150 and 1200°C.

the crystallite-shape factor [15, 16] and being *N* = 0.9 a good approximation in the absence of detailed information [17].

Substituting the relevant data from XRD profile measurement, the average crystallite sizes and its errors bars are shown in **Figure 3**.

A crystallite size of about 85 nm was observed in the samples heat-treated at 1050, 1100, 1150°C, which only presents LiFe5 O8 crystal phase, and in the sample heat-treated at 1200°C. The sample treated at 1000°C has the lowest crystallite size, 31 ± 1 nm.

The samples presenting LiFe5 O8 as major crystal phase, that is, heat-treated at temperatures between 400 and 1400°C, were also analysed using Raman spectroscopy (**Figure 4**).

**Figure 4.** Raman spectra for the samples with heat treatments between 400 and 1400°C. Adapted from Refs. [13, 14].

According to the Raman spectroscopy spectra, all the samples show the vibration mode characteristic of both ordered and disordered lithium ferrite phases.

For the samples treated between 1000 and 1400°C, the vibrational peaks at 199–206 and 237–241 cm−1 indicate the presence of the ordered α-LiFe<sup>5</sup> O8 phase [18]. All the vibrational peaks of the LiFe5 O8 phase are given in **Table 1**. In the samples heat-treated at 600, 1000 and 1400°C, besides the vibrational modes that mark the presence of lithium ferrite, the vibrational mode characteristic of α-Fe<sup>2</sup> O3 is also present [19].

According to the Raman spectra, for the sample heat-treated at 1200°C and crossing with the XRD results, we can infer about the vibration modes of the lithium ferrate (Li<sup>2</sup> FeO3 ). The Lithium Ferrite: Synthesis, Structural Characterization and Electromagnetic Properties http://dx.doi.org/10.5772/110790 37


**Table 1.** Raman peaks identification for the different samples.

the crystallite-shape factor [15, 16] and being *N* = 0.9 a good approximation in the absence of

Substituting the relevant data from XRD profile measurement, the average crystallite sizes

A crystallite size of about 85 nm was observed in the samples heat-treated at 1050, 1100,

According to the Raman spectroscopy spectra, all the samples show the vibration mode char-

**Figure 4.** Raman spectra for the samples with heat treatments between 400 and 1400°C. Adapted from Refs. [13, 14].

For the samples treated between 1000 and 1400°C, the vibrational peaks at 199–206 and 237–241

the vibrational modes that mark the presence of lithium ferrite, the vibrational mode character-

According to the Raman spectra, for the sample heat-treated at 1200°C and crossing with

the XRD results, we can infer about the vibration modes of the lithium ferrate (Li<sup>2</sup>

O8

phase are given in **Table 1**. In the samples heat-treated at 600, 1000 and 1400°C, besides

phase [18]. All the vibrational peaks of the

FeO3

). The

acteristic of both ordered and disordered lithium ferrite phases.

cm−1 indicate the presence of the ordered α-LiFe<sup>5</sup>

is also present [19].

LiFe5 O8

istic of α-Fe<sup>2</sup>

O3

between 400 and 1400°C, were also analysed using Raman spectroscopy (**Figure 4**).

crystal phase, and in the sample heat-treated at 1200°C.

as major crystal phase, that is, heat-treated at temperatures

O8

The sample treated at 1000°C has the lowest crystallite size, 31 ± 1 nm.

O8

detailed information [17].

and its errors bars are shown in **Figure 3**.

36 Magnetic Spinels- Synthesis, Properties and Applications

1150°C, which only presents LiFe5

The samples presenting LiFe5

assignment of vibrational modes related with lithium ferrite and magnetite (Fe3 O4 ) [20] was also made. In the particular case of lithium ferrate, it is interesting to focus that the vibrational band with higher intensity is centred at 125 cm−1 and the bands at 437 and 523 cm−1 show lower intensity. **Table 1** shows all vibration modes present for each sample.

In the morphological analysis of the samples (**Figure 5**), the increasing of the particle size is clearly visible from 100 nm for the sample heat-treated at 400°C to 4 µm approximately for the sample heat-treated at 1400°C.

**Figure 5.** SEM micrographs for samples with heat treatments at 200, 400, 600, 1000, 1050, 1100, 1150, 1200 and 1400°C. Adapted from Refs. [5, 13, 14].

The aggregation of the spherical grains is quite evident, related to the Fe2 O3 , with the increase in the heat-treatment temperature. The formation of the LiFe5 O8 phase shows a different microstructure, with prismatic grains clearly visible in the sample with heat treatment at 1150°C. In the sample treated at 1400°C, the formation of small grains attached to the prismatic grains is evident. As the shape of these grains is spherical, it could be attributed to the formation of Fe2 O3 , once this shape is the same as the one present in the samples treated at low temperatures. This aggregation to the prismatic particles also seems to appear in the sample treated at 1200°C. These results support the ones obtained by XRD and Raman measurements.

#### **3.2. Electrical and dielectric measurements**

The electrical measurements were performed on the samples heat-treated at temperatures between 400 and 1200°C. To interpret the temperature dependence of the dc conductivity, σdc data, the Arrhenius expression [21] has been used:

ddata, the Arrhenius expression [21] has been used: 
$$\sigma\_{dc} = \sigma\_o \exp\left(-\frac{E\_{d(t)}}{KT}\right) \tag{5}$$

Here *σ<sup>0</sup>* is a pre-exponential factor, *Ea*(dc) the dc activation energy, *K* the Boltzmann constant and *T* the temperature. **Figure 6** shows the experimental data and the fit for all the treated samples.

The maximum of the conductivity is obtained for the sample heat-treated at 1100°C, which according to the XRD pattern only contains the LiFe<sup>5</sup> O8 crystal phase. For the other samples, which also contain hematite, the conductivity increases with the temperature of heat treatment, and the activation energy decreases. This behaviour can be explained by the decrease in the hematite phase until the treatment temperature reaches 1100°C. The lower conductivity of the sample treated at 1200°C compared to the one treated at 1100°C can be related to the presence of lithium ferrate crystal.

**Figure 6.** Log (σdc) versus 1000/T.

assignment of vibrational modes related with lithium ferrite and magnetite (Fe3

intensity. **Table 1** shows all vibration modes present for each sample.

The aggregation of the spherical grains is quite evident, related to the Fe2

microstructure, with prismatic grains clearly visible in the sample with heat treatment at 1150°C. In the sample treated at 1400°C, the formation of small grains attached to the prismatic grains is evident. As the shape of these grains is spherical, it could be attributed to

**Figure 5.** SEM micrographs for samples with heat treatments at 200, 400, 600, 1000, 1050, 1100, 1150, 1200 and 1400°C.

at low temperatures. This aggregation to the prismatic particles also seems to appear in the sample treated at 1200°C. These results support the ones obtained by XRD and Raman

The electrical measurements were performed on the samples heat-treated at temperatures between 400 and 1200°C. To interpret the temperature dependence of the dc conductivity, σdc

*T* the temperature. **Figure 6** shows the experimental data and the fit for all the treated samples. The maximum of the conductivity is obtained for the sample heat-treated at 1100°C, which

*E* \_*a*(*dc*)

is a pre-exponential factor, *Ea*(dc) the dc activation energy, *K* the Boltzmann constant and

O8

in the heat-treatment temperature. The formation of the LiFe5

the sample heat-treated at 1400°C.

38 Magnetic Spinels- Synthesis, Properties and Applications

the formation of Fe2

Adapted from Refs. [5, 13, 14].

measurements.

Here *σ<sup>0</sup>*

O3

**3.2. Electrical and dielectric measurements**

data, the Arrhenius expression [21] has been used:

*<sup>σ</sup>dc* <sup>=</sup> *<sup>σ</sup>*<sup>0</sup> *exp*(<sup>−</sup>

according to the XRD pattern only contains the LiFe<sup>5</sup>

also made. In the particular case of lithium ferrate, it is interesting to focus that the vibrational band with higher intensity is centred at 125 cm−1 and the bands at 437 and 523 cm−1 show lower

In the morphological analysis of the samples (**Figure 5**), the increasing of the particle size is clearly visible from 100 nm for the sample heat-treated at 400°C to 4 µm approximately for

O4

O3

*KT* ) (5)

crystal phase. For the other samples,

O8

, once this shape is the same as the one present in the samples treated

, with the increase

phase shows a different

) [20] was

**Figure 7.** Dependence of the ac activation energy (*Ea*(ac)) and ac conductivity (σac), at 300 K and 100 kHz, with heattreatment temperatures.

**Figure 7** shows the behaviour of the ac conductivity with the temperature of heat treatment. For samples treated at 1000, 1050, 1100 and 1150°C, there is a similar tendency between *ac* activation energy and conductivity. Similar to the dc conductivity variation of Eq. (3), the Arrhenius behaviour also fits correctly the ac data:

$$\begin{aligned} \text{Arhenius behaviour also fits correctly the ac data:}\\ \sigma\_{\rm ac} = \sigma\_0 \exp\left(-\frac{E\_{s(\nu)}}{KT}\right) \end{aligned} \tag{6}$$

**Table 2** shows a comparison of the ac and dc activation energy for each sample.


**Table 2.** The *dc* and *ac* activation energies for the samples.

The dielectric measurements of *Cp* and *Rp* allowed us to calculate the real, ε′, and the imaginary, ε″, part of the complex permittivity using the equations [22]:

$$
\varepsilon' \le \mathcal{C}\_p \frac{d}{A \,\, \varepsilon\_0} \tag{7}
$$

$$
\varepsilon'' = \frac{d}{\omega \,\, R\_p} \varepsilon\_0 \tag{8}
$$

Here *d* represents the sample thickness, *A* the electrode area, *ε<sup>0</sup>* the empty space permittivity and *ω* the angular frequency, respectively. These relations are only valid if *d << A*. The frequency dependence of the real part of the complex permittivity, ε′, and of the imaginary part of the complex permittivity, ε″, at constant temperature, *T* = 300 K, is shown in **Figure 8**.

According to **Figure 8**, the sample heat-treated at 1200°C presents the higher values of ε′, but the ε″ results are not suitable for their intended use due to their high losses, tan*δ* = 1.12 at 300 K and 1 kHz. On the other hand, the samples with heat treatments at 1050, 1100 and 1150°C have high dielectric constant and low losses at the same conditions of temperature and frequency: 0.86, 0.40 and 0.84, respectively.

Again, the behaviour is similar to that one observed with the other measurements. The increase in the complex permittivity with the treatment temperature is due to the structural and morphologic changes observed. This behaviour occurs for other ferrites [23, 24], where an increase in ε′ with the temperature of the heat treatment is observed. The crystallite size of the particles (**Figure 3**) influences the dielectric response, that is, the increase in the crystallite size, which is maximum for the samples treated at 1050, 1100, 1150 and 1200°C, leads to an increase in the dielectric constant.

Lithium Ferrite: Synthesis, Structural Characterization and Electromagnetic Properties http://dx.doi.org/10.5772/110790 41

**Figure 8.** Frequency dependence of the complex permittivity, at T = 300 K [14].

**Figure 7** shows the behaviour of the ac conductivity with the temperature of heat treatment. For samples treated at 1000, 1050, 1100 and 1150°C, there is a similar tendency between *ac* activation energy and conductivity. Similar to the dc conductivity variation of Eq. (3), the

**Table 2** shows a comparison of the ac and dc activation energy for each sample.

**Heating temperature (°C)** *Ea***(ac) ± ∆***Ea***(ac) (kJ/mol)** *Ea***(dc) ± ∆***Ea***(dc) (kJ/mol)**

400 21.0 ± 2.6 69.4 ± 0.7 1000 17.0 ± 0.6 47.4 ± 0.5

1100 26 ± 2 39.1 ± 1.6

1200 17.7 ± 0.9 23.6 ± 0.2

and *Rp*

\_\_\_*d A ε*<sup>0</sup>

*ω Rp ε*<sup>0</sup>

ity and *ω* the angular frequency, respectively. These relations are only valid if *d << A*. The frequency dependence of the real part of the complex permittivity, ε′, and of the imaginary part of the complex permittivity, ε″, at constant temperature, *T* = 300 K, is shown in **Figure 8**. According to **Figure 8**, the sample heat-treated at 1200°C presents the higher values of ε′, but the ε″ results are not suitable for their intended use due to their high losses, tan*δ* = 1.12 at 300 K and 1 kHz. On the other hand, the samples with heat treatments at 1050, 1100 and 1150°C have high dielectric constant and low losses at the same conditions of temperature and fre-

Again, the behaviour is similar to that one observed with the other measurements. The increase in the complex permittivity with the treatment temperature is due to the structural and morphologic changes observed. This behaviour occurs for other ferrites [23, 24], where an increase in ε′ with the temperature of the heat treatment is observed. The crystallite size of the particles (**Figure 3**) influences the dielectric response, that is, the increase in the crystallite size, which is maximum for the samples treated at 1050, 1100, 1150 and 1200°C, leads to an increase in the dielectric constant.

nary, ε″, part of the complex permittivity using the equations [22]:

Here *d* represents the sample thickness, *A* the electrode area, *ε<sup>0</sup>*

*E* \_*a*(*ac*)

*KT* ) (6)

allowed us to calculate the real, ε′, and the imagi-

(7)

(8)

the empty space permittiv-

Arrhenius behaviour also fits correctly the ac data:

40 Magnetic Spinels- Synthesis, Properties and Applications

*<sup>σ</sup>ac* <sup>=</sup> *<sup>σ</sup>*<sup>0</sup> *exp*(<sup>−</sup>

The dielectric measurements of *Cp*

1050 20 ± 1

1150 18 ± 1

*ε*′= *Cp*

**Table 2.** The *dc* and *ac* activation energies for the samples.

quency: 0.86, 0.40 and 0.84, respectively.

*ε*″ = \_\_\_\_\_\_ *<sup>d</sup>*

The modulus formalism, where M\* = 1/ε\*, proposed by Macedo et al. [25] was used to study the dielectric response. **Figure 9** shows the frequency dependence of the imaginary part of the modulus (M″) for the sample that was heat-treated at 1050°C.

**Figure 9.** Imaginary part of the complex modulus, M″, for the sample treated at 1050°C, in the temperature range between 260 and 360 K, in steps of 10 K [14].

**Figure 10.** Nyquist plot fit for the sample heat-treated at 400°C for a temperature of measurement of 300 K [5].

**Figure 11.** Nyquist plot for the sample treated at 1050°C for a range of temperatures between 300 and 360 K. Adapted from Ref. [14].

For all samples, a relaxation process is visible, as the one shown in **Figure 10**, which has a shape of a decentred semicircle, with its centre situated below the abscissa axis. **Figure 11** shows sample heat-treated at 1050°C, the evolution of the Nyquist plot with the temperature. From these results, the maximum of the relaxation time, τmax, (**Figure 11** inset) shows a typical behaviour, that is, a decrease in the τmax with increase in the temperature. This Cole-Cole analysis can also be made with the magnetic ac susceptibility data as the work presented by Wang and Seehra [26].

This profile indicates that the simple exponential decay, corresponding to a Debye relaxation, is inappropriate to describe the relaxation phenomena and should be replaced by an empirical model, such as Cole-Cole analysis [27]:

$$M^\* = M\_\omega + \frac{\Delta M}{1 + (iw\,\tau\_M\,)^{1\cdots n\_s}}\tag{9}$$

Eq. (9) represents a modification of the Debye equation since for *αM* = 0, the Debye model corresponding to a single relaxation time is recovered. In Eq. (9), *αM* is a parameter between 0 and 1, which reflects the dipole interaction in the system; also *M∞* is the relaxed modulus; *∆M* is the modulus relaxation strength; and *τM* is the relaxation time.

According to the values of the exponent parameter *αM*, the system is a non-Debye, and for all samples, *αM* decreases with the temperature. It decreases from about 0.56 to 0.50 in the sample treated at 400°C and from about 0.43 to 0.30 at 1200°C treated one. For modulus relaxation strength ∆*M*, the behaviour is similar to exponent parameter *αM*, decreasing with temperature for each heat treatment (**Figure 12**).

**Figure 12.** Temperature dependence of the αCole-Cole parameter and ∆M for sample heat-treated at 1100°C [14].

The relaxation frequency, *f max* <sup>=</sup> \_\_\_\_ <sup>1</sup> <sup>2</sup>*πτ*, can be expressed by the Arrhenius law, where *f max* <sup>∝</sup> *exp*(<sup>−</sup> *<sup>E</sup>*\_*<sup>a</sup> KT*) (10)

For all samples, a relaxation process is visible, as the one shown in **Figure 10**, which has a shape of a decentred semicircle, with its centre situated below the abscissa axis. **Figure 11** shows sample heat-treated at 1050°C, the evolution of the Nyquist plot with the temperature. From these results, the maximum of the relaxation time, τmax, (**Figure 11** inset) shows a typical behaviour, that is, a decrease in the τmax with increase in the temperature. This Cole-Cole analysis can also be made with the magnetic ac susceptibility data as the work presented by

**Figure 11.** Nyquist plot for the sample treated at 1050°C for a range of temperatures between 300 and 360 K. Adapted

**Figure 10.** Nyquist plot fit for the sample heat-treated at 400°C for a temperature of measurement of 300 K [5].

42 Magnetic Spinels- Synthesis, Properties and Applications

Wang and Seehra [26].

from Ref. [14].

In Eq. (10), *Ea* is the activation energy for the relaxation process. The logarithmic representation of the relaxation frequency versus the inverse temperature, the relaxation map, allows to obtain the activation energy (**Figure 13**). Also in this process, the activation energy decreases with the temperature of the treatment unless for the samples treated at 1050, 1100 and 1150°C which increases. This may be related to structural changes, since at this heat treatment temperature only the crystalline phase of lithium ferrite is present. The same tendency as the one observed in the ac conductivity regime, in the samples with only one crystal phase, LiFe5 O8 . **Table 3** resumes all the activation energies of the relaxation process.

**Figure 13.** Ln (fmax) versus 1000/T [14].


**Table 3.** The activation energy for the relaxation process for all the samples investigated here.

#### **3.3. Magnetic measurements**

The magnetic measurements were performed on the samples heat-treated at 200, 400, 600, 1000, 1050, 1100, 1150, 1200 and 1400°C. Initially, the measurements were performed in ZFC conditions with an applied magnetic field (*B*) of 0.1 T, from 5 K up to 300 K. At 300 K, magnetization (*M)* versus *B* measurements were performed. Then, FC measurements were performed from 300 K down to 5 K under the magnetic field of 0.1 T. Again, at 5 K, *M* versus *B* measurements were also performed. This experimental sequence is important to explain why after the M versus B at 300 K, an increase of magnetic susceptibility in the FC curves is observed, which can be ascribed to the remnant magnetization of the sample (**Figure 14a** and **b**).

observed in the ac conductivity regime, in the samples with only one crystal phase, LiFe5

The magnetic measurements were performed on the samples heat-treated at 200, 400, 600, 1000, 1050, 1100, 1150, 1200 and 1400°C. Initially, the measurements were performed in ZFC condi-

 **± ∆***Ea*

 **(kJ/mol)**

**Table 3** resumes all the activation energies of the relaxation process.

44 Magnetic Spinels- Synthesis, Properties and Applications

**3.3. Magnetic measurements**

Adapted from Ref. [14].

**Figure 13.** Ln (fmax) versus 1000/T [14].

**Heat-treated sample (°C)** *Ea*

400 21 ± 3 1000 32 ± 2

1050 46.0 ± 0.8 1100 37.3 ± 0.8

1150 34.45 ± 0.01 1200 12.2 ± 0.7

**Table 3.** The activation energy for the relaxation process for all the samples investigated here.

O8 .

**Figure 14.** Magnetic susceptibility versus temperature, recorded under zero field cooled (ZFC) and field cooled (FC) sequences with *B* = 0.1 T, between 5 and 300 K, for the samples with a heat treatment of 200°C (a) and 400°C (b). Adapted from Ref. [13].

In **Figure 14a**, in the sample treated at 200°C, the results of the magnetic susceptibility recorded under ZFC and FC show the presence of a blocking temperature (TB) between 50 and 70 K. This blocking temperature was observed with the translation of the FC curve into the ZFC curve, where TB is the temperature which separates the FC and ZFC curves. **Figure 14b**, shows that in the sample treated at 400 °C, TB is slightly higher, around 70 K, than in the sample treated at 200 °C. This difference can be related to the particles size, which is higher for the sample heat-treated at 400°C (**Figure 5**). The dependence of the magnetic susceptibility on temperature is shown in **Figure 15**.

**Figure 15.** Magnetic susceptibility versus temperature, recorded under field cooled (FC) with an applied magnetic field of 0.1 T, between 5 and 300 K. Adapted from Ref. [13].

With the exception of samples treated at 200 and 400°C, a decrease in the magnetic susceptibility with increase in the temperature of measurement is observed in the remaining samples. This behaviour of the dependence of the susceptibility with the temperature was expected because it is characteristic of ferromagnetic materials. This feature will change to a non-magnetic order (paramagnetic characteristic) above Curie temperature, which is, according to Iliev et al. [8], about 893 K for lithium ferrite This property was not observed because in our experimental procedure the maximum temperature of measurement was 300 K (**Figure 15**). The sample heat-treated at 1200°C shows the highest magnetic susceptibility.

As noted earlier, the XRD diffraction patterns of the samples heat-treated at 1050, 1100 and 1150°C are characteristic of a single lithium ferrite phase (**Figure 2**). The SEM micrographs of these samples (**Figure 5**) show an increase in the grain size, changing from about 100 nm for sample treated at 400°C to 4 µm for sample treated at 1400°C. This promotes the increase in the probability of the random distribution of magnetic moments and therefore an increase in the soft magnetic type response.

**Figure 16a** and **b** shows the magnetization versus applied field, measured at 5 K, for all the samples. It should be noticed that **Figure 16b** is presented only to show a better graphical visualization of the magnetization of the samples treated between 1000 and 1200°C. The samples heat-treated at 200 and 400°C present a low magnetization, due to the fact that the major phase is antiferromagnetic α-Fe<sup>2</sup> O3 .

**Figure 16.** Magnetic hysteresis curves (*T* = 5 K). Adapted from Ref. [13].

In the literature [28, 29], the magnetization of the lithium ferrite is around 60 emu/g, which is rather lower than the one obtained in this work (**Figure 16**). In these samples, the generation of the lithium ferrite phase takes to the decrease in the contribution of the α-Fe<sup>2</sup> O3 particles with low magnetization. XRD and Raman results confirm that the samples heat-treated at temperatures between 1000 and 1200°C have the ordered phase α-LiFe<sup>5</sup> O8 as the major phase. Very likely, this ordered ferrite phase is developed from the thermal-activated reaction between α-Fe<sup>2</sup> O3 and "free" lithium ions present in the lattice, suggesting the existence of some amorphous phase, whose amount decreases with the increase in the heat-treatment temperature. The presence of this lithium ferrite phase also promotes the increase in the magnetization (**Figure 16**), showing a maximum of 73 emu/g, for the sample treated at 1200°C, which is a similar value to the one obtained by Singhal [30] on lithium ferrite prepared by aerosol route. This high magnetization is attributed to the formation of Fe<sup>3</sup> O4 (Ms = 92 emu/g [31]) as proved by XRD results. For this sample, the minimum magnetic field that saturates the sample is around 0.1 T, meaning that this sample magnetizes easily [13]. The further increase in the heat-treatment temperature of 1400°C also promotes the development of hematite, α-Fe<sup>2</sup> O3 (**Figure 2**), whose magnetization of saturation is around ~10 emu/g [32, 33]. This should be the reason for the observed decrease in magnetization from sample treated at 1200 (73 emu/g) to sample treated at 1400°C (30 emu/g) (**Figure 16**). Moreover, the contribution of Li2 FeO3 to the absolute magnetization should be lower than the one of LiFe5 O8 in accordance with Hessien et al. [34] who states that the increase in the molar ratio between Fe3+ and Li+ leads to lower magnetization values.

Shirsath et al. [35] have studied this particular type of ferrite, prepared using also nitrates as initial materials but following a sol-gel method. Comparing their results with ours and taking into account the fact that the followed method was the solid-state route, the magnitudes of the magnetization for our samples are higher, nearly 73 and 55 emu/g for the sample heat-treated at 1200 and 1000°C respectively. The values for the same treatment temperatures, obtained by Shirsath et al. through the sol-gel method, are around 55 and 45 emu/g, respectively, and related to the particle size. In the referred work, as the particle size increases, the magnetization decreases. For the sample treated at 600°C, which has also a large amount of hematite (**Figure 2**), the results are similar for both methods.

## **4. Conclusions**

With the exception of samples treated at 200 and 400°C, a decrease in the magnetic susceptibility with increase in the temperature of measurement is observed in the remaining samples. This behaviour of the dependence of the susceptibility with the temperature was expected because it is characteristic of ferromagnetic materials. This feature will change to a non-magnetic order (paramagnetic characteristic) above Curie temperature, which is, according to Iliev et al. [8], about 893 K for lithium ferrite This property was not observed because in our experimental procedure the maximum temperature of measurement was 300 K (**Figure 15**).

As noted earlier, the XRD diffraction patterns of the samples heat-treated at 1050, 1100 and 1150°C are characteristic of a single lithium ferrite phase (**Figure 2**). The SEM micrographs of these samples (**Figure 5**) show an increase in the grain size, changing from about 100 nm for sample treated at 400°C to 4 µm for sample treated at 1400°C. This promotes the increase in the probability of the random distribution of magnetic moments and therefore an increase in

**Figure 16a** and **b** shows the magnetization versus applied field, measured at 5 K, for all the samples. It should be noticed that **Figure 16b** is presented only to show a better graphical visualization of the magnetization of the samples treated between 1000 and 1200°C. The samples heat-treated at 200 and 400°C present a low magnetization, due to the fact that the major

In the literature [28, 29], the magnetization of the lithium ferrite is around 60 emu/g, which is rather lower than the one obtained in this work (**Figure 16**). In these samples, the generation of

low magnetization. XRD and Raman results confirm that the samples heat-treated at tempera-

likely, this ordered ferrite phase is developed from the thermal-activated reaction between

 and "free" lithium ions present in the lattice, suggesting the existence of some amorphous phase, whose amount decreases with the increase in the heat-treatment temperature. The presence of this lithium ferrite phase also promotes the increase in the magnetization (**Figure 16**), showing a maximum of 73 emu/g, for the sample treated at 1200°C, which is a

O3

as the major phase. Very

O8

particles with

the lithium ferrite phase takes to the decrease in the contribution of the α-Fe<sup>2</sup>

tures between 1000 and 1200°C have the ordered phase α-LiFe<sup>5</sup>

**Figure 16.** Magnetic hysteresis curves (*T* = 5 K). Adapted from Ref. [13].

The sample heat-treated at 1200°C shows the highest magnetic susceptibility.

O3 .

the soft magnetic type response.

46 Magnetic Spinels- Synthesis, Properties and Applications

phase is antiferromagnetic α-Fe<sup>2</sup>

α-Fe<sup>2</sup> O3 The LiFe5 O8 crystal phase was obtained using nitrates as raw materials by an easy and relatively inexpensive route. From the structural and morphological results, the lithium ferrite crystal phase obtained is the ordered one, α-LiFe<sup>5</sup> O8 , and is mostly present in the samples with thermal treatment from 1000 to 1200°C. Heat treatments above 1150°C promote the formation of the Li2 FeO3 and Fe3 O4 crystal phases. Spherical grains related to α-Fe<sup>2</sup> O3 were detected in the sample heat-treated at 1400°C. The formation of lithium ferrite phases leads to a different microstructure (prismatic grains), whose size increases with the increase in heattreatment temperature, obtaining a maximum for 1200°C. In the sample treated at 1400°C, SEM micrograph shows modification in the surface that is related to the lithium ferrate crystal phase and the appearance of α-Fe<sup>2</sup> O3 .

Electrical measurements suggest that the samples with heat treatments at 1000, 1050 and 1150°C have a good dielectric response; however, the sample treated at 1100°C is more suitable for application in electronic devices.

Magnetic analysis confirms that the presence of α-Fe<sup>2</sup> O3 that leads to a decrease in the magnetization as a function of the applied field. The presence of α-LiFe<sup>5</sup> O8 and Fe3 O4 contributes to the maximum magnetization magnitude observed (73 emu/g at the sample treated at 1200°C). The magnetic susceptibility as a function of temperature has a maximum value of nearly 1750 emu (gT)−1 for the sample treated at 1200°C confirming that this sample has a good magnetic response.

## **Acknowledgements**

This work was financed by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT—Portuguese Foundation for Science and Technology under the project UID/CTM/50025/2013. S. Soreto Teixeira also acknowledges to the FCT for a Ph D. Grant SFRH/BD/105211/2014.

## **Author details**

Sílvia Soreto\*, Manuel Graça, Manuel Valente and Luís Costa

\*Address all correspondence to: silvia.soreto@ua.pt

Department of Physics, I3N - University of Aveiro, Aveiro, Portugal

## **References**


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Sílvia Soreto\*, Manuel Graça, Manuel Valente and Luís Costa

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\*Address all correspondence to: silvia.soreto@ua.pt

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## **Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties Ferrite Nanoparticles of Desired Size and Magnetic Properties**

**Optimizing Processing Conditions to Produce Cobalt** 

Oscar Perales-Pérez and Yarilyn Cedeño-Mattei

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66842

Oscar Perales-Pérez and Yarilyn Cedeño-Mattei

#### **Abstract**

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50 Magnetic Spinels- Synthesis, Properties and Applications

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The excellent chemical stability, good mechanical hardness, and a large positive first order magnetocrystalline anisotropy constant of cobalt ferrite (CoFe2 O4 ) make it a prom‐ ising candidate for magneto‐optical recording media. For practical applications, the capability to control particle size at the nanoscale is required in addition to precise con‐ trol of the composition and structure of CoFe2 O4. It has been well established that a fine tuning in cobalt ferrite nanocrystal size within the magnetic single domain region would lead to the achievement of extremely high coercivity values at room temperature. The development of a size‐sensitive phase separation method for cobalt ferrite that is based on a selective dissolution of the superparamagnetic fraction and subsequent size‐sensi‐ tive magnetic separation of single‐domain nanoparticles is presented. The attained room temperature coercivity value (11.9 kOe) was mainly attributed to the enlargement of the average crystal size within the single domain region coupled with the removal of the superparamagnetic fraction. The strong influence of crystal size, ferrite composition, and cation distribution in the ferrite lattice on the corresponding magnetic properties at the nanoscale was also confirmed. The superparamagnetic and magnetic single domain lim‐ its were experimentally determined.

**Keywords:** cobalt ferrite, nanocrystals, size‐controlled synthesis, high coercivity, magnetic properties

## **1. Introduction**

Technological applications of cobalt ferrite (CoFe2 O4 ) nanocrystals include their potential use in ferrofluids, hyperthermia, and biological treatment agents due to their unusual properties

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1, 2]. In addition, CoFe2 O4 possesses excellent chemical stability, good mechanical hardness, and a large positive first order crystalline anisotropy constant, making it a promising can‐ didate for magneto‐optical recording media also [3]. Control on particle size and shape, ion distribution, and/or structure could allow a fine‐tuning of the magnetic properties of ferrites [4–7]. In this regard, magnetic nanocrystals exhibit strong size‐dependent properties that may provide valuable information on estimating the scaling limits of magnetic storage while con‐ tributing to the development of high‐density data storage devices.

To the best of our knowledge, there is still a lack of a systematic effort to restrict the growth of single nanocrystals within the magnetic single domain region where enhancement of coerciv‐ ity could be achieved. Theoretically, the single domain region ranges between 5 and 40 nm [8]. Maximum coercivity value of around 5.3 kOe [9] has also been reported for 40 nm nanocrystals. Since coercivity is strongly dependent on particle size, any attempt to achieve higher coercivity values in cobalt ferrite must consider the development of alternative approaches in order to obtain more homogeneous crystal sizes with less or null presence of superparamagnetic par‐ ticles, which have near‐zero coercivity.

It is desired to select a synthesis procedure capable of producing nanocrystals with a narrow size distribution due to the above‐mentioned direct dependence of coercivity on crystal size. Synthesis approaches such as reverse micelles and thermal decomposition meet this criterion but the excessive consumption of resources, namely, synthesis reagents and experimental time, must be minimized. The use of toxic solvents and surfactants make these processes less attractive. On the other hand, aqueous‐based synthesis routes (e.g., coprecipitation method) are environmentally friendly; the experimental time and reagents consumption are minimum and, most important, can allow a fine‐tuning of crystal size.

Although coercivity is mainly governed by the magnetocrystalline anisotropy energy, contribution from surface anisotropy becomes important, particularly on the nanoscale. Additionally, the strain anisotropy and shape anisotropy as well as the ferrite composition will also contribute to the magnetic anisotropy and superexchange interaction energies.

Based on the above considerations, the present chapter addresses the experimental optimiza‐ tion of the synthesis parameters leading to the precise control of the coercivity of cobalt ferrite nanocrystals. In particular, the systematic study on composition, size, and cation distribution allowed the determination of the experimental limits of the single and multidomain regions as a function of the ferrite crystal size.

## **2. Theoretical background**

#### **2.1. Ferrites**

The spinel structure derives from the mineral MgAl2 O4 whose structure was elucidated in 1915. Analogous to it, the spinel structure in ferrites has the general formula MFe2 O4 , where M corresponds to a divalent metal (i.e. Co2+, Mn2+, Ni2+, and Zn2+). The spinel lattice [10] is composed of a close‐packed oxygen arrangement with 32 oxygen atoms forming the unit Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties http://dx.doi.org/10.5772/66842 53

**Figure 1.** The spinel structure [10].

[1, 2]. In addition, CoFe2

O4

52 Magnetic Spinels- Synthesis, Properties and Applications

ticles, which have near‐zero coercivity.

as a function of the ferrite crystal size.

The spinel structure derives from the mineral MgAl2

**2. Theoretical background**

**2.1. Ferrites**

tributing to the development of high‐density data storage devices.

and, most important, can allow a fine‐tuning of crystal size.

possesses excellent chemical stability, good mechanical hardness,

and a large positive first order crystalline anisotropy constant, making it a promising can‐ didate for magneto‐optical recording media also [3]. Control on particle size and shape, ion distribution, and/or structure could allow a fine‐tuning of the magnetic properties of ferrites [4–7]. In this regard, magnetic nanocrystals exhibit strong size‐dependent properties that may provide valuable information on estimating the scaling limits of magnetic storage while con‐

To the best of our knowledge, there is still a lack of a systematic effort to restrict the growth of single nanocrystals within the magnetic single domain region where enhancement of coerciv‐ ity could be achieved. Theoretically, the single domain region ranges between 5 and 40 nm [8]. Maximum coercivity value of around 5.3 kOe [9] has also been reported for 40 nm nanocrystals. Since coercivity is strongly dependent on particle size, any attempt to achieve higher coercivity values in cobalt ferrite must consider the development of alternative approaches in order to obtain more homogeneous crystal sizes with less or null presence of superparamagnetic par‐

It is desired to select a synthesis procedure capable of producing nanocrystals with a narrow size distribution due to the above‐mentioned direct dependence of coercivity on crystal size. Synthesis approaches such as reverse micelles and thermal decomposition meet this criterion but the excessive consumption of resources, namely, synthesis reagents and experimental time, must be minimized. The use of toxic solvents and surfactants make these processes less attractive. On the other hand, aqueous‐based synthesis routes (e.g., coprecipitation method) are environmentally friendly; the experimental time and reagents consumption are minimum

Although coercivity is mainly governed by the magnetocrystalline anisotropy energy, contribution from surface anisotropy becomes important, particularly on the nanoscale. Additionally, the strain anisotropy and shape anisotropy as well as the ferrite composition will also contribute to the magnetic anisotropy and superexchange interaction energies.

Based on the above considerations, the present chapter addresses the experimental optimiza‐ tion of the synthesis parameters leading to the precise control of the coercivity of cobalt ferrite nanocrystals. In particular, the systematic study on composition, size, and cation distribution allowed the determination of the experimental limits of the single and multidomain regions

1915. Analogous to it, the spinel structure in ferrites has the general formula MFe2

M corresponds to a divalent metal (i.e. Co2+, Mn2+, Ni2+, and Zn2+). The spinel lattice [10] is composed of a close‐packed oxygen arrangement with 32 oxygen atoms forming the unit

O4

whose structure was elucidated in

O4

, where

cell and includes two types of atomic arrangements, called A and B sites, where the cations are accommodated. The site A is tetrahedrally and the B site is octahedrally coordinated by oxygen atoms; the spinel unit cell contains 64 tetrahedral sites, only 8 being occupied, and 32 octahedral sites, with half of them occupied. More specifically, a spinel unit cell can be consid‐ ered to consist of two types of subcells (**Figure 1**) that alternate in a three‐dimensional array. The magnetic properties exhibited by this kind of structures are also influenced by the inter‐ action of cations on the A and B sites; for instance, large angles and short distances between cations would be conducive to the enhancement of the exchange coupling and hence to the corresponding magnetic properties. The angles in the spinel structure for the A‐A, B‐B, and A‐B interactions are 79.63°, 90°/125.3°, and 125.15°/154.57°, respectively, thus A‐B exchange interactions are the strongest.

#### **2.2. The cobalt ferrite**

Cubic ferrites could be classified as normal, inverse, or mixed spinels. In the case of a normal spinel, the divalent ions occupy all the tetrahedral sites, whereas the trivalent ions do the same with the octahedral sites. An example of a material with a normal spinel structure is ZnFe2 O4 . In the case of inverse spinels such as cobalt ferrite, all tetrahedral sites are occupied by the trivalent ion (Fe3+) whereas octahedral sites are equally occupied by divalent (Co2+) and trivalent ions (Fe3+) [11]. The magnetic moment = 5 µB from octahedral Fe3+ ions is antiparallel to the magnetic moment = 5 µB from the tetrahedral Fe3+ ions, thus compensating each other. Accordingly, the magnetization in cobalt ferrite is attributed to the magnetic moment = 3 µ<sup>B</sup> provided by Co2+ ions on the B‐sites.

#### **2.3. Magnetic properties and particle size**

There is a relationship between coercivity and particle size [12] that is based on the presence of magnetic domains. Magnetic particles would behave as single domain (SD) or multido‐ main (MD) depending on particle size (as seen in **Figure 2**). This SD region is subdivided into two main regions characterized by their magnetic stability and they are known as the unstable and the stable regions. The unstable region corresponds to the superparamagnetic particles (SPM). It is a size‐dependent issue where the thermal energy overcomes the anisot‐ ropy energy causing the spins rotate and randomize acting as paramagnetic (do not retain magnetization and coercivity after magnetic field removal).

As seen in Eq. (1), the critical radius below which particles behave as a single domain can be calculated by [13, 14]:

$$r\_c = \frac{9}{\mu\_0 M\_s^{\frac{1}{2}}} \tag{1}$$

**Figure 2.** Dependence of coercivity with particle diameter for cobalt ferrite.

*A* is the exchange stiffness (constant characteristic of the material related to the critical temperature for magnetic ordering), *K*u is the uniaxial anisotropy constant; *μ*<sup>0</sup> is the vacuum permeability, and *M*<sup>s</sup> the saturation magnetization. For the stable single domain region, a simple model developed by Stoner and Wohlfarth [15] assumes coherent spin rotation whereby all spins within the single‐domain particle are collinear (the magnetization is uniform) and rotate in unison. The model predicts the field strength necessary to reverse the spin orientation direction or coercivity. In this stable region, the magnetocrystalline energy gradually overcomes the thermal energy and becomes responsible for the increase in coercivity. The only way to magnetize a material is to rotate the spins, a process that involves high energies and, hence, high coercivity. Thus, SD grains are magnetically hard and have high coercivity and remanent magnetization. In the cobalt ferrite case, the limit between the single and multidomain has been established to be around 40 nm with an expected coercivity of 5.3 kOe at room temperature. For the multidomain region, domain walls are present and coercivity tends to decrease with an increase in particle size [15]. In turn, the magnetization process in a multidomain, particle is controlled by domain wall movement, which is an ener‐ getically easier process.

Based on the above considerations, a precise control on the particle size will allow a fine tun‐ ing of the magnetic properties at the nanoscale. In this regard, our modified coprecipitation method described here allows the required control in crystal size based on enhancement of the heterogeneous nucleation mechanism. Consequently, a control in nucleation and growth steps could be achieved, which are key points for crystal size control.

## **3. Methodology**

by the trivalent ion (Fe3+) whereas octahedral sites are equally occupied by divalent (Co2+) and trivalent ions (Fe3+) [11]. The magnetic moment = 5 µB from octahedral Fe3+ ions is antiparallel to the magnetic moment = 5 µB from the tetrahedral Fe3+ ions, thus compensating each other. Accordingly, the magnetization in cobalt ferrite is attributed to the magnetic moment = 3 µ<sup>B</sup>

There is a relationship between coercivity and particle size [12] that is based on the presence of magnetic domains. Magnetic particles would behave as single domain (SD) or multido‐ main (MD) depending on particle size (as seen in **Figure 2**). This SD region is subdivided into two main regions characterized by their magnetic stability and they are known as the unstable and the stable regions. The unstable region corresponds to the superparamagnetic particles (SPM). It is a size‐dependent issue where the thermal energy overcomes the anisot‐ ropy energy causing the spins rotate and randomize acting as paramagnetic (do not retain

As seen in Eq. (1), the critical radius below which particles behave as a single domain can be

\_\_1 2 \_\_\_\_\_\_\_ *μ*<sup>0</sup> *Ms*

<sup>2</sup> (1)

provided by Co2+ ions on the B‐sites.

54 Magnetic Spinels- Synthesis, Properties and Applications

calculated by [13, 14]:

**2.3. Magnetic properties and particle size**

magnetization and coercivity after magnetic field removal).

*rc* <sup>=</sup> <sup>9</sup> (*<sup>A</sup> Ku*)

**Figure 2.** Dependence of coercivity with particle diameter for cobalt ferrite.

#### **3.1. Conventional coprecipitation method**

All reagents used in the synthesis and treatment of cobalt ferrite nanocrystals were of analyti‐ cal grade and used without further purification. Ferrite nanocrystals are synthesized by the cconventional coprecipitation method. In the conventional approach, an aqueous solution containing Co (II) and Fe(III) ions was rapidly contacted with an excess of hydroxide (OH‐ ) ions. The hydrolysis reaction in the presence of an excess of OH‐ ions leads to the formation of a paramagnetic Fe‐Co hydroxide, which undergoes dehydration and atomic rearrangement conducive to a ferrite structure with no need of further annealing, according to:

$$2\text{Fe}^{(3+)} + \text{Co}^{(2+)} + 8\text{OH}^- \underset{\Delta}{\to} \text{Fe}\_2\text{Co(OH)}\_8 \underset{\Delta}{\to} \text{CoFe}\_2\text{O}\_4 + 4\text{H}\_2\text{O} \tag{2}$$

The nucleation rate is quite high at the beginning of the precipitation process whereas the excess of OH‐ ions provides a net negative surface charge to the nuclei limiting their further growth and aggregation. Under these conditions, polydispersed particles of less than 30 nm in diameter are typically produced.

The reactant solution was mechanically stirred at 500 rpm and intensively heated to acceler‐ ate the dissolution/recrystallization stages involved with the ferrite formation. The intensive heating helped to reduce the reaction time dramatically. Cobalt ferrite nanocrystals were washed out with deionized water, dried at 80°C for 24 hours and characterized.

#### **3.2. Modified coprecipitation method**

In order to enhance the magnetic properties by controlling the nucleation and growth condi‐ tions of the ferrite crystals, the conventional coprecipitation route was modified by control‐ ling the flow rate of addition of the metal ions solution to the alkaline one under intensive heating conditions. For this purpose, a microperistaltic pump with a precise control of flow rate was used.

#### **3.3. Combined acid washing and magnetically assisted size‐sensitive separation**

#### *3.3.1. Single acid washing process*

In order to improve the monodispersity of the as‐synthesized cobalt ferrite nanocrystals, they were contacted with HCl solution; it is expected that a higher solubility of the smaller par‐ ticles when compared to the bigger sized ones, would lead to a narrow size distribution and, therefore, higher coercivity values. Also, the acidic treatment could remove the "magnetically dead" surface in remaining particles. On an experimental basis, the ferrite nanocrystals pro‐ duced using the above described modified coprecipitation method were then treated with the acidic solution for1 hour.

As‐synthesized nanocrystals were first contacted with 10% v/v HCl solution for 30 minutes at a 0.1 g ferrite \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 10 mL acidicsolution ratio. At the end of this acid treatment stage, the recovered solids were dis‐ persed in water and submitted for the magnetically assisted separation stage using a commer‐ cial N38 (field strength ≥ 1.2 T) neodymium permanent magnet. The particles suspension was contacted with the magnet for 2 minutes at the end of which, settled particles were separated from the suspended ones that remained in the supernatant. The solids in this supernatant represented the first fraction of the size‐sensitive separation process. In turn, the magneti‐ cally settled particles were processed through the same water dispersion‐magnetic separation cycle for two more times. The fractions corresponding to the solids recovered from their cor‐ responding supernatants and the last sediment were submitted for structural and magnetic characterization.

#### *3.3.2. Double acid washing process*

Five grams of ferrite synthesized by the above indicated modified coprecipitation method was used in the size‐sensitive phase separation process and characterization. The ferrite to acidic solution mass/volume ratio was the same as described in the previous section. After a first acid washing and size‐sensitive separation, the settled fraction with the largest amount of particles was used as a starting material for a second size‐sensitive separation cycle (sec‐ ond settled fraction in this case). This experimental procedure will be known as combined

Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties http://dx.doi.org/10.5772/66842 57

**Figure 3.** The acid washing and magnetically assisted size‐sensitive separation.

The reactant solution was mechanically stirred at 500 rpm and intensively heated to acceler‐ ate the dissolution/recrystallization stages involved with the ferrite formation. The intensive heating helped to reduce the reaction time dramatically. Cobalt ferrite nanocrystals were

In order to enhance the magnetic properties by controlling the nucleation and growth condi‐ tions of the ferrite crystals, the conventional coprecipitation route was modified by control‐ ling the flow rate of addition of the metal ions solution to the alkaline one under intensive heating conditions. For this purpose, a microperistaltic pump with a precise control of flow

In order to improve the monodispersity of the as‐synthesized cobalt ferrite nanocrystals, they were contacted with HCl solution; it is expected that a higher solubility of the smaller par‐ ticles when compared to the bigger sized ones, would lead to a narrow size distribution and, therefore, higher coercivity values. Also, the acidic treatment could remove the "magnetically dead" surface in remaining particles. On an experimental basis, the ferrite nanocrystals pro‐ duced using the above described modified coprecipitation method were then treated with the

As‐synthesized nanocrystals were first contacted with 10% v/v HCl solution for 30 minutes

persed in water and submitted for the magnetically assisted separation stage using a commer‐ cial N38 (field strength ≥ 1.2 T) neodymium permanent magnet. The particles suspension was contacted with the magnet for 2 minutes at the end of which, settled particles were separated from the suspended ones that remained in the supernatant. The solids in this supernatant represented the first fraction of the size‐sensitive separation process. In turn, the magneti‐ cally settled particles were processed through the same water dispersion‐magnetic separation cycle for two more times. The fractions corresponding to the solids recovered from their cor‐ responding supernatants and the last sediment were submitted for structural and magnetic

Five grams of ferrite synthesized by the above indicated modified coprecipitation method was used in the size‐sensitive phase separation process and characterization. The ferrite to acidic solution mass/volume ratio was the same as described in the previous section. After a first acid washing and size‐sensitive separation, the settled fraction with the largest amount of particles was used as a starting material for a second size‐sensitive separation cycle (sec‐ ond settled fraction in this case). This experimental procedure will be known as combined

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 10 mL acidicsolution ratio. At the end of this acid treatment stage, the recovered solids were dis‐

washed out with deionized water, dried at 80°C for 24 hours and characterized.

**3.3. Combined acid washing and magnetically assisted size‐sensitive separation**

**3.2. Modified coprecipitation method**

56 Magnetic Spinels- Synthesis, Properties and Applications

*3.3.1. Single acid washing process*

acidic solution for1 hour.

0.1 g ferrite

characterization.

*3.3.2. Double acid washing process*

at a

rate was used.

acid washing and magnetically assisted size‐sensitive separation (**Figure 3**), double acid washing process.

#### **3.4. Effect of the ferrite composition: Variation of the Fe:Co mole ratio**

Cobalt ferrite nanocrystals with initial Fe:Co mole ratios of 3:1, 2:1, 1.7:1, and 1.4:1 were pro‐ duced by the conventional and the modified coprecipitation method (flow rate: 0.67 mL/min). The reaction time was kept constant at 1 hour.

#### **3.5. Inhibition of crystal growth by using surfactants or polymers**

As an attempt to determine the superparamagnetic limits in cobalt ferrite nanoparticles, oleic acid sodium salt (Na‐oleate) was used in the synthesis of cobalt ferrite in order to inhibit crys‐ tal growth. This surfactant was introduced into the same vessel with the sodium hydroxide solution and heated as in the conventional coprecipitation method although for very short reaction times (5 minutes). Prolonged reaction times favored crystal growth. In a modified route, the boiling hydroxide and surfactant solution was removed from the heating source followed by its contact with the ionic solution containing iron (III) and cobalt (II).

## **4. Results and discussion**

#### **4.1. Optimization of synthesis parameters: 23 Factorial design**

The coprecipitation method employed in the synthesis of cobalt ferrite nanocrystals allows the manipulation of synthesis parameters such as reaction time (A), control on flow rate of the addition of reactants (B), and the NaOH concentration (C). A deep understanding of those parameters will allow a control in the nucleation and growth steps, key points in size‐control approaches [8, 16, 17]. In order to increase coercivity, the superparamagnetic limit must be surpassed; this limit has been estimated at 5 nm [18].

It is important to take into account each parameter and the interactions between them in order to tune crystal size and hence, the magnetic properties. A 23 factorial design is a useful tool in the study of the synthesis parameters and its interactions. The factorial design considers a low and a high level of each parameter under study. Each level was selected based on previ‐ ous studies and taking into account the experimental limitations such as the capacity of the peristaltic pump used to control the flow rate of addition of reactants. The low and high levels for each parameter under study are summarized in **Table 1**. The levels were also coded using (‐) and (+) signs for low and high, respectively.

In addition to the ABC Design, three replicates at the center of it were used to estimate the experimental error. **Table 1** also summarizes the response variable, i.e., coercivity. A wide range of coercivity values (between 870 and 4626 Oe) was obtained. The 23 factorial design sug‐ gested that reaction time is not a significant parameter. Taking it into account, the reaction time was set to 1 hour in later experiments. Otherwise, the flow rate of addition of reactants, NaOH concentration, and the interaction between these two parameters are the most significant.

#### **4.2. Combined acid washing and magnetically assisted size‐sensitive separation**

The modified size‐controlled coprecipitation method to synthesize ferrite nanocrystals can allow a fine tuning of the average crystallite size within the single magnetic domain region.


**Table 1.** Experimental conditions for the 23 factorial design and the corresponding room temperature coercivity, Hc [19]. However, the product is still polydispersed in size [19]. Accordingly, any attempt to achieve higher coercivity values in cobalt ferrite must consider the development of an alternative approach in order to obtain more homogeneous crystal sizes with less or null presence of superparamagnetic particles. In this regard, a rapid and simple size‐sensitive phase separa‐ tion treatment based on the size‐dependence of nanoparticles solubility in an aqueous phase was developed. In the case of particles with narrow size distribution, the dissolution behavior will depend on the ferrite degree of inversion and composition [20]. However, when moder‐ ately polydispersed nanocrystals are synthesized, the selective dissolution of tiny individual crystals can be expected according to the Ostwald‐Freundlich law [21], i.e., particles with smaller diameter will be more soluble than bigger ones. This fact was taken into account to get rid of the superparamagnetic or smaller particles that do make the coercivity of the powders to decrease. The selective dissolution of superparamagnetic particles will be complemented by a magnetically assisted size‐separation stage. The separation stage consists of contacting the nanoparticles/acid solution with a magnet in order to separate the settled particles from the suspended (smaller) ones.

#### *4.2.1. Single acid washing process*

**4. Results and discussion**

58 Magnetic Spinels- Synthesis, Properties and Applications

**4.1. Optimization of synthesis parameters: 23**

surpassed; this limit has been estimated at 5 nm [18].

(‐) and (+) signs for low and high, respectively.

**Combinations A B C Design A: Reaction time** 

**Table 1.** Experimental conditions for the 23

to tune crystal size and hence, the magnetic properties. A 23

range of coercivity values (between 870 and 4626 Oe) was obtained. The 23

**(min)**

**4.2. Combined acid washing and magnetically assisted size‐sensitive separation**

 **Factorial design**

factorial design is a useful tool

factorial design sug‐

[19].

**B: Flow rate (mL/min) C: NaOH (M) Hc (Oe)**

factorial design and the corresponding room temperature coercivity, Hc

The coprecipitation method employed in the synthesis of cobalt ferrite nanocrystals allows the manipulation of synthesis parameters such as reaction time (A), control on flow rate of the addition of reactants (B), and the NaOH concentration (C). A deep understanding of those parameters will allow a control in the nucleation and growth steps, key points in size‐control approaches [8, 16, 17]. In order to increase coercivity, the superparamagnetic limit must be

It is important to take into account each parameter and the interactions between them in order

in the study of the synthesis parameters and its interactions. The factorial design considers a low and a high level of each parameter under study. Each level was selected based on previ‐ ous studies and taking into account the experimental limitations such as the capacity of the peristaltic pump used to control the flow rate of addition of reactants. The low and high levels for each parameter under study are summarized in **Table 1**. The levels were also coded using

In addition to the ABC Design, three replicates at the center of it were used to estimate the experimental error. **Table 1** also summarizes the response variable, i.e., coercivity. A wide

gested that reaction time is not a significant parameter. Taking it into account, the reaction time was set to 1 hour in later experiments. Otherwise, the flow rate of addition of reactants, NaOH concentration, and the interaction between these two parameters are the most significant.

The modified size‐controlled coprecipitation method to synthesize ferrite nanocrystals can allow a fine tuning of the average crystallite size within the single magnetic domain region.

1 ‐ ‐ ‐ 5 0.85 0.34 4518 A + ‐ ‐ 180 0.85 0.34 4626 B ‐ + ‐ 5 20 0.34 871 AB + + ‐ 180 20 0.34 870 C ‐ ‐ + 5 0.85 0.54 2877 AC + ‐ + 180 0.85 0.54 3448 BC ‐ + + 5 20 0.54 922 ABC + + + 180 20 0.54 1007 The corresponding average crystallite size varied from 16 ± 2 nm in the as‐synthesized sample to 22 ± 2 nm in the solid fraction recovered after 6 minutes of magnetic separation after treat‐ ment with 10% HCl solution. This enlargement of average crystallite size can be attributed to the preferential acidic dissolution of small nanoparticles including the superparamagnetic ones along with an efficient magnetically assisted size classification.

The full set of fractions recovered after treatment with 10% HCl solution is shown in **Figure 4**. The increment in crystal size with an increment in separation time is evident.

Transmission electron microscopy‐energy dispersive spectroscopy (TEM‐EDS) analyses were performed to measure the elemental composition and calculate the experimental Fe:Co mole ratio. TEM‐EDS of cobalt ferrite nanocrystals suggested that selective dissolution of Fe could have taken place after contacting them with the 10% v/v HCl solution. The Fe:Co mole ratio decreased from 1.81:1 in the nontreated sample down to 1.58:1 after the acidic treatment. The selective dissolution of Fe in bulk ferrite was suggested by Figueroa et al. [22]; they attrib‐ uted the drop in the Fe:Co ratio to the removal of the less crystalline surface layer of iron oxide in cobalt ferrite produced by thermal decomposition. As‐synthesized particles show agglomeration while treated particles have better dispersion. It may be a result of electrostatic

**Figure 4.** TEM images of CoFe2 O4 powders before (a) and after acidic treatment with 10% HCl followed by magnetically assisted separation at different times (b–e). The images correspond to the solids contained in the fractions collected after 2 minutes (b), 4 minutes (c), and 6 minutes (d) of magnetic separation and the sediment at the end of this stage (e).

repulsion resulting from the chemisorption of charged species, in this case, H+ , on the nano‐ crystal surfaces.

The coercivity of the as‐synthesized ferrite powders was 5.4 kOe. It increased up to 9.4 kOe after treating the powders with 10% w/w HCl. The maximum magnetization of this high coercivity sample is 58 emu/g. The "constricted loops" observed in the central part of the M‐H loops suggest a mixture of soft and hard material in the powders. In this case, the soft material corresponds to the superparamagnetic fraction. In turn, the large room temperature coercivity in these powders can be attributed to the enlargement of their average crystal size caused by the removal of the superparamagnetic fraction during the acidic treatment and the subsequent size‐sensitive magnetic separation stages. This interpretation is supported by the results provided by TEM and XRD analyses on these samples. Furthermore, the reduction in the Fe:Co atomic ratio in the size‐selected cobalt ferrite particles, suggested by TEM‐EDS analyses, could also be involved with the drastic change in coercivity. In this case, acidic treat‐ ment should have promoted the removal of a poorly crystalline and magnetically disordered surface layer of the ferrite oxide.

Mössbauer spectra for the cobalt ferrite powders without treatment showed a broadened cen‐ tral peak, attributed to the presence of superparamagnetic particles, in addition to the hyper‐ fine splitting typical of magnetically ordered iron species in the ferrite lattice. The relative abundance of the superparamagnetic portion was calculated at 19.3% while the combined three magnetically split sites accounted for 81.7% of the remainder of the cobalt ferrite. No central peak was observed in the Mössbauer spectrum for the sample recovered at the end of the magnetic separation stage, which suggest the complete removal of the superparamagnetic fraction after the acidic treatment and magnetic separation stages. The internal magnetic field for the first site, which was assigned to Fe in the tetrahedral site (FeTetra1), was 449.97 kOe with quadrupole splitting of ‐1.584 mm/s and isomer shift of 1.087 mm/s, while its relative abun‐ dance was 29.1%. The other two sites corresponded to Fe in the octahedral ferrite sites (FeOct1). The first one was characterized by the internal magnetic field of 481.13 kOe, quadrupole split‐ ting of ‐0.974 mm/s and isomer shift of 0.024 mm/s with a relative abundance of 41.8%. The second octahedral site, FeOct2, was fitted with an internal magnetic field of 391.31 kOe, quad‐ rupole splitting of ‐0.640 mm/s, isomer shift of 0.085 mm/s, and relative abundance of 29.1%. The fittings are consistent with an inverse ferrite structure whereby Fe3+ cations randomly occupied both the tetrahedral and octahedral sites [23, 24]. Based on these considerations and since an equal occupation of the tetrahedral and octahedral sites by Fe3+ cations did not take place, an incomplete inversion in synthesized cobalt ferrite nanocrystals can be considered. This partial inversion in ferrite structure can also account for the unusual coercivity value.

#### *4.2.2. The double acid washing process*

As an attempt to explore the possibility of further enhancement of the ferrite coercivity by narrowing the size distribution even more, previously acid‐washed ferrite powders were retreated by following a similar acid washing/magnetic separation cycles. Starting cobalt fer‐ rite powders were synthesized by the modified coprecipitation method at 0.81 mL/min flow rate and a NaOH concentration of 0.315 M, which corresponds to the optimum concentration determined from the experimental design. A ferrite to acidic solution ratio of 5.0 g ferrite to Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties http://dx.doi.org/10.5772/66842 61

**Figure 5.** Room temperature M‐H measurements of CoFe2 O4 powders submitted to two cycles of acid treatment and magnetically assisted separation stages.

500 mL HCl 10% v/v was used. The coercivity increased starting from 3.3 up to 9.7 kOe for the third fraction after 6 minutes of magnetically assisted settling; this increment in coercivity is around three times its initial value. Again, "constricted" hysteresis loops were observed (**Figure 5**), which are typical of a mixture of soft and hard magnetic materials [25]. In this case, this sort of "necking" in the central part of the loop can be attributed to the coexistence of superparamagnetic single‐domain cobalt ferrite nanoparticles. Fractions exhibiting larger coercivity values did not show this "necking" confirming the removal of the superparamag‐ netic fraction.

The second settled fraction (corresponding to 4 minutes of settling time) was submitted to the second cycle of our size‐sensitive phase separation process. This time, the ferrite to HCl ratio was 0.8 g ferrite to 80 mL HCl 10% v/v. The sharpening in the corresponding XRD peaks sug‐ gested an improvement in crystallinity after the second treatment cycle.

The initially 9.2 kOe achieved in the second fraction generated during the first separation cycle was increased up to 11.9 kOe. This pretty large coercivity was obtained in the third fraction produced during the second acid washing/magnetic separation cycle. This dramatic enhancement in coercivity can be attributed to the larger crystal size in the corresponding fractions and a more efficient removal of any remaining superparamagnetic particles.

#### **4.3. Effect of the ferrite composition**

repulsion resulting from the chemisorption of charged species, in this case, H+

The coercivity of the as‐synthesized ferrite powders was 5.4 kOe. It increased up to 9.4 kOe after treating the powders with 10% w/w HCl. The maximum magnetization of this high coercivity sample is 58 emu/g. The "constricted loops" observed in the central part of the M‐H loops suggest a mixture of soft and hard material in the powders. In this case, the soft material corresponds to the superparamagnetic fraction. In turn, the large room temperature coercivity in these powders can be attributed to the enlargement of their average crystal size caused by the removal of the superparamagnetic fraction during the acidic treatment and the subsequent size‐sensitive magnetic separation stages. This interpretation is supported by the results provided by TEM and XRD analyses on these samples. Furthermore, the reduction in the Fe:Co atomic ratio in the size‐selected cobalt ferrite particles, suggested by TEM‐EDS analyses, could also be involved with the drastic change in coercivity. In this case, acidic treat‐ ment should have promoted the removal of a poorly crystalline and magnetically disordered

Mössbauer spectra for the cobalt ferrite powders without treatment showed a broadened cen‐ tral peak, attributed to the presence of superparamagnetic particles, in addition to the hyper‐ fine splitting typical of magnetically ordered iron species in the ferrite lattice. The relative abundance of the superparamagnetic portion was calculated at 19.3% while the combined three magnetically split sites accounted for 81.7% of the remainder of the cobalt ferrite. No central peak was observed in the Mössbauer spectrum for the sample recovered at the end of the magnetic separation stage, which suggest the complete removal of the superparamagnetic fraction after the acidic treatment and magnetic separation stages. The internal magnetic field for the first site, which was assigned to Fe in the tetrahedral site (FeTetra1), was 449.97 kOe with quadrupole splitting of ‐1.584 mm/s and isomer shift of 1.087 mm/s, while its relative abun‐ dance was 29.1%. The other two sites corresponded to Fe in the octahedral ferrite sites (FeOct1). The first one was characterized by the internal magnetic field of 481.13 kOe, quadrupole split‐ ting of ‐0.974 mm/s and isomer shift of 0.024 mm/s with a relative abundance of 41.8%. The second octahedral site, FeOct2, was fitted with an internal magnetic field of 391.31 kOe, quad‐ rupole splitting of ‐0.640 mm/s, isomer shift of 0.085 mm/s, and relative abundance of 29.1%. The fittings are consistent with an inverse ferrite structure whereby Fe3+ cations randomly occupied both the tetrahedral and octahedral sites [23, 24]. Based on these considerations and since an equal occupation of the tetrahedral and octahedral sites by Fe3+ cations did not take place, an incomplete inversion in synthesized cobalt ferrite nanocrystals can be considered. This partial inversion in ferrite structure can also account for the unusual coercivity value.

As an attempt to explore the possibility of further enhancement of the ferrite coercivity by narrowing the size distribution even more, previously acid‐washed ferrite powders were retreated by following a similar acid washing/magnetic separation cycles. Starting cobalt fer‐ rite powders were synthesized by the modified coprecipitation method at 0.81 mL/min flow rate and a NaOH concentration of 0.315 M, which corresponds to the optimum concentration determined from the experimental design. A ferrite to acidic solution ratio of 5.0 g ferrite to

crystal surfaces.

60 Magnetic Spinels- Synthesis, Properties and Applications

surface layer of the ferrite oxide.

*4.2.2. The double acid washing process*

, on the nano‐

#### *4.3.1. Variation of the Fe:Co mole ratio*

The magnetic properties of cobalt ferrite depend on diverse factors such as crystal size [26], morphology [27], chemical composition [28, 29], and/or cation distribution [30]. The formation of nonstoichiometric cobalt ferrite nanocrystals will lead to atomic rearrangement between A‐ and B‐sites and/or creation of vacancies [31]. Consequently, a change in magnetic proper‐ ties will take place. On this basis, cobalt ferrite nanocrystals with different initial Fe:Co mole ratios (3:1, 2:1, 1.7:1, and 1.4:1) were synthesized by the traditional and modified coprecipita‐ tion routes. For this latter case, the flow rate at which the reactants were contacted was set to 0.67 mL/min. The reaction time was 1 hour in all our experiments. In addition to crystal growth, cation distribution, internal magnetic field, morphology, and chemical composition, the presence of a secondary phase (α‐Fe<sup>2</sup> O3 ) by X‐ray diffraction, see **Figure 6**, were identified responsible for the observed wide range of magnetic properties.

Average crystallite sizes in produced ferrite powders ranging between 11–12 nm and 15–19 nm were obtained using the conventional and the modified coprecipitation methods respec‐ tively. Excess of iron, (3:1 Fe:Co mole ratio), caused the formation of a secondary phase that was identified as hematite, α‐Fe<sup>2</sup> O3 . In turn, less crystalline powders were obtained when the Fe:Co mole ratio was decreased from 3:1 to 1.4:1 [32].

**Table 2** summarizes the nominal and experimental (measured) Fe:Co mole ratios in synthe‐ sized ferrite nanocrystals. The experimental Fe:Co mole ratios represent an average from mea‐ surements at five different regions in the sample using energy dispersive X‐ray spectroscopy. For all cases, approximately 78% of the Fe present in starting solutions was incorporated into the ferrite structure.

Average crystallite sizes of cobalt ferrite synthesized without control on the flow rate were quite similar (11–12 nm). Thus, any change in magnetic properties could be attributed to the

**Figure 6.** XRD patterns of cobalt ferrite nanocrystals synthesized without control on flow rate at different Fe:Co mole ratios. The peak with the asterisk corresponds to hematite, α‐Fe<sup>2</sup> O3 [32].

Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties http://dx.doi.org/10.5772/66842 63


**Table 2.** Summary of Fe:Co mole ratios of cobalt ferrite synthesized with and without control on flow rate [32].

of nonstoichiometric cobalt ferrite nanocrystals will lead to atomic rearrangement between A‐ and B‐sites and/or creation of vacancies [31]. Consequently, a change in magnetic proper‐ ties will take place. On this basis, cobalt ferrite nanocrystals with different initial Fe:Co mole ratios (3:1, 2:1, 1.7:1, and 1.4:1) were synthesized by the traditional and modified coprecipita‐ tion routes. For this latter case, the flow rate at which the reactants were contacted was set to 0.67 mL/min. The reaction time was 1 hour in all our experiments. In addition to crystal growth, cation distribution, internal magnetic field, morphology, and chemical composition,

Average crystallite sizes in produced ferrite powders ranging between 11–12 nm and 15–19 nm were obtained using the conventional and the modified coprecipitation methods respec‐ tively. Excess of iron, (3:1 Fe:Co mole ratio), caused the formation of a secondary phase that

**Table 2** summarizes the nominal and experimental (measured) Fe:Co mole ratios in synthe‐ sized ferrite nanocrystals. The experimental Fe:Co mole ratios represent an average from mea‐ surements at five different regions in the sample using energy dispersive X‐ray spectroscopy. For all cases, approximately 78% of the Fe present in starting solutions was incorporated into

Average crystallite sizes of cobalt ferrite synthesized without control on the flow rate were quite similar (11–12 nm). Thus, any change in magnetic properties could be attributed to the

**Figure 6.** XRD patterns of cobalt ferrite nanocrystals synthesized without control on flow rate at different Fe:Co mole

O3 [32].

) by X‐ray diffraction, see **Figure 6**, were identified

. In turn, less crystalline powders were obtained when the

O3

responsible for the observed wide range of magnetic properties.

O3

Fe:Co mole ratio was decreased from 3:1 to 1.4:1 [32].

ratios. The peak with the asterisk corresponds to hematite, α‐Fe<sup>2</sup>

the presence of a secondary phase (α‐Fe<sup>2</sup>

62 Magnetic Spinels- Synthesis, Properties and Applications

was identified as hematite, α‐Fe<sup>2</sup>

the ferrite structure.

net effect of chemical composition. For this set of samples, the highest coercivity value (548 Oe) was obtained for the sample synthesized at a 3:1 Fe:Co mole ratio. This sample is a mixture of cobalt ferrite and hematite, so surface anisotropy and interparticle interactions that contribute to the net anisotropy [33] are different when compared to pure cobalt ferrite.

Since the flow rate was kept constant in all the experiments reported in this section (0.67 mL/ min), any change in the average crystallite size of the ferrite could be attributed to the varia‐ tion of the chemical composition of the powders. For instance, the sample synthesized at a starting Fe:Co mole ratio of 1.7:1 yielded an average crystallite size of 18 nm, whereas it was 19 nm for the sample produced with Fe:Co mole ratio of 3:1. The corresponding coercivity magnitudes were 4412 Oe and 4249 Oe, respectively. As reported in our earlier studies, the nonstoichiometry of cobalt ferrite powders (Fe/Co < 2) would influence the coercivity due to the distribution of Fe ions within A‐ and B‐sites in the spinel structure [26].

Mössbauer spectroscopy measurements help to study the Fe cationic environment and how their distribution between octahedral and tetrahedral sites changes in addition to the internal magnetic field. This technique can also elucidate whether surface effects are present. These results are presented below.

## *4.3.2. Influence of the Fe:Co mole ratio on the ferrite magnetic structure: Mössbauer spectroscopy measurements*

The fitting of the spectra corresponding to the ferrite synthesized at a Fe:Co mole ratio of 2 and 1.7 were carried out with the hyperfine field distribution (HFD) model, considering four sites. Samples were synthesized at a flow rate of 0.67 mL/min. The doublet peaks in **Figure 7** at the central part of the Mössbauer spectra is attributed to the phenomenon of superpara‐ magnetic relaxation, arising from particles with single domain attributes. Given the broad aspects of this component, we can confirm some distribution of particle size within this super‐ paramagnetic fraction, with some of them having their blocking temperature close to 298 K (room temperature conditions).

The most remarkable discrepancy between the two spectra of **Figure 7** relies on both the relative abundances in each subsites, and the internal magnetic field of the octahedral and tetrahedral cationic positions. Based on the features of each Mössbauer spectrum, the super‐ paramagnetic components in each sample was estimated to be 17% of the total material

**Figure 7.** Fitted Mössbauer spectra corresponding to cobalt ferrite nanocrystals synthesized at 0.67 mL/min and nominal Fe:Co mole ratios of 2:1 (a) and 1.7:1 (b). The green, blue, cyan, and magenta fittings correspond to sites 1, 2, 3, and 4, respectively [32].

suggesting that the synthesis process did not affect the particle distribution. The corresponding internal magnetic field of the octahedral and tetrahedral Fe is found to be very similar in both samples. A noticeable difference between both spectra arises from the fourth component. The fourth component of the spectrum "b" (Fe:Co 1.7:1), accounted for 10% of the sample, which was very high when compared to the component but for sample "a" (Fe:Co 2:1) where it represented 0.9% of the sample. The surface cations (site‐4) exhibit smaller internal magnetic field and broadened absorption lines indicating a more disordered state at the surface (spin canting) being responsible for the lack of magnetization saturation and higher coercivity value due to surface anisotropy [34].

#### *4.3.3. Effect of the flow rate on the ferrite magnetic structure: Mössbauer spectroscopy measurements*

Mössbauer spectra of cobalt ferrite nanocrystals produced at a 1.4:1 Fe:Co mole ratio with, and without control of the flow rate, were analyzed. Site‐1 is attributed to Fe cations in the octahedral position of the spinel structure, while site‐2 corresponds to the Fe located in the tetrahedral position.

Regarding the analysis of the spectrum corresponding to the sample synthesized without control of flow rate, the internal magnetic field values corresponding to the Fe‐sites were higher than those for the powders synthesized at 0.67 mL/min. Furthermore, the relative abundance of sites‐1 and 2 in the samples synthesized without control of flow rate (42.32 and 41.26%, respectively) followed an antagonistic trend when compared to the same parameters for the samples produced at 0.67 mL/min (36.80 and 42.75%); i.e., there are more Fe cations in site‐1 when the powders are synthesized with no control of the flow rate. In other words, the control of the flow rate of the addition of reactants during the synthesis of the cobalt ferrite nanocrystals affects the average crystallite size and the distribution of Fe ions within A and B sites in the spinel structure. This unexpected change in the atomic distribution should also be involved with the magnetic properties observed in those high‐ coercivity samples.

## **4.4. Inhibition of crystal growth: use of oleic acid sodium salt during the cobalt ferrite crystal formation**

The use of surfactants or polymers comes from the necessity to produce extremely small par‐ ticles which could help us to determine the actual superparamagnetic limit in the cobalt fer‐ rite. Oleic acid sodium salt (Na‐oleate) was used to inhibit crystal growth, because of expected surface interaction between polar groups and nanoparticles, as well as to prevent nanopar‐ ticle aggregation through strong steric interactions promoted by the adsorption of the surfac‐ tant ("capping ligand"). This surfactant has long chains that confer a physical impediment preventing particle growth and/or aggregation.

As discussed above, a reaction time as short as 5 minutes was conducive to the formation of ferrite nanocrystals in the 10–11 nm range, which suggested a very fast formation and growth of earlier ferrite nuclei. Therefore, as an attempt to avoid crystal growth, the cobalt ferrite powder was removed right after the metal solution contacted the boiling NaOH/Na‐oleate solution.

The corresponding average crystallite sizes were estimated at 4 and 9 nm when the synthesis took place with and without addition of the surfactant, respectively. This result suggests that the ferrite formation was interrupted in the nucleation stage with practically no time for the nuclei to grow any further.

suggesting that the synthesis process did not affect the particle distribution. The corresponding internal magnetic field of the octahedral and tetrahedral Fe is found to be very similar in both samples. A noticeable difference between both spectra arises from the fourth component. The fourth component of the spectrum "b" (Fe:Co 1.7:1), accounted for 10% of the sample, which was very high when compared to the component but for sample "a" (Fe:Co 2:1) where it represented 0.9% of the sample. The surface cations (site‐4) exhibit smaller internal magnetic field and broadened absorption lines indicating a more disordered state at the surface (spin canting) being responsible for the lack of magnetization saturation and higher coercivity value

**Figure 7.** Fitted Mössbauer spectra corresponding to cobalt ferrite nanocrystals synthesized at 0.67 mL/min and nominal Fe:Co mole ratios of 2:1 (a) and 1.7:1 (b). The green, blue, cyan, and magenta fittings correspond to sites 1, 2, 3, and 4,

*4.3.3. Effect of the flow rate on the ferrite magnetic structure: Mössbauer spectroscopy measurements* Mössbauer spectra of cobalt ferrite nanocrystals produced at a 1.4:1 Fe:Co mole ratio with, and without control of the flow rate, were analyzed. Site‐1 is attributed to Fe cations in the octahedral position of the spinel structure, while site‐2 corresponds to the Fe located in the

Regarding the analysis of the spectrum corresponding to the sample synthesized without control of flow rate, the internal magnetic field values corresponding to the Fe‐sites were higher than those for the powders synthesized at 0.67 mL/min. Furthermore, the relative abundance of sites‐1 and 2 in the samples synthesized without control of flow rate (42.32 and 41.26%, respectively) followed an antagonistic trend when compared to the same parameters for the samples produced at 0.67 mL/min (36.80 and 42.75%); i.e., there are more Fe cations in site‐1 when the powders are synthesized with no control of the flow rate. In

due to surface anisotropy [34].

64 Magnetic Spinels- Synthesis, Properties and Applications

tetrahedral position.

respectively [32].

The extremely small crystal size was also confirmed by TEM analyses. TEM images from **Figure 8** confirmed the formation of nanocrystals with a diameter around 4 nm.

**Figure 8.** TEM images of cobalt ferrite nanocrystals synthesized in presence of 0.011 M Na‐oleate.

**Figure 9.** Mössbauer spectrum of cobalt ferrite synthesized in presence of Na‐oleate.

The 9 nm nanoparticles exhibited a coercivity of 189 Oe whereas the 4 nm ones reported coer‐ civity as low as 3 Oe. The latter value falls within the experimental error of the instrument; i.e., these particles practically did not show any coercivity.

The presence of the quadrupole splitting in the Mössbauer spectrum of the 4 nm cobalt fer‐ rite nanocrystals (**Figure 9**) may suggest the superparamagnetic nature of the synthesized crystals. Electric quadrupole interaction occurs if at least one of the nuclear states involved possesses a quadrupole moment (which is the case for nuclear states with the spin *I* > 1/2) and if the electric field at the nucleus is inhomogeneous. In the case of <sup>57</sup>Fe, the first excited state (14.4 keV state) has a spin *I* = 3/2 and therefore also an electric quadrupole moment. It can be visualized by the precession of the quadrupole moment vector about the field gradient axis sets in and splits the degenerate *I* = 3/2 level into two substates with mag‐ netic spin quantum numbers *mI* = ± 3/2 and ± 1/2. The energy difference between the two substates (ΔEQ) is observed in the spectrum as the separation between the two resonance lines [35]. On this basis, the superparamagnetic nature of the 4 nm nanocrystals can be proposed.

#### **4.5. ZFC/FC measurements as a function of ferrite crystal size**

In order to study the magnetic properties as a function of crystal size in more detail, cobalt ferrite nanocrystals with different crystal sizes in the 10–23 nm range were selected from previous sections. The magnetization curves of the superparamagnetic sample (4 nm in aver‐ age size) were investigated in the zero‐field‐cooled/field‐cooled (ZFC/FC) protocols using a Quantum Design SQUID unit, under an external magnetic field of 100 Oe and in the tempera‐ ture range from 300 to 2 K. The powders were fixed in a solid matrix of poly(styrene‐divinyl‐ benzene) as described by Calero‐Diaz del Castillo and Rinaldi [36]. The ZFC/FC profile for the

Optimizing Processing Conditions to Produce Cobalt Ferrite Nanoparticles of Desired Size and Magnetic Properties http://dx.doi.org/10.5772/66842 67

**Figure 10.** XRD patterns of cobalt ferrite with different average crystallite sizes.

The 9 nm nanoparticles exhibited a coercivity of 189 Oe whereas the 4 nm ones reported coer‐ civity as low as 3 Oe. The latter value falls within the experimental error of the instrument; i.e.,

The presence of the quadrupole splitting in the Mössbauer spectrum of the 4 nm cobalt fer‐ rite nanocrystals (**Figure 9**) may suggest the superparamagnetic nature of the synthesized crystals. Electric quadrupole interaction occurs if at least one of the nuclear states involved possesses a quadrupole moment (which is the case for nuclear states with the spin *I* > 1/2) and if the electric field at the nucleus is inhomogeneous. In the case of <sup>57</sup>Fe, the first excited state (14.4 keV state) has a spin *I* = 3/2 and therefore also an electric quadrupole moment. It can be visualized by the precession of the quadrupole moment vector about the field gradient axis sets in and splits the degenerate *I* = 3/2 level into two substates with mag‐ netic spin quantum numbers *mI* = ± 3/2 and ± 1/2. The energy difference between the two substates (ΔEQ) is observed in the spectrum as the separation between the two resonance lines [35]. On this basis, the superparamagnetic nature of the 4 nm nanocrystals can be

In order to study the magnetic properties as a function of crystal size in more detail, cobalt ferrite nanocrystals with different crystal sizes in the 10–23 nm range were selected from previous sections. The magnetization curves of the superparamagnetic sample (4 nm in aver‐ age size) were investigated in the zero‐field‐cooled/field‐cooled (ZFC/FC) protocols using a Quantum Design SQUID unit, under an external magnetic field of 100 Oe and in the tempera‐ ture range from 300 to 2 K. The powders were fixed in a solid matrix of poly(styrene‐divinyl‐ benzene) as described by Calero‐Diaz del Castillo and Rinaldi [36]. The ZFC/FC profile for the

these particles practically did not show any coercivity.

66 Magnetic Spinels- Synthesis, Properties and Applications

**Figure 9.** Mössbauer spectrum of cobalt ferrite synthesized in presence of Na‐oleate.

**4.5. ZFC/FC measurements as a function of ferrite crystal size**

proposed.

4 nm crystals indicated they were blocked below 115 K, i.e., these nanoparticles would behave ferromagnetically below that blocking temperature [17]. As evident in **Figure 10**, the sharpen‐ ing and intensity of the XRD peaks of cobalt ferrite powders were enhanced in those powders exhibiting larger average crystallite sizes.

Finally, the M‐H loops of the different samples were also measured in the SQUID unit at 2K and 300K. As the M‐H loop of **Figure 11** shows, the coercivity of the 23 nm samples

**Figure 11.** M‐H loops at 2 K of cobalt ferrite powders with different average crystallite sizes.

**Figure 12.** M‐H loops at 300 K of cobalt ferrite powders with different average crystallite size.

at 2 K reached a value as high as 30 kOe. To our knowledge, this is the highest coercivity value reported for cobalt ferrite nanocrystals at 2 K. Sun et al. [37] and Meron et al. [38] reported 20 and 15 kOe, respectively, for highly monodisperse cobalt ferrite, measured at 10 K. The maximum magnetization also increases at low temperatures due to the absence of thermal energy responsible for spin rotation and randomization. The M‐H loops at 2 and 300 K are shown in **Figures 11** and **12**. An increase in coercivity as a function of crystal size was observed as expected. Coercivity values ranged between 17–30 kOe at 2 K and 0.2–12.9 kOe at 300 K.

**Figure 13.** Variation of coercivity with particle size in cobalt ferrite particles synthesized in the present study.

#### **4.6. Particle size dependence of coercivity revisited**

In the above, the particle size dependence of the coercivity in cobalt ferrite nanocrystals has been demonstrated and discussed. Different approaches such as experimental design, size‐sen‐ sitive phase separation method, and surfactants discussed above were the essential tools to obtain particles with a wide range of sizes. They helped us to achieve the main objective of this research: to determine the limits of the single‐domain and multidomain regions as a function of the composition, structure, and crystal size in ferrimagnetic ferrites. It is important to notice that the theoretical coercivity values have been greatly surpassed. An experimental plot of coercivity versus particle size summarizes some of the values obtained and it is shown in **Figure 13**. Data corresponding to 150 and 200 nm were obtained using a postsynthesis thermal treatment [39].

## **5. Conclusions**

at 2 K reached a value as high as 30 kOe. To our knowledge, this is the highest coercivity value reported for cobalt ferrite nanocrystals at 2 K. Sun et al. [37] and Meron et al. [38] reported 20 and 15 kOe, respectively, for highly monodisperse cobalt ferrite, measured at 10 K. The maximum magnetization also increases at low temperatures due to the absence of thermal energy responsible for spin rotation and randomization. The M‐H loops at 2 and 300 K are shown in **Figures 11** and **12**. An increase in coercivity as a function of crystal size was observed as expected. Coercivity values ranged between 17–30 kOe at 2 K and

**Figure 13.** Variation of coercivity with particle size in cobalt ferrite particles synthesized in the present study.

**Figure 12.** M‐H loops at 300 K of cobalt ferrite powders with different average crystallite size.

0.2–12.9 kOe at 300 K.

68 Magnetic Spinels- Synthesis, Properties and Applications

Tuning the magnetic properties of cobalt ferrite at the nanoscale was achieved by controlling crystal size, chemical composition, and cation distribution. Average crystallite sizes ranging between 4 and 23 nm were successfully synthesized. The corresponding room temperature coercivity values varied between 3 Oe and 11.9 kOe. The 23 nm nanocrystals exhibited coer‐ civity as high as 11.9 kOe, which is reported here for the first time. The corresponding magne‐ tization and squareness ratio were 48 emu/g and 0.72, respectively.

The suitable combination of flow rate‐controlled synthesis complemented by acid washing and magnetically assisted size‐sensitive separation processes provided favorable conditions for the enhancement of nanoparticles monodispersity and tailoring of the corresponding magnetic properties. Smaller and more soluble nanocrystals that contribute negatively to coercivity (superparamagnetic particles) were selectively dissolved during the acid washing step. This selective dissolution of the superparamagnetic fraction took place in addition to the removal of the poorly crystalline layer on the surface of the nanocrystals.

The effect of the nominal Fe:Co mole ratio in starting solutions on the structural and magnetic properties of the nanocrystals was also investigated. Findings revealed that the cationic dis‐ tribution in the ferrite was dependent on the nominal Fe:Co mole ratio whereas the contribu‐ tion of the surface cations, and hence the surface anisotropy, became remarkable under flow rate‐controlled synthesis conditions. Accordingly, the colossal coercivity attained in nanomet‐ ric cobalt ferrite crystals became possible not exclusively by control of crystal size, but also through the promotion of the mentioned effects viz. surface anisotropy and atomic rearrange‐ ments of Fe species within the ferrite lattice.

About 4 nm cobalt ferrite crystals were produced using Na‐oleate as a surfactant that inhib‐ ited crystal growth. The superparamagnetic behavior of these nanocrystals was confirmed by M‐H measurements and Mössbauer spectroscopy techniques.

The temperature dependence of the magnetic properties of cobalt ferrite was studied as a function of crystal size. The 23 nm sample (room temperature coercivity of 11.9 kOe) reported a 2 K coercivity as high as 30 kOe.

## **Acknowledgements**

This material is based upon work supported by The National Science Foundation under Grant No. HRD 13455156 (CREST II program).

## **Author details**

Oscar Perales‐Pérez1 \* and Yarilyn Cedeño‐Mattei2, 3

\*Address all correspondence to: oscarjuan.perales@upr.edu

1 Department of Engineering Sciences and Materials, University of Puerto Rico, Mayagüez, Puerto Rico

2 Department of Biology, Chemistry, and Environmental Sciences, Interamerican University of Puerto Rico, San Germán, Puerto Rico

3 Department of Chemistry and Physics, University of Puerto Rico, Ponce, Puerto Rico

## **References**


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**Acknowledgements**

**Author details**

Oscar Perales‐Pérez1

Puerto Rico

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No. HRD 13455156 (CREST II program).

70 Magnetic Spinels- Synthesis, Properties and Applications

of Puerto Rico, San Germán, Puerto Rico

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1 Department of Engineering Sciences and Materials, University of Puerto Rico, Mayagüez,

2 Department of Biology, Chemistry, and Environmental Sciences, Interamerican University

[2] Arulmurugan R, Vaidyanathan G, Sendhilnathan S, Jeyadevan BJ. Magn. Magn. Mater.

[3] Terzzoli MC, Duhalde S, Jacobo S, Steren L, Moina CJ. Alloys Compd. 2004;**369**:209–212.

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[11] Callister Jr. W. Materials Science and Engineering an Introduction. 6th ed. New Jersey:

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3 Department of Chemistry and Physics, University of Puerto Rico, Ponce, Puerto Rico

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[6] Khedr MH, Omar AA, Abdel‐Moaty SA. Colloids Surf. A. 2006;**281**:8–14.

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\* and Yarilyn Cedeño‐Mattei2, 3

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**Electronic and Magnetic Properties**

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[39] Cedeño‐Mattei Y, PhD Dissertation, University of Puerto Rico: Mayaguez Campus, 2011.

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72 Magnetic Spinels- Synthesis, Properties and Applications

#### **Nature of Magnetic Ordering in Cobalt‐Based Spinels Nature of Magnetic Ordering in Cobalt**‐**Based Spinels**

Subhash Thota and Sobhit Singh Subhash Thota and Sobhit Singh

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65913

#### **Abstract**

In this chapter, the nature of magnetic ordering in cobalt‐based spinels Co3O4, Co2SnO4, Co2TiO4, and Co2MnO4 is reviewed, and some new results that have not been reported before are presented. A systematic comparative analysis of various results available in the literature is presented with a focus on how occupation of the different cations on the A‐ and B‐sites and their electronic states affect the magnetic properties. This chapter specifically focuses on the issues related to (i) surface and finite‐size effects in pure Co3O4, (ii) magnetic‐compensation effect, (iii) co‐existence of ferrimagnetism and spin‐glass‐like ordering, (iv) giant coercivity (*H*C) and exchange bias (*H*EB) below the glassy state, and (v) sign‐reversal behavior of *H*EB across the ferri/ antiferromagnetic Néel temperature (*T*N) in Co2TiO4 and Co2SnO4. Finally, some results on the low‐temperature anomalous magnetic behavior of Co2MnO4 spinels are presented.

**Keywords:** ferrimagnetic materials, Néel temperature, spin‐glass, exchange bias

## **1. Introduction**

The atomic arrangement of the spinel compounds is interpreted as a pseudo‐close‐packed arrangement of the oxygen anions with divalent cations occupying tetrahedral A‐sites and trivalent cations residing at the octahedral B‐sites of the cubic unit cell of space group Fd‐3m(227). A spinel with the configuration (A2+) [B2 3+] O4 is termed as "normal spinel" whereas the other possible configuration (B3+) [A2+B3+] O4 is called "inverse spinel." The continuum of possible atomic distribution between these two extremes is quantified by a parameter denoted as *x* (inversion parameter), which describes the fraction of "B" cations on tetrahedral sites. Thus, *x* = 0 for a normal spinel, 2/3 for a spinel with entirely arbitrary configuration, and 1 for a fully inverse spinel. Among many varieties of spinel compounds,

ferrites and cobaltites are widely used in the high‐frequency electronic circuit components such as transformers, noise filters, and magnetic recording heads [1, 2]. The key property of these spinels is that at high frequencies (>1 MHz), their dielectric permittivity (*ε*) and magnetic permeability (*μ*) are much higher than those of metals with low loss‐factor (tan*δ*). These properties make them very advantageous for the development of magnetic components used in the power electronics industry. Also, the nanostructures of these spinels continue to receive large attention because of their potential applications in solid‐oxide fuel cells, Li‐ion batteries, thermistors, magnetic recording, microwave, and RF devices [1, 2].

In this review, we mainly focus on the nature of magnetic ordering of several insulating cobalt spinels of type Co2MO4 (where "M" is the tetravalent or trivalent metal cation such as Sn, Ti, Mn, Si, etc.) which are not yet well studied in literature. This review will primarily illustrate how the magnetic ordering changes when we substitute the above‐listed metal cations at the tetrahedral B‐sites. It is well known that the dilution of magnetic elements significantly disrupts the long‐range magnetic ordering and leads to more exotic properties like magnetic frustration, polarity reversal exchange bias, and reentrant spin‐glass state near the magnetic‐ phase transition [3, 4]. The dilution essentially alters the super‐exchange interactions of *J*AB, *J*BB, and *J*AA between the magnetic ions, which is the main source of anomalous magnetic behavior. In this review, we first start with the simplest case of antiferromagnetic (AFM) normal‐spinel Co3O4 with configuration (Co2+)[Co2 3+]O4 and discuss the role of surface and finite‐size effects on antiferromagnetic (AFM) ordering. In the second section, we focus on the coexistence of ferrimagnetism and low‐temperature spin‐glass behavior of cobalt orthostannate (Co2SnO4) and cobalt orthotitanate (Co2TiO4). A detailed comparative analysis of some recent experi‐ mental results dealing with the temperature and frequency dependence of ac‐magnetic susceptibility is presented. In the subsequent section, some unusual magnetic properties of Co2MnO4 are discussed.

## **2. Magnetic properties of bulk versus nanocrystalline Co3O4**

Cobalt forms two binary compounds with oxygen: CoO and Co3O4. While CoO has face‐ centered cubic (NaCl‐type) structure, Co3O4 shows a normal‐spinel structure with a cubic close packed arrangement of oxygen ions and Co2+ and Co3+ ions occupying the tetrahedral "8a" and the octahedral "16d" sites, respectively [5]. The magnetic properties of Co3O4 were first investigated over 58 years ago; however, its magnetic behavior under reduced dimensions still attracted immense scientific interest mainly because of its distinctly different magnetic ordering under nanoscale as compared to its bulk counterpart [6]. Co3O4 can be synthesized in various nanostructural forms such as nanorods, nanosheets, and ordered nanoflowers with ultrafine porosity [7–10]. Such engineered nanostructures play vital roles as catalysts, gas sensors, magneto‐electronics, electrochromic devices, and high‐temperature solar selective absorbers [11–18]. At first glance, the normal‐spinel structure of Co3O4 may look similar to that of Fe3O4 (inverse spinel) but Co3O4 exhibits strikingly different magnetic ordering as compared to Fe3O4. In particular, Co3O4 does not exhibit ferrimagnetic ordering of the type observed in Fe3O4 because Co3+ ions on the octahedral B‐sites are in the low spin *S* = 0 state [5]. Instead, it exhibits antiferromagnetic ordering with each Co2+ ion at the A‐site having four neighboring Co2+ ions of opposite spins (with an effective magnetic moment of *μ*eff ∼ 4.14 μB) [5]. Earlier studies by Roth reported that below the Néel temperature *T*<sup>N</sup> ∼ 40 K, Co3O4 becomes antiferromagnetic in which the uncorrelated spins of the 8Co2+ (in 8(a), F.C. +000, 1 4 1 4 1 4) cations in the paramagnetic state (space group O7 h—Fd‐3m) are split in the antiferromagnetic state (space group T2 d—F43m) into the two sublattices with oppositely directed spins of 4Co2+ ↑ (4(a), +000) and 4Co2+ ↓ (4(c) <sup>1</sup> 4 1 4 1 4) [5–7]. For *T* < *T*N, the neutron diffraction studies did not show any evidence of a structural phase transition.

ferrites and cobaltites are widely used in the high‐frequency electronic circuit components such as transformers, noise filters, and magnetic recording heads [1, 2]. The key property of these spinels is that at high frequencies (>1 MHz), their dielectric permittivity (*ε*) and magnetic permeability (*μ*) are much higher than those of metals with low loss‐factor (tan*δ*). These properties make them very advantageous for the development of magnetic components used in the power electronics industry. Also, the nanostructures of these spinels continue to receive large attention because of their potential applications in solid‐oxide fuel cells, Li‐ion batteries,

In this review, we mainly focus on the nature of magnetic ordering of several insulating cobalt spinels of type Co2MO4 (where "M" is the tetravalent or trivalent metal cation such as Sn, Ti, Mn, Si, etc.) which are not yet well studied in literature. This review will primarily illustrate how the magnetic ordering changes when we substitute the above‐listed metal cations at the tetrahedral B‐sites. It is well known that the dilution of magnetic elements significantly disrupts the long‐range magnetic ordering and leads to more exotic properties like magnetic frustration, polarity reversal exchange bias, and reentrant spin‐glass state near the magnetic‐ phase transition [3, 4]. The dilution essentially alters the super‐exchange interactions of *J*AB, *J*BB, and *J*AA between the magnetic ions, which is the main source of anomalous magnetic behavior. In this review, we first start with the simplest case of antiferromagnetic (AFM) normal‐spinel

on antiferromagnetic (AFM) ordering. In the second section, we focus on the coexistence of ferrimagnetism and low‐temperature spin‐glass behavior of cobalt orthostannate (Co2SnO4) and cobalt orthotitanate (Co2TiO4). A detailed comparative analysis of some recent experi‐ mental results dealing with the temperature and frequency dependence of ac‐magnetic susceptibility is presented. In the subsequent section, some unusual magnetic properties of

Cobalt forms two binary compounds with oxygen: CoO and Co3O4. While CoO has face‐ centered cubic (NaCl‐type) structure, Co3O4 shows a normal‐spinel structure with a cubic close packed arrangement of oxygen ions and Co2+ and Co3+ ions occupying the tetrahedral "8a" and the octahedral "16d" sites, respectively [5]. The magnetic properties of Co3O4 were first investigated over 58 years ago; however, its magnetic behavior under reduced dimensions still attracted immense scientific interest mainly because of its distinctly different magnetic ordering under nanoscale as compared to its bulk counterpart [6]. Co3O4 can be synthesized in various nanostructural forms such as nanorods, nanosheets, and ordered nanoflowers with ultrafine porosity [7–10]. Such engineered nanostructures play vital roles as catalysts, gas sensors, magneto‐electronics, electrochromic devices, and high‐temperature solar selective absorbers [11–18]. At first glance, the normal‐spinel structure of Co3O4 may look similar to that of Fe3O4 (inverse spinel) but Co3O4 exhibits strikingly different magnetic ordering as compared to Fe3O4. In particular, Co3O4 does not exhibit ferrimagnetic ordering of the type observed in Fe3O4 because Co3+ ions on the octahedral B‐sites are in the low spin *S* = 0 state [5].

**2. Magnetic properties of bulk versus nanocrystalline Co3O4**

3+]O4 and discuss the role of surface and finite‐size effects

thermistors, magnetic recording, microwave, and RF devices [1, 2].

Co3O4 with configuration (Co2+)[Co2

76 Magnetic Spinels- Synthesis, Properties and Applications

Co2MnO4 are discussed.

As shown in **Figure 1**, the recent magnetic studies by Dutta et al. [6] have reported a significant difference in the antiferromagnetic ordering temperature *T*<sup>N</sup> ∼ 30 K of Co3O4 as compared to the earlier data (40 K); this new result however is in excellent agreement with *T*<sup>N</sup> = 29.92 ± 0.03 K obtained by the heat capacity *C*p versus *T* measurements reported by Khriplovich et al. [19]. It is well known that the peak in the magnetic susceptibility data of antiferromagnets usually occurs at a temperature few percent higher than *T*N because the magnetic specific heat of a simple antiferromagnet (in particular, the singular behavior in the region of the transition) should be closely similar to the behavior of the function d(*χ*p*T*)/d*T* [14]. Therefore, *T*N is better

**Figure 1.** (a) Temperature dependence of the dc‐magnetic susceptibility χ(*T*) for bulk Co3O4 under the zero‐field‐cooled (ZFC) and field‐cooled (FC) conditions. Here, *T*<sup>p</sup> denotes the peak position in *χ* versus *T* plots. (b) Plots of (*χ*p*T*) versus *T* (LHS scale) and d(*χ*p*T*)/d*T* versus *T* plots (RHS scale) for the bulk Co3O4. Here, the paramagnetic susceptibility χp = χ–χ0 with χ0 = 3.06 × 10‐6 emu/g Oe being the temperature‐independent contribution [6, 7].

defined by the peak in ∂(*χT*)/∂*T* versus *T* plot [20]. **Figure 1** shows the temperature dependence of paramagnetic susceptibility χp(*T*) (LHS scale) and d(*χ*p*T*)/d*T* versus *T* (RHS scale). For bulk Co3O4 the peak temperature value (30 K) in the d(*χ*p*T*)/d*T* versus *T* plots is lower than *T*<sup>N</sup> ≃ 40 K often quoted for Co3O4 [5–7, 9–10]. Thus, *T*N = 30 K determined from two independent techniques (i.e., *χ*p and *C*p measurements) is consistent with each other and is the accurate characteristic value for bulk Co3O4. On the other hand, the nanoparticles of Co3O4 exhibit lower *T*N values and reduced magnetic moment than the bulk value (30 K, 4.14 μB) which is a consequence of finite‐size and surface effects [6]. Salabas et al. first reported Co3O4 nanowires of diameter 8 nm and lengths of up to 100 nm by the nanocasting route and observed *T*<sup>B</sup> ≃ 30 K and exchange bias (He) for *T* < *T*B [10].

**Figure 2.** Variation of the Néel temperature *T*N of Co3O4 as a function of particle size (*d*). The data pertaining to solid‐ square symbols are taken from Refs. [6–8] in which *T*N is considered as a peak point in"d(*χ*p*T*)/dT" versus"T" data. However, the data related to solid green circles are taken from Refs. [8, 9] in which *T*N is considered as just the peak point in the "χ"versus"T" plot, not from the derivative plots. The scattered symbols are the raw data corresponding to *T*N and the solid lines are the best fit to Eq. (1).

A plot of *T*N values versus particle size *d* reported by several authors for various crystallite sizes of Co3O4 is shown in **Figure 2**. The lowest *T*<sup>N</sup> value reported till now is about 15 ± 2 K for 4.34 nm size Co3O4 particles [8]. These nanoparticles were synthesized using biological containers of Listeria innocua Dps proteins and LDps as constraining vessels. Lin and Chen studied the magnetic properties of various sizes (diameter *d* = 16, 35, and 75 nm) of Co3O4 nanoparticles prepared by chemical methods using CoSO4 and CoCl2 as precursors [9]. These authors reported that the variation of *T*N follows the finite‐size scaling relation:

#### Nature of Magnetic Ordering in Cobalt‐Based Spinels http://dx.doi.org/10.5772/65913 79

$$\mathbf{T\_N}\left(\mathbf{D}\right) = \mathbf{T\_N}\left(\infty\right) \left[\mathbf{l} - \left(\frac{\tilde{\xi\_0}}{d}\right)^{\lambda}\right] \tag{1}$$

for various sizes of Co3O4 nanoparticles. Accordingly, they obtained the shift exponent = 1.1 ± 0.2 and the correlation length *ξ*o = 2.8 ± 0.3 nm from the fitting analysis of *T*N versus *d* (**Figure 2**). However, these authors considered *T*N values as the direct peak temperature values from χ versus *T* instead of the peak point in d(*χ*p*T*)/d*T*. Also, for the bulk grain sizes *T*N (∞) = 40 K was considered instead of 30 K obtained from d(*χ*p*T*)/d*T* analysis as discussed above. Therefore, we repeated the analysis but considering *T*<sup>N</sup> values obtained from d(*χ*p*T*)/d*T* versus *T* and the *T*<sup>N</sup> (∞) = 30 K for various sizes of the Co3O4 nanoparticles obtained by sol‐gel process (these values were obtained from our earlier works [6, 7]). Accordingly, we obtained = 1.201 ± 0.2 and the correlation length *ξ*o = 2.423 ± 0.46 nm, which are slightly different from the earlier reported values = 1.1 ± 0.2 and the correlation length *ξ*o = 2.8 ± 0.3 nm [9]. Nonetheless, in both the cases *T*N follows the finite‐size scaling relation Eq. (1).

defined by the peak in ∂(*χT*)/∂*T* versus *T* plot [20]. **Figure 1** shows the temperature dependence of paramagnetic susceptibility χp(*T*) (LHS scale) and d(*χ*p*T*)/d*T* versus *T* (RHS scale). For bulk Co3O4 the peak temperature value (30 K) in the d(*χ*p*T*)/d*T* versus *T* plots is lower than *T*<sup>N</sup> ≃ 40 K often quoted for Co3O4 [5–7, 9–10]. Thus, *T*N = 30 K determined from two independent techniques (i.e., *χ*p and *C*p measurements) is consistent with each other and is the accurate characteristic value for bulk Co3O4. On the other hand, the nanoparticles of Co3O4 exhibit lower *T*N values and reduced magnetic moment than the bulk value (30 K, 4.14 μB) which is a consequence of finite‐size and surface effects [6]. Salabas et al. first reported Co3O4 nanowires of diameter 8 nm and lengths of up to 100 nm by the nanocasting route and observed *T*<sup>B</sup> ≃ 30

**Figure 2.** Variation of the Néel temperature *T*N of Co3O4 as a function of particle size (*d*). The data pertaining to solid‐ square symbols are taken from Refs. [6–8] in which *T*N is considered as a peak point in"d(*χ*p*T*)/dT" versus"T" data. However, the data related to solid green circles are taken from Refs. [8, 9] in which *T*N is considered as just the peak point in the "χ"versus"T" plot, not from the derivative plots. The scattered symbols are the raw data corresponding to

A plot of *T*N values versus particle size *d* reported by several authors for various crystallite sizes of Co3O4 is shown in **Figure 2**. The lowest *T*<sup>N</sup> value reported till now is about 15 ± 2 K for 4.34 nm size Co3O4 particles [8]. These nanoparticles were synthesized using biological containers of Listeria innocua Dps proteins and LDps as constraining vessels. Lin and Chen studied the magnetic properties of various sizes (diameter *d* = 16, 35, and 75 nm) of Co3O4 nanoparticles prepared by chemical methods using CoSO4 and CoCl2 as precursors [9]. These

authors reported that the variation of *T*N follows the finite‐size scaling relation:

K and exchange bias (He) for *T* < *T*B [10].

78 Magnetic Spinels- Synthesis, Properties and Applications

*T*N and the solid lines are the best fit to Eq. (1).

For *T* > *T*N, the data of *χ* versus *T* (**Figure 3**) are fitted to the modified Curie‐Weiss law *χ*P = χ0 + [*C/(T + θ)*] with *C* = *Nμ*<sup>2</sup> /3*k*B, *μ*<sup>2</sup> = *g*<sup>2</sup> *J*(*J* + 1)μB 2 , *θ* is the Curie‐Weiss temperature and *χ*<sup>0</sup> contains two contributions: the temperature‐independent orbital contribution mentioned earlier and

**Figure 3.** 1/*χ*p versus *T* plots for the bulk and nanocrystalline (∼17 nm) Co3O4 with χ0 = 3.06 × 10‐6 emu/g Oe (LHS scale). The solid lines represent linear fit to the Curie‐Weiss law: *χ*p = *C*/(*T* + *θ*). On the RHS scale same figures are plotted except for *χ*0 = 9 × 10‐6 and 7.5 × 10‐6 emu/g Oe for the bulk and Co3O4 nanoparticles of size ∼17 nm, respectively [6, 7].

the diamagnetic component *χd* = −3.3 × 10−7 emu/g Oe [6]. Usually *χ0* is estimated from the plot of *χ* versus 1/*T* in the limit of 1/*T* → 0 using the high‐temperature data. The value of *χ*<sup>0</sup> was estimated as 3.06 × 10−6 emu/g Oe for bulk Co3O4 using the inverse paramagnetic susceptibility (1/*χ*P) versus temperature (*T*) data (shown in the left‐hand‐side scale of **Figure 3**) [5, 6]. A similar procedure for experimental data, shown in the right‐hand side scale of **Figure 3**, yields *χ*0 = 9 × 10−6 and 7.5 × 10−6 emu/g Oe for the bulk and nanoparticles (size ∼17 nm) of Co3O4, respectively.

It is well known that the origin of the antiferromagnetic ordering in transition metal oxides can be explained by the super‐exchange interaction between the magnetic elements via oxygen ion. In the present case, there are two possible paths for super‐exchange interaction between magnetic ions in Co3O4, i.e., Co2+ ions: (tetrahedral site) A – O (oxygen) – A (tetrahedral site) and A – O – B – O – A with the number of nearest‐neighbors *z*<sup>1</sup> = 4 and next‐nearest‐neighbors *z*2 = 12, respectively. If the corresponding exchange constants are represented by *J*1ex and *J*2ex, the expressions for *T*N and *θ*, using the molecular‐field theory, can be written as [5, 6]

$$\text{CT}\_{\text{N}} = \frac{J(J+\text{l})}{3k\_{\text{g}}} \left( J\_{1\alpha} z\_1 - J\_{2\alpha} z\_2 \right) \tag{2}$$

$$\partial \theta = \frac{J(J+\mathbb{I})}{3k\_B} (J\_{1\alpha} z\_1 + J\_{2\alpha} z\_2) \tag{3}$$

In order to determine *J*1ex and *J*2ex, the magnitude of effective *J(J* + 1) for Co2+ is required. Since the Curie constant *C* is equivalent to *Nμ*<sup>2</sup> /3*k*B with *μ* = *g* [ *J(J* + 1)]½*μ*B where *g* is the Landé *g*‐ factor and *J* is the total angular momentum. Using the magnitude of *g* = 2 and *C* from **Fig‐ ure 3**, one can estimate the effective magnetic moment *μ*eff = 4.27μB for bulk Co3O4 and *μ* = 4.09μB for Co3O4 nanoparticles of size ∼17 nm. The spin contribution to the above magnitudes of *μ* is 3.87μB for Co2+ with spin *S* = 3/2. Obviously, there is some additional contribution resulting from the partially restored orbital angular moment for the 4 *F*9/2 ground state of Co2+ [5, 6]. Using Eqs. (2) and (3) and the values of "*θ*," "*T*N," and "*μ*" for the two cases yields *J* 1ex = 11.7 and *J*2ex = 2.3 K for bulk, and *J*1ex = 11.5 and *J*2ex = 2.3 K for the Co3O4 nanoparticles (*d* ∼ 17 nm). Thus, both the exchange constants *J* 1ex and *J*2ex correspond to antiferromagnetic coupling. From the magnitudes of *C* in **Figure 3**, the value of *μ* is obtained as 3.28 and 3.43 μB for bulk and Co3O4 nanoparticles (*d* ∼17 nm), respectively. These magnitudes of *μ* are lower than the spin contribution (3.87 μB) of Co2+ ion itself. Consequently, the magnitudes of "*θ*" in **Figure 3** seem to be questionable. This may be due to the fact that the use of molecular‐field theory in determining the exchange constants has its own limitations since higher order spin correlations are neglected in this model [6].

For a typical bulk antiferromagnet, below *T*N, the magnetization is expected to vary linearly with applied external magnetic field *H* below the spin‐flop field. Therefore, the corresponding coercive field *H*<sup>c</sup> and exchange‐bias field *H*<sup>e</sup> must become zero. This was indeed observed in bulk Co3O4 (**Figure 4a**) [5, 6]. Conversely, for the Co3O4 nanoparticles (*d* ∼ 17 nm), the data at

the diamagnetic component *χd* = −3.3 × 10−7 emu/g Oe [6]. Usually *χ0* is estimated from the plot of *χ* versus 1/*T* in the limit of 1/*T* → 0 using the high‐temperature data. The value of *χ*<sup>0</sup> was estimated as 3.06 × 10−6 emu/g Oe for bulk Co3O4 using the inverse paramagnetic susceptibility (1/*χ*P) versus temperature (*T*) data (shown in the left‐hand‐side scale of **Figure 3**) [5, 6]. A similar procedure for experimental data, shown in the right‐hand side scale of **Figure 3**, yields *χ*0 = 9 × 10−6 and 7.5 × 10−6 emu/g Oe for the bulk and nanoparticles (size ∼17 nm) of Co3O4,

It is well known that the origin of the antiferromagnetic ordering in transition metal oxides can be explained by the super‐exchange interaction between the magnetic elements via oxygen ion. In the present case, there are two possible paths for super‐exchange interaction between magnetic ions in Co3O4, i.e., Co2+ ions: (tetrahedral site) A – O (oxygen) – A (tetrahedral site) and A – O – B – O – A with the number of nearest‐neighbors *z*<sup>1</sup> = 4 and next‐nearest‐neighbors *z*2 = 12, respectively. If the corresponding exchange constants are represented by *J*1ex and *J*2ex,

the expressions for *T*N and *θ*, using the molecular‐field theory, can be written as [5, 6]

<sup>N</sup> ( 11 2 2 ) ( 1) <sup>T</sup> 3 *ex ex*

*J J Jz J z*

( 11 2 2 ) ( 1) 3 *ex ex*

In order to determine *J*1ex and *J*2ex, the magnitude of effective *J(J* + 1) for Co2+ is required. Since

factor and *J* is the total angular momentum. Using the magnitude of *g* = 2 and *C* from **Fig‐ ure 3**, one can estimate the effective magnetic moment *μ*eff = 4.27μB for bulk Co3O4 and *μ* = 4.09μB for Co3O4 nanoparticles of size ∼17 nm. The spin contribution to the above magnitudes of *μ* is 3.87μB for Co2+ with spin *S* = 3/2. Obviously, there is some additional contribution

Co2+ [5, 6]. Using Eqs. (2) and (3) and the values of "*θ*," "*T*N," and "*μ*" for the two cases yields *J* 1ex = 11.7 and *J*2ex = 2.3 K for bulk, and *J*1ex = 11.5 and *J*2ex = 2.3 K for the Co3O4 nanoparticles (*d* ∼ 17 nm). Thus, both the exchange constants *J* 1ex and *J*2ex correspond to antiferromagnetic coupling. From the magnitudes of *C* in **Figure 3**, the value of *μ* is obtained as 3.28 and 3.43 μB for bulk and Co3O4 nanoparticles (*d* ∼17 nm), respectively. These magnitudes of *μ* are lower than the spin contribution (3.87 μB) of Co2+ ion itself. Consequently, the magnitudes of "*θ*" in **Figure 3** seem to be questionable. This may be due to the fact that the use of molecular‐field theory in determining the exchange constants has its own limitations since higher order spin

For a typical bulk antiferromagnet, below *T*N, the magnetization is expected to vary linearly with applied external magnetic field *H* below the spin‐flop field. Therefore, the corresponding coercive field *H*<sup>c</sup> and exchange‐bias field *H*<sup>e</sup> must become zero. This was indeed observed in bulk Co3O4 (**Figure 4a**) [5, 6]. Conversely, for the Co3O4 nanoparticles (*d* ∼ 17 nm), the data at

*J J Jz J z*

<sup>+</sup> <sup>=</sup> - (2)

= + (3)

/3*k*B with *μ* = *g* [ *J(J* + 1)]½*μ*B where *g* is the Landé *g*‐

*F*9/2 ground state of

*B*

*B*

*k*

resulting from the partially restored orbital angular moment for the 4

q<sup>+</sup>

the Curie constant *C* is equivalent to *Nμ*<sup>2</sup>

80 Magnetic Spinels- Synthesis, Properties and Applications

correlations are neglected in this model [6].

*k*

respectively.

**Figure 4.** The magnetization (*M*) versus external applied field (*H*) plots recorded in standard five‐cycle hysteresis mode for bulk and nanoparticles (*d* ∼17 nm) of Co3O4 measured at 5 K in the lower field region of ±1 kOe. (a) Irreversibility observed for the direct and reverse field scans for bulk Co3O4, however, (b) a asymmetric shift in the hysteresis loop with enhanced coercivity can be clearly noticed in the case of nanoparticles (*d* ∼ 17 nm) of Co3O4 measured under field‐cooled protocol (FC) of *H* = 20 kOe [6, 7].

5 K show a symmetric hysteresis loop with *H*<sup>c</sup> = 200 Oe for the zero‐field‐cooled sample and asymmetric (shifted) hysteresis loop with *H*<sup>c</sup> = 250 Oe and *H*e = −350 Oe for the sample cooled in magnetic field *H* = 20 kOe from 300 to 5 K as shown in **Figure 4b**. Thus, cooling the sample in a magnetic field produces an exchange bias and leads to the enhancement of *H*<sup>c</sup> as well. The temperature dependence of *H*c and *H*<sup>e</sup> for the nanoparticles of Co3O4 cooled under *H* = 20 kOe from 300 K to the measuring temperature is shown in **Figure 5**. Both *H*c and *H*e approach to zero above *T*N. The inset of **Figure 5** depicts the training effect, i.e., change in the magnitude of *H*<sup>e</sup> for the sample cycled through several successive hysteresis loops (designated by "n" at 5 K) [6, 10]. A similar effect has been recently reported by Salabas et al. [10] in the Co3O4 nanowires of 8 nm diameter although the magnitudes of *H*e and *H*c in their case are somewhat smaller. The existence of the exchange bias suggests the presence of a ferromagnetic (shell)/ antiferromagnetic (core) interface with FM‐like surface spins covering the core of the antifer‐ romagnetically ordered spins in the nanoparticles of Co3O4. Salabas et al. reported that *H*<sup>e</sup> falls by ~25% measured between the first and the second loops. The observation of the training effect and open loops of up to 55 kOe suggests that the surface spins are in an unstable spin‐ glass‐like state [10]. Such a spin‐glass ordering results from the weaker exchange coupling experienced by the surface spins due to reduced coordination at the surface. These effects however disappear above *T*<sup>N</sup> when the spins in the core become disordered. The observation of somewhat lower magnetic moment per Co2+ ion, smaller values of exchange constants *J*1ex and *J*2ex, and lower *T*<sup>N</sup> was noticed for the nanoparticles of Co3O4 in relation to the bulk Co3O4. This could be due to the weak exchange coupling and reduced coordination of the surface spins.

**Figure 5.** The temperature dependence of *H*c and *H*<sup>e</sup> for the nanoparticles of Co3O4 (*d* ∼ 17nm) measured from *T* = 5 to 40 K under field‐cooled (FC) mode at 20 kOe and at 5 K under zero‐field‐cooled (ZFC) condition [6]. One can clearly notice *H*<sup>c</sup> → 0, *H*<sup>e</sup> → 0 as *T* approaches *T*N. The inset shows progressive decrease of the magnitude of *H*<sup>e</sup> after succes‐ sive scan (number of cycles"n") at 5 K [6].

## **3. Co‐existence of ferrimagnetism and spin‐glass states in some inverted spinels**

In 1975, Sherrington and Kirkpatrick (SK) first predicted the reentrant behavior of spinels using mean‐field approach for certain relative values of the temperature and exchange interaction [21, 22]. Later, Gabay and Toulouse extended the SK Ising model calculation to the vector spin glasses and showed that it is possible to have multiple phase transitions such as ferro/ferri/ antiferromagnetic state paramagnetic state Mixed phase‐1 Mixed phase‐2 [22, 23]. The present section deals with such kind of systems in which the longitudinal ferrimag‐ netic ordering coexists with the transverse spin‐glass state below the Néel temperature *T*<sup>N</sup> [23– 28]. In this connection, we mainly focus on the magnetic ordering in two inverse‐spinel systems, namely (i) cobalt orthostannate (Co2SnO4) and (ii) cobalt orthotitanate (Co2TiO4) which exhibits the reentrant spin‐glass behavior [24–40]. At first glimpse, both systems Co2SnO4 and Co2TiO4 are expected to show similar magnetic properties because of the fact that nonmagnetic ions Sn and Ti play identical role on the global magnetic ordering of the system. But in reality, they exhibit markedly different magnetic structures below their ferrimagnetic Néel temperatures [24–40], which is discussed in detail below.

of somewhat lower magnetic moment per Co2+ ion, smaller values of exchange constants *J*1ex and *J*2ex, and lower *T*<sup>N</sup> was noticed for the nanoparticles of Co3O4 in relation to the bulk Co3O4. This could be due to the weak exchange coupling and reduced coordination of the surface

**Figure 5.** The temperature dependence of *H*c and *H*<sup>e</sup> for the nanoparticles of Co3O4 (*d* ∼ 17nm) measured from *T* = 5 to 40 K under field‐cooled (FC) mode at 20 kOe and at 5 K under zero‐field‐cooled (ZFC) condition [6]. One can clearly notice *H*<sup>c</sup> → 0, *H*<sup>e</sup> → 0 as *T* approaches *T*N. The inset shows progressive decrease of the magnitude of *H*<sup>e</sup> after succes‐

**3. Co‐existence of ferrimagnetism and spin‐glass states in some inverted**

In 1975, Sherrington and Kirkpatrick (SK) first predicted the reentrant behavior of spinels using mean‐field approach for certain relative values of the temperature and exchange interaction [21, 22]. Later, Gabay and Toulouse extended the SK Ising model calculation to the vector spin glasses and showed that it is possible to have multiple phase transitions such as ferro/ferri/ antiferromagnetic state paramagnetic state Mixed phase‐1 Mixed phase‐2 [22, 23]. The present section deals with such kind of systems in which the longitudinal ferrimag‐ netic ordering coexists with the transverse spin‐glass state below the Néel temperature *T*<sup>N</sup> [23– 28]. In this connection, we mainly focus on the magnetic ordering in two inverse‐spinel systems, namely (i) cobalt orthostannate (Co2SnO4) and (ii) cobalt orthotitanate (Co2TiO4) which exhibits the reentrant spin‐glass behavior [24–40]. At first glimpse, both systems Co2SnO4 and Co2TiO4 are expected to show similar magnetic properties because of the fact that

spins.

82 Magnetic Spinels- Synthesis, Properties and Applications

sive scan (number of cycles"n") at 5 K [6].

**spinels**

Usually, the ferrimagnetic ordering in Co2SnO4 and Co2TiO4 arises from the unequal magnetic moments of Co2+ ions at the tetrahedral A‐sites and octahedral B‐sites [24–40]. The corre‐ sponding magnetic moment at the tetrahedral A‐sites *μ*(A) is equal to 3.87 μB and the magnetic moment at octahedral B‐sites *μ*(B) is equal to 5.19 and 4.91 μB for Co2TiO4 and Co2SnO4, respectively [27–33]. In 1976, Harmon et al. first reported the low‐temperature magnetic properties of polycrystalline Co2SnO4 system and showed the evidence for ferrimagnetic ordering with *T*<sup>N</sup> ∼ 44 ± 2 K [24]. They also suggested that Co2SnO4 should contain two equally populated sublattices that align collinearly and couple antiferromagnetically [24]. On the basis of the Mössbauer spectroscopy results, these authors calculated the internal dipolar fields at the Sn sites from the two Co2+ sublattices to be > 80 kOe [24]. They also reported very high values of coercive field *H*<sup>C</sup> > 50 kOe below *T*N [24]. The reported magnetization value at 16 K per Co2+ ion was about 2.2 × 10−3 μB with zero magnetization value at 12 K. The Curie‐Weiss constant (*C*) = 4.3 ± 0.2 emu/mol, and the effective magnetic moment of the Co2+ ions = 5.0 ± 0.2 μB was close to the standard value of 4.13 emu/mol and 4.8 μB, respectively. A year later, Sagredo et al. reported that the zero‐field‐cooled and field‐cooled magnetization curves of single crystal Co2SnO4 exhibit strong irreversibility below *T*N [39].

Sagredo et al. reported that thermoremanent magnetization, magnetic training effects, and spin‐glass phases present in this system are driven by the disordered‐spin configurations [39]. Accordingly, they speculated that the random distribution of Sn4+ ions on the B‐sites might break the octahedral symmetry of the crystal field and result in the frustrated magnetic behavior [39]. In 1987, Srivastava et al. reported multiple peaks in the temperature dependence of ac‐magnetic susceptibility *χ*ac(*T*) for both Co2SnO4 and Co2TiO4 below their *T*<sup>N</sup> providing the evidence of Gabay and Tolouse mixed‐phase transitions [25, 28]. Nevertheless, some recent studies proved the existence of transverse spin‐glass state *T*SG (∼39 K) just below the *T*N (= 41 K) in Co2SnO4 [27, 38, 40]. Similar type of results in Co2TiO4 was reported by Hubsch et al. and Srivastava et al. but with different *T*SG (∼46 K) and *T*N (=55 K) [25, 28, 31, 34].

In order to get a precise understanding of the magnetic properties of these systems, we have plotted the temperature dependence of dc‐magnetic susceptibility *χ*dc(*T*) for both Co2SnO4 and Co2TiO4 measured under ZFC and FC (H@100 Oe) conditions in **Figure 6**. These χdc(*T*) plots show typical characteristics of ferrimagnetic ordering with peaks across the Néel temperatures *T*<sup>N</sup> = 47 K (for Co2TiO4) and 39 K (for Co2SnO4). However, for *T* ≤ 31.7 K an opposite trend in the *χ*dc(*T*) values was noticed for Co2TiO4 with *χ*dc ∼ 0 at magnetic‐compensation temperature *T*CMP = 31.7 K at which the two‐bulk sublattices magnetizations completely balances with each other [31–33]. Such compensation behavior in Co2SnO4 system is expected to appear at very low temperatures (*T* < 10 K) as *χ*dc(*T*) approaches to zero. Consequently, *χ*dc‐ZFC exhibits negative magnetization until *T*SG. It is expected that the different magnetic moments on the tetrahedral (A) and the octahedral (B) sites, and their different temperature dependence (i.e., μA(*T*), μB(*T*)) play a major role on the global magnetic ordering of both systems.

**Figure 6.** The temperature dependence of dc‐magnetic susceptibility *χ*dc(*T*) measured under ZFC and FC (H@100 Oe) conditions for both Co2TiO4 (LHS) and Co2SnO4 (RHS). The dotted line shows the *T*CMP.

Recent X‐ray photoelectron spectroscopic studies reveal that the crystal structure of Co2TiO4 consists of some fraction of trivalent cobalt and titanium ions at the octahedral sites, i.e., [Co2+][Co3+Ti3+]O4 instead of [Co2+][Co2+Ti4+]O4 [34]. On the contrary, the Co2SnO4 shows the perfect tetravalent nature of stannous ions without any trivalent signatures of Co3+ [Co2+] [Co2+Sn4+]O4 [27]. Such distinctly different electronic structure of the ions on the B‐sites of cobalt orthotitanate plays a significant role on the anomalous magnetic ordering below *T*N, for example, exhibiting the magnetic‐compensation behavior, sign reversible zero‐field exchange‐ bias, and negative slopes in the Arrott plots (*H/M* versus *M2* ) [27, 34].

At high temperatures (for all *T* > *T*N), the experimental data of inverse dc‐magnetic suscepti‐ bility (*χ*−1) for both the systems Co2TiO4 and Co2SnO4 fit well with the modified Néel expression for ferrimagnets (1/*χ*) = (*T/C*) + (1/*χ* 0) – [*σ*0/(*T − θ*)]. **Table 1** summarizes various fitting parameters obtained from the Néel expression for both Co2SnO4 and Co2TiO4. The fit for Co2TiO4 yields the following parameters: *χ*<sup>0</sup> = 41.92 × 10−3 emu/mol‐Oe, *σ*<sup>0</sup> = 31.55 mol‐Oe‐K/ emu, *C* = 5.245 emu K/mol Oe, *θ* = 49.85 K. The ratio *C*/*χ*0 = *T*<sup>a</sup> =125.1 K represents the strength of the antiferromagnetic exchange coupling between the spins on the A‐ and B‐sites and is often termed as the asymptotic Curie temperature *T*a. For both the systems, the effective magnetic moment *μ*eff is determined from the formula *C* = *Nμ*eff2 /3*k*B. The experimentally observed magnetic moments at the B‐sites *μ*(B) = 5.19 μB obtained from the temperature dependence of magnetization values are in line with the above‐discussed spectroscopic properties of Co2TiO4, i.e., the total moment *μ*(B) is perfectly matching with the contribution

from the magnetic moments due to Co3+ (4.89 μB) and Ti3+ (1.73 μB), *μ*(B) = Co+3 2 + Ti+3 2

[34]. Also, the analysis of the dc and ac susceptibilities combined with the weak anomalies observed in the *C*p versus *T* data has shown the existence of a quasi‐long‐range ferrimagnetic state below *T*N ~ 47.8 K and a compensation temperature of *T*CMP ~ 32 K [34].


**Table 1.** The list of various parameters obtained from the Néel fit of *χ*−1 versus *T* curve recorded under zero‐field‐ cooled condition.

**Figure 6.** The temperature dependence of dc‐magnetic susceptibility *χ*dc(*T*) measured under ZFC and FC (H@100 Oe)

Recent X‐ray photoelectron spectroscopic studies reveal that the crystal structure of Co2TiO4 consists of some fraction of trivalent cobalt and titanium ions at the octahedral sites, i.e., [Co2+][Co3+Ti3+]O4 instead of [Co2+][Co2+Ti4+]O4 [34]. On the contrary, the Co2SnO4 shows the perfect tetravalent nature of stannous ions without any trivalent signatures of Co3+ [Co2+] [Co2+Sn4+]O4 [27]. Such distinctly different electronic structure of the ions on the B‐sites of cobalt orthotitanate plays a significant role on the anomalous magnetic ordering below *T*N, for example, exhibiting the magnetic‐compensation behavior, sign reversible zero‐field exchange‐

At high temperatures (for all *T* > *T*N), the experimental data of inverse dc‐magnetic suscepti‐ bility (*χ*−1) for both the systems Co2TiO4 and Co2SnO4 fit well with the modified Néel expression for ferrimagnets (1/*χ*) = (*T/C*) + (1/*χ* 0) – [*σ*0/(*T − θ*)]. **Table 1** summarizes various fitting parameters obtained from the Néel expression for both Co2SnO4 and Co2TiO4. The fit for Co2TiO4 yields the following parameters: *χ*<sup>0</sup> = 41.92 × 10−3 emu/mol‐Oe, *σ*<sup>0</sup> = 31.55 mol‐Oe‐K/ emu, *C* = 5.245 emu K/mol Oe, *θ* = 49.85 K. The ratio *C*/*χ*0 = *T*<sup>a</sup> =125.1 K represents the strength of the antiferromagnetic exchange coupling between the spins on the A‐ and B‐sites and is often termed as the asymptotic Curie temperature *T*a. For both the systems, the effective

observed magnetic moments at the B‐sites *μ*(B) = 5.19 μB obtained from the temperature dependence of magnetization values are in line with the above‐discussed spectroscopic properties of Co2TiO4, i.e., the total moment *μ*(B) is perfectly matching with the contribution

[34]. Also, the analysis of the dc and ac susceptibilities combined with the weak anomalies observed in the *C*p versus *T* data has shown the existence of a quasi‐long‐range ferrimagnetic

) [27, 34].

/3*k*B. The experimentally

2 + Ti+3 2

Co+3

conditions for both Co2TiO4 (LHS) and Co2SnO4 (RHS). The dotted line shows the *T*CMP.

84 Magnetic Spinels- Synthesis, Properties and Applications

bias, and negative slopes in the Arrott plots (*H/M* versus *M2*

magnetic moment *μ*eff is determined from the formula *C* = *Nμ*eff2

from the magnetic moments due to Co3+ (4.89 μB) and Ti3+ (1.73 μB), *μ*(B) =

state below *T*N ~ 47.8 K and a compensation temperature of *T*CMP ~ 32 K [34].

The real and imaginary components of the temperature dependence of ac‐susceptibility data *χ*ac(*T*) (= *χ′*(*T*) + *i χ″*(*T*)) recorded at different frequencies for both the polycrystalline samples Co2SnO4 and Co2TiO4 show the dispersion in their peak positions (*T*P(*f*)) similar to the com‐ pounds exhibiting spin‐glass‐like ordering [27, 33]. **Figure 8** shows the *χ*′(*T*) and *χ*″(*T*) data of Co2SnO4 and Co2TiO4 recorded at different measuring frequencies ranging from 0.17 to 1202 Hz with peak‐to‐peak field amplitude *H*ac = 4 Oe under zero dc‐bias field. It is clear from these figures that the peaks seen in both cases show pronounced frequency dependence, which suggests the dynamical features analogous to that of observed in spin‐glass systems. A detailed analysis of such frequency dependence of *χ*′(*T*) and *χ*″(*T*) using two scaling laws described below provides the evidence for spin‐glass‐like characteristics below *T*N. For example, applying the Vogel‐Fulcher law (below equation) for interacting particles

$$\tau = \tau\_0 \exp\left(\frac{E\_a}{k\_B \left(T - T\_0\right)}\right) \tag{4}$$

and the best fits of the experimental data (the logarithmic variation of relaxation time"*τ"* as a function of 1/(*TF ‐ T0*) as shown in **Figure 8a** yields the following parameters: interparticle interaction strength *T*0 = 39.3 K and relaxation time constant *τ* 0 = 7.3 × 10−8 s for Co2SnO4. Here, we define the freezing temperature for each frequency is *T*F, angular frequency *ω* as 2*π f* (*ω* =1/ *τ*), *k*B is the Boltzmann constant, and *Ea* is an activation energy parameter. Such large value of *τ*0 indicates the presence of interacting magnetic spin clusters of significant sizes in the polycrystalline Co2SnO4 system. The origin of such spin clusters may arise from a short‐range magnetic order occurring due to the competition between ferrimagnetism and magnetic frustration. Another characteristic feature that the spin‐glass systems follows is the power law (Eq. (5)) of critical slowing down in a spin‐glass phase transition at *T*SG (note that the *T*P(*f*) data represent a relatively small temperature interval):

$$
\pi = \pi\_0 \left(\frac{T}{T\_g} - 1\right)^{-\varepsilon\nu} \tag{5}
$$

**Figure 7(a).** The temperature dependence of the ac‐magnetic susceptibilities (i) real *χ*′(*T*) component and (ii) imaginary χ″(*T*) component of bulk polycrystalline Co2SnO4 system recorded at various frequencies under warming condition us‐ ing dynamic magnetic field of amplitude *h*ac = 4 Oe and zero static magnetic field *H*dc = 0. The lines connecting the data points are visual guides [27].

**Figure 7(b).** The temperature dependence of the ac‐magnetic susceptibilities (iii) real *χ*′(*T*) component and (iv) imagi‐ nary χ″(*T*) component of bulk polycrystalline Co2TiO4 system recorded at various frequencies under warming condi‐ tion using dynamic magnetic‐field of amplitude *h*ac = 4 Oe and zero static magnetic field *H*dc = 0. The lines connecting the data points are visual guides [33].

The least‐square fit using the powerlaw of the data shown in **Figure 7** is depicted in **Figure 8b**. Here, *T*SG is the freezing temperature, *τ*<sup>0</sup> is related to the relaxation of the individual cluster magnetic moment, and *zν* is a critical exponent. The least‐square fit analysis for Co2SnO4 gives *T*SG = 39.6 K, *τ*<sup>0</sup> = 1.4 × 10−15 s, and *zν* = 6.4. Since the value of *zν* obtained in the present case lies well within the range (6–8) of a typical spin‐glass systems; thus, one can conclude that Co2SnO4 exhibits spin‐glass‐like phase transition across 39 K just below the *T*<sup>N</sup> ∼ 41 K [20, 27]. In these studies, the difference in *T*<sup>0</sup> and *T*SG is very small (∼0.3 K) suggesting the close resemblance between the current Co2SnO4 system and the compounds exhibiting spin‐glass‐ like transition. However, the situation for Co2TiO4 is bit different; in particular, the best fit to the Vogel‐Fulcher law yields *T*0 = 45.8 K and *τ*0 = 3.2 × 10−16 s and the power law yielded fairly unphysical values of the fitting parameters: for example, *τ*<sup>0</sup> ~ 10−33 s with *zν* > 16, indicating the lack of spin‐glass‐like phase transition [33]. Although, the magnitude and shift of the ac‐ susceptibility values both *χ*′(*T*) and *χ*″(*T*) strongly suppressed in the presence of dc‐magnetic field (*H*DC) in a similar way as it occurs in a typical spin‐glass system perfectly following the linear behavior of *H*2/3 versus *T*<sup>P</sup> (AT‐line analysis). Under such tricky situation, it is very difficult to conclude that Co2TiO4 is a perfect spin‐glass or not (of course one can call it as a pseudo‐spin‐glass system). Nevertheless, the ac‐magnetic susceptibility data and its analysis suggested that the both Co2SnO4 and Co2TiO4 systems consist of interacting magnetic clusters close to a spin‐glass state.

**Figure 7(a).** The temperature dependence of the ac‐magnetic susceptibilities (i) real *χ*′(*T*) component and (ii) imaginary χ″(*T*) component of bulk polycrystalline Co2SnO4 system recorded at various frequencies under warming condition us‐ ing dynamic magnetic field of amplitude *h*ac = 4 Oe and zero static magnetic field *H*dc = 0. The lines connecting the data

**Figure 7(b).** The temperature dependence of the ac‐magnetic susceptibilities (iii) real *χ*′(*T*) component and (iv) imagi‐ nary χ″(*T*) component of bulk polycrystalline Co2TiO4 system recorded at various frequencies under warming condi‐ tion using dynamic magnetic‐field of amplitude *h*ac = 4 Oe and zero static magnetic field *H*dc = 0. The lines connecting

points are visual guides [27].

86 Magnetic Spinels- Synthesis, Properties and Applications

the data points are visual guides [33].

Another interesting feature of both Co2SnO4 and Co2TiO4 is that they show asymmetry in M‐ H hysteresis loops unveiling giant coercivities and bipolar exchange bias under both ZFC and FC cases below their *T*<sup>N</sup> [27, 31, 33]. Earlier studies by Hubsch et al. have shown unusual temperature dependence of coercive field *H*C(*T*) in polycrystalline Co2TiO4 sample where the M‐H loops were measured in 20‐kOe field at different temperatures below 60 K [31]. It is well known that the discovery of exchange‐bias (*H*EB) effect in the structurally single‐phase materials with mixed magnetic phases has recently gained tremendous attention because of its technological applications in the development of Read/Write heads of the magnetic

**Figure 8.** The best fit of the relaxation times to the (a) Vogel‐Fulcher law and the (b) power law for the spinels Co2SnO4 and Co2TiO4.

recording devices [41]. Generally, *H*EB has been experimentally observed only in the systems cooled in the presence of external magnetic field (FC mode) from above the Néel temperature or spin‐glass freezing point. Such systems usually comprise of variety of interfaces such as ferromagnetic (FM)‐antiferromagnetic (AFM), FM‐SG, FM‐ferrimagnetic, AFM‐ferrimagnetic, and AFM‐SG [41–49]. However, few recent papers have reported significant *H*EB even under the zero‐field‐cooled samples of bulk Ni‐Mn‐In alloys and in bulk Mn2PtGa [48, 49]. The source of such unusual *H*EB under zero‐field‐cooled sample was attributed to the presence of complex magnetic interfaces such as ferrimagnetic/spin‐glass or AFM/spin‐glass phases [48–51]. Some recent reports have suggested that large exchange anisotropy can originate from the exchange interaction between the compensated host and ferromagnetic clusters [48–51]. Strikingly, Hubsch et al. observed the *H*C→0 anomalies across *T*CMP, *T*SG, and *T*<sup>N</sup> in the temperature‐ dependent data of *H*C for Co2TiO4 samples [31]. Slightly different results were reported by Nayak et al. in Ref. [33], where *H*C values drops monotonically on approaching *T*N. However, the behavior of temperature dependence of exchange‐bias field *H*EB(*T*) and remanent magnet‐ ization *M*R(*T*) in Ref. [33] closely resembles with the trend of *H*C(*T*) reported by Hubsch et. al. in polycrystalline Co2TiO4 samples. On the other hand, the temperature behavior of *H*EB(*T*), *H*C(*T*), and *M*R(*T*) in Co2SnO4 is way different from that of Co2TiO4 though they are isostructural with each other. It is likely that the different magnitudes and different temperature depend‐ ences of the moments on the Co2+ ions on the "A"‐ and "B"‐sites in Co2SnO4 are responsible for the anomalous behavior in the *H*EB(*T*), *H*C(*T*), and *M*R(*T*) observed below *T*N. Moreover, in Co2SnO4 below about 15 K, the data suggest that there is nearly complete effective balance of the antiferromagnetically coupled Co2+ moments at the"A"‐ and"B"‐sites leading to negligible values of *H*C and *M*R.

Results from neutron diffraction in Co2TiO4 suggested the presence of canted‐spins, likely resulting from magnetic frustration caused by the presence of nonmagnetic Ti4+ ions on the"B"‐ sites. A similar canting of the spins might be present in Co2SnO4 although neutron diffraction studies are needed to verify this suggestion [27, 31, 33]. Other Co‐based spinel compounds that display the reversal in the orientation of the magnetic moments along with negative magnet‐ ization due to the magnetic‐compensation phenomena are CoCr2O4 and Co(Cr0.95Fe0.05)2O4 [3, 52, 53].

## **4. Magnetic properties of bulk and nanocrystalline Co2MnO4**

Among various Co2XO4 (X = Mn, Ni, Co, Zn, etc.) spinels, Co2MnO4 has retained a unique place. In particular, Mn‐ and Co‐based spinel oxides have gained considerable interest in the recent past due to their numerous applications in the Li‐ion batteries [54, 55], sensors [56–58], thermistors [59], energy‐conversion devices [60], and as a catalyst for the reduction of nitrogen oxides [61]. Moreover, Co2MnO4 nanocrystals have demonstrated outstanding catalytic properties for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) [60]. ORR and OER are the essential reactions in the electrochemistry‐based energy‐storage and energy‐conversion devices. Co2MnO4 has shown superior catalytic activities compared to the commercial 30 wt% platinum supported on carbon black (Pt/C). Due to the special surface morphology [62], Co2MnO4 spinel is a very promising pseudo‐capacitor material [63, 64]. Co2MnO4 has also demonstrated potential applications for protective coating on ferrite stainless steel interconnects in solid‐oxide fuel cells (SOFCs) [65, 66]. Furthermore, colossal magnetoresistance (CMR) has been observed in the Mn‐ and Co‐based spinel oxides [67].

recording devices [41]. Generally, *H*EB has been experimentally observed only in the systems cooled in the presence of external magnetic field (FC mode) from above the Néel temperature or spin‐glass freezing point. Such systems usually comprise of variety of interfaces such as ferromagnetic (FM)‐antiferromagnetic (AFM), FM‐SG, FM‐ferrimagnetic, AFM‐ferrimagnetic, and AFM‐SG [41–49]. However, few recent papers have reported significant *H*EB even under the zero‐field‐cooled samples of bulk Ni‐Mn‐In alloys and in bulk Mn2PtGa [48, 49]. The source of such unusual *H*EB under zero‐field‐cooled sample was attributed to the presence of complex magnetic interfaces such as ferrimagnetic/spin‐glass or AFM/spin‐glass phases [48–51]. Some recent reports have suggested that large exchange anisotropy can originate from the exchange interaction between the compensated host and ferromagnetic clusters [48–51]. Strikingly, Hubsch et al. observed the *H*C→0 anomalies across *T*CMP, *T*SG, and *T*<sup>N</sup> in the temperature‐ dependent data of *H*C for Co2TiO4 samples [31]. Slightly different results were reported by Nayak et al. in Ref. [33], where *H*C values drops monotonically on approaching *T*N. However, the behavior of temperature dependence of exchange‐bias field *H*EB(*T*) and remanent magnet‐ ization *M*R(*T*) in Ref. [33] closely resembles with the trend of *H*C(*T*) reported by Hubsch et. al. in polycrystalline Co2TiO4 samples. On the other hand, the temperature behavior of *H*EB(*T*), *H*C(*T*), and *M*R(*T*) in Co2SnO4 is way different from that of Co2TiO4 though they are isostructural with each other. It is likely that the different magnitudes and different temperature depend‐ ences of the moments on the Co2+ ions on the "A"‐ and "B"‐sites in Co2SnO4 are responsible for the anomalous behavior in the *H*EB(*T*), *H*C(*T*), and *M*R(*T*) observed below *T*N. Moreover, in Co2SnO4 below about 15 K, the data suggest that there is nearly complete effective balance of the antiferromagnetically coupled Co2+ moments at the"A"‐ and"B"‐sites leading to negligible

Results from neutron diffraction in Co2TiO4 suggested the presence of canted‐spins, likely resulting from magnetic frustration caused by the presence of nonmagnetic Ti4+ ions on the"B"‐ sites. A similar canting of the spins might be present in Co2SnO4 although neutron diffraction studies are needed to verify this suggestion [27, 31, 33]. Other Co‐based spinel compounds that display the reversal in the orientation of the magnetic moments along with negative magnet‐ ization due to the magnetic‐compensation phenomena are CoCr2O4 and Co(Cr0.95Fe0.05)2O4 [3,

Among various Co2XO4 (X = Mn, Ni, Co, Zn, etc.) spinels, Co2MnO4 has retained a unique place. In particular, Mn‐ and Co‐based spinel oxides have gained considerable interest in the recent past due to their numerous applications in the Li‐ion batteries [54, 55], sensors [56–58], thermistors [59], energy‐conversion devices [60], and as a catalyst for the reduction of nitrogen oxides [61]. Moreover, Co2MnO4 nanocrystals have demonstrated outstanding catalytic properties for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) [60]. ORR and OER are the essential reactions in the electrochemistry‐based energy‐storage and energy‐conversion devices. Co2MnO4 has shown superior catalytic activities compared to the commercial 30 wt% platinum supported on carbon black (Pt/C). Due to the special surface

**4. Magnetic properties of bulk and nanocrystalline Co2MnO4**

values of *H*C and *M*R.

88 Magnetic Spinels- Synthesis, Properties and Applications

52, 53].

In addition to the novel catalytic properties, Co2MnO4 spinel exhibits intriguing magnetic properties. Lotgering first observed the existence of ferromagnetic ordering in Co2MnO4 spinels [68]. Ríos et al. systematically studied the effect of Mn concentration on the magnetic properties of Co3‐*x*Mn*x*O4 solid solutions prepared by spray pyrolysis [69]. As we have discussed in Section 2 that Co3O4 has an antiferromagnetic order with *T*N = 30 K. When we replace Co in Co3O4 by Mn cation, large ferromagnetic ordering appears, which ultimately dominates the antiferromagnetic ordering at *x* = 1. Therefore, pure Co2MnO4 shows ferromag‐ netic behavior and this has been confirmed by detailed magnetic measurements [70, 71]. However, for value of *x* other than 0 (Co3O4) and 1 (Co2MnO4), both ferromagnetic and antiferromagnetic magnetic exchange interactions coexist in the system, which yields a ferrimagnetic ordering in the Co3‐*x*Mn*x*O4 (0 < *x* < 1) solid solutions [72]. Tamura performed pressure‐dependent study of Curie temperature (*T*C) and found that *T*<sup>C</sup> decreases with increase in pressure [71].

Pure Co2MnO4 possess a cubic inverse‐spinel structure: (B3+)[A2+B3+]O4 (shown in **Figure 9**). In an ideal case, the octahedral [B] sites are occupied by divalent cations together with half of the trivalent cations and the rest of the trivalent cations occupy the tetrahedral (A) sites in the spinel structure. However, due to the presence of different oxidation states of Mn and Co cati‐ ons at (A) and [B] sites, the actual cationic distribution of Co2MnO4 is very complex and it has been a topic of considerable debate [59, 70–84]. Different sample preparation conditions also play an important role in the cationic distribution of Co2MnO4. On the basis of X‐ray diffrac‐ tion, electrical conductivity, magnetic, physiochemical, and neutron diffraction measure‐ ments, several different cationic distributions for nonstoichiometric Co3‐*x*Mn*x*O4 (0 < *x* < 1) have been reported in literature [59, 70–84]. From the magnetic measurements, Wickham and Croft proposed the following cationic distribution: Co2 +[Co2 − 3 + Mn 3 +]O4(0 < < 2) for solid solu‐ tions of Co3‐*x*Mn*x*O4 systems obtained after the thermal decomposition of co‐precipitated man‐ ganese and cobalt salts [72]. Later studies by Blasse suggested a different cationic distribution: Co2 +[Co2 − 2 + Mn 4 +]O4 [73]. Based on the physicochemical properties, Ríos et al. proposed <sup>a</sup> more complicated cationic distribution: Co0.88 2 + Mn0.12 2 + [Co0.87 3 + Co0.22 2 + Mn0.09 3 + Mn0.76 4 + ■0.06]O4 for Co2MnO4 powder samples prepared by thermal decomposition of nitrate salts [74]. From the neutron diffraction and magnetic measurements, Boucher et al. reported the cationic distribu‐ tion Co2 +[Co2 − 3 + Mn 3 +]O4 similar to the one reported by Wickham and Croft [72, 75]. Yama‐ moto et al. [76] performed neutron diffraction measurements on Co2MnO4 oxides prepared by chemical methods at low temperatures, and reported Mn1‐*n*Co*n*[Mn*x*Co2‐*n*]O4 as atomic distri‐ bution. Here, *n* is the inversion parameter of the inverse‐spinel structure. Gautier et al. sug‐ gested two different possible cationic distributions: Co2+[Co3+Mn0.35 2 + Mn0.29 3 + Mn0.36 4 + ]O4 and Co2+[0.95 3 + Mn0.015 2 + Mn0.50 3 + Mn0.485 4 + ■0.05]O4 [77, 78]. On the contrary, the electrical conductivity measurements suggest <sup>a</sup> different cationic distribution: Co2+[ 2 +Co2(1 − ) 3 + Mn 4 +]O4, and Co2+[Co2+Mn4+]O4 or Co3+[Co3+Mn2+]O4 [59, 79] for Co2MnO4 spinel. Aoki studied the phase diagram and cationic distribution of various compositions of manganese and cobalt mixed spinel oxides [80]. He further investigated the effect of temperature and Mn concentration on the structure of manganese‐cobalt spinel oxide systems. Control over morphology, crystallite site, grain size, and specific surface area of Co2MnO4 powders can be achieved by thermal decomposition of precursors in a controlled atmosphere [81, 82].

**Figure 9.** Cubic inverse‐spinel structure of Co2MnO4 in Fd‐3m (227) space group.

In 2008, Bazuev et al. investigated the effect of oxygen stoichiometry on the magnetic proper‐ ties of Co2MnO4+δ [83]. Accordingly, two oxygen‐rich compositions, (i) Co2MnO4.62 and (ii) Co2MnO4.275, were prepared by the thermal decomposition of presynthesized Co and Mn binary oxalates (Mn1/3Co2/3C2O4· 2H2O). Above studies also report existence of anomalous behavior in the magnetic properties of Co2MnO4.275 spinel at low temperatures and high magnetocrystalline anisotropy in Co2MnO4.62. Bazuev et al. also noticed that *T*N of Co2MnO4+δ is highly sensitive to the oxygen stoichiometry, imperfections in the cationic sublattice and variation in the Mn oxidation states. The imperfect Co2MnO4+δ inherits ferrimagnetic ordering that arises due to the antiferromagnetic exchange between Co2+ ( 4 2 <sup>3</sup> ) and Mn4+ ( 2 <sup>3</sup> 0)) cations located at the tetrahedral and octahedral sites, respectively. To further investigate the electronic states of Mn and Co cations in the Co2MnO4 lattice, Bazuev at al. employed the X‐ ray absorption near‐edge spectroscopy (XANES) to probe the electronic states of the absorbing atoms and their local neighborhood [83]. XANES spectra of both Co2MnO4.62 and Co2MnO4.275 compositions revealed that Co is present in both Co2+ and Co3+ oxidation states while Mn is

present as Mn4+ and Mn3+. Additionally, it was found that Mn is located in a higher symmetry octahedral crystal field environment [83]. Bazuev at al. further proposed following cationic distributions for Co2MnO4.275 and Co2MnO4.62 compositions: Co0.936 2 + [Co0.936 III Mn0.421 3 + Mn0.515 4 + ]O4 and Co0.66 2 + [Mn0.866 4 + Co1.072 III ]O4, respectively. Here, CoIII is a low‐spin cation while Co2+ and Mn3+ are high‐spin cations.

Co2+[0.95

3 + Mn0.015

2 + Mn0.50

90 Magnetic Spinels- Synthesis, Properties and Applications

3 + Mn0.485

measurements suggest <sup>a</sup> different cationic distribution: Co2+[

decomposition of precursors in a controlled atmosphere [81, 82].

**Figure 9.** Cubic inverse‐spinel structure of Co2MnO4 in Fd‐3m (227) space group.

that arises due to the antiferromagnetic exchange between Co2+ (

Co2+[Co2+Mn4+]O4 or Co3+[Co3+Mn2+]O4 [59, 79] for Co2MnO4 spinel. Aoki studied the phase diagram and cationic distribution of various compositions of manganese and cobalt mixed spinel oxides [80]. He further investigated the effect of temperature and Mn concentration on the structure of manganese‐cobalt spinel oxide systems. Control over morphology, crystallite site, grain size, and specific surface area of Co2MnO4 powders can be achieved by thermal

In 2008, Bazuev et al. investigated the effect of oxygen stoichiometry on the magnetic proper‐ ties of Co2MnO4+δ [83]. Accordingly, two oxygen‐rich compositions, (i) Co2MnO4.62 and (ii) Co2MnO4.275, were prepared by the thermal decomposition of presynthesized Co and Mn binary oxalates (Mn1/3Co2/3C2O4· 2H2O). Above studies also report existence of anomalous behavior in the magnetic properties of Co2MnO4.275 spinel at low temperatures and high magnetocrystalline anisotropy in Co2MnO4.62. Bazuev et al. also noticed that *T*N of Co2MnO4+δ is highly sensitive to the oxygen stoichiometry, imperfections in the cationic sublattice and variation in the Mn oxidation states. The imperfect Co2MnO4+δ inherits ferrimagnetic ordering

cations located at the tetrahedral and octahedral sites, respectively. To further investigate the electronic states of Mn and Co cations in the Co2MnO4 lattice, Bazuev at al. employed the X‐ ray absorption near‐edge spectroscopy (XANES) to probe the electronic states of the absorbing atoms and their local neighborhood [83]. XANES spectra of both Co2MnO4.62 and Co2MnO4.275 compositions revealed that Co is present in both Co2+ and Co3+ oxidation states while Mn is present as Mn4+ and Mn3+. Additionally, it was found that Mn is located in a higher symmetry octahedral crystal field environment [83]. Bazuev at al. further proposed following cationic

4 + ■0.05]O4 [77, 78]. On the contrary, the electrical conductivity

2 +Co2(1 − ) 3 + Mn

> 4 2

<sup>3</sup> ) and Mn4+ (

2 <sup>3</sup> 0))

4 +]O4, and

Co2MnO4 spinels have gained peculiar interest of researchers due to their unusual magnetic hysteresis behavior at low temperatures. Joy and Date [70] first observed the unusual magnetic hysteresis behavior in Co2MnO4 nanoparticles below 120 K. By means of the magnetic hysteresis loop measurements at low temperatures, they realized that the initial magnetization curve (virgin curve) lies outside the main hysteresis loop at 120 K. However, for *T* > 120 K, they observed normal hysteresis behavior in Co2MnO4. This unusual behavior of hysteresis loop at low temperatures can be associated with the irreversible domain wall motion. At low magnetic fields (*H* < *H*C), domain walls experience substantial resistance during their motion with increasing magnetic field. Similar behavior has been observed for some other alloys [85–87]. Such irreversible movement of domain walls was ascribed to the rearrangement of valence electrons at low temperatures. Generally, in a system with mixed oxidation states of Mn at high temperatures, short‐range diffusion of Co ions, Co3+ ⇆ Co2+ associated with Mn3+ ⇆ Mn4+, gets activated at low temperatures. This may cause change in the local ordering of the ions at the octahedral sites. Consequently, the resistance for domain wall motion increases and this slows down the motion of domain walls. Soon after Joy and Date, Borges et al. [84] confirmed that the unusual hysteresis of Co2MnO4 compound indeed arises due to the irreversible domain wall motion. Borges et al. prepared various different size nanoparticles of Co2MnO4 by Pechini method and performed the magnetic hysteresis measurements at low temperatures [84]. They observed that the samples below a critical diameter (*d* < 39 nm) exhibit normal hysteresis behavior, while the bulk grain size samples (*d* ∼200 nm) show unusual hysteresis behavior at low temperatures. Using the spherical particle model, Borges et al. further calculated the critical diameter (*d*cr) of a single‐domain wall in Co2MnO4 and obtained that *d*cr = 39 nm [88]. Therefore, all particles with diameter *d*< *d*cr can be considered as a single‐domain particle. Since particles with *d* < *d*cr show normal hysteresis while particles with *d* > *d*cr show unusual hysteresis behavior, one can conclude that the unusual hysteresis behavior is indeed due to the irrever‐ sible motion of the domain walls.

The dynamic magnetic properties of Co2MnO4 nanoparticles of average diameter 28 nm were reported by Thota et al. [89]. A detailed study of dc‐ and ac‐magnetic susceptibility measure‐ ments of these nanoparticles reveals the low temperature spin‐glass‐like characteristics together with the memory and aging effects (**Figure 10**). **Figure 10** shows the temperature dependence of real and imaginary part of the ac‐susceptibility (*χ′*(*T*) and *χ″*(*T*)) of Co2MnO4 nanoparticles recorded at different values of frequencies (*f*) between 1 Hz and 1.48 kHz at a peak‐to‐peak amplitude of 1 Oe. Both *χ′(T)* and *χ″*(*T*) exhibit a sharp peak at the onset of ferromagnetic ordering (*T*C = *T*1 = 176.4 K) and a broad cusp centered at *T*2 (<*T*C).

The temperature at which both *χ′*(*T*) and *χ″*(*T*) attain the maximum value shifts toward high‐ temperature side as the frequency increases from 1 Hz and 1.48 kHz similar to spin‐glass behavior. Such frequency dependence of *χ′*(*T*) and *χ″*(*T*) follows the Vogel‐Fulcher law (Eq. (4) and insets of **Figures 10a(ii)** and **b(ii)**) and power law of critical slowing down (Eq. (5) and insets of **Figures 10a(i)** and **b(i)**). Least‐square fit to these equation yields the following parameters (insets of **Figure 10**): interparticle interaction strength ( *T*0) = 162 K for *T*<sup>1</sup> (118 K for *T*2) and relaxation time constant *τ*<sup>0</sup> = 6.18 × 10−15 s for *T*<sup>1</sup> (4.4 × 10‐15 s for *T*2), critical exponent (*zν*) *=* 6.01 for *T*1 (7.14 for *T*2), and spin‐glass transition temperature (*T*SG) = 162.6 K for *T*<sup>1</sup> (119.85 K for *T*2). Since the values of *zν* for both the peaks *T*1 and *T*2 of Co2MnO4 nanoparticles lie well within the range (6–8) of a typical spin‐glass systems, one can conclude that Co2MnO4 exhibits spin‐glass‐like phase transition across 162.6 K just below the *T*<sup>C</sup> ∼ 176.4 K [89]. **Figure 11a** shows the magnetization relaxation of Co2MnO4 nanoparticles under ZFC and FC protocols with a temperature quench to 70 K at *H* = 250 Oe [89]. The magnetization relaxation during the third cycle appears as a continuation of first cycle (**Figures 11b** and **c**). Relaxation of ZFC magnetization with temperature quenching confirms the existence of memory effects in Co2MnO4 nanoparticles. A noticeable wait‐time (*t*wt) dependence of magnetization relaxation (*aging*) at 50 K in both *M*ZFC and *M*FC was noticed in these Co2MnO4 nanoparticles, which further supports the presence of the spin‐glass behavior observed in this system.

**Figure 10.** The real and imaginary components of the ac‐magnetic susceptibilities (*χ′(T)* and *χ″(T)*) of Co2MnO4 nano‐ particles measured at various frequencies. The insets a(i) and b(i) represent the Vogel‐Fulcher law whereas the insets a(ii) and b(ii) represent the power law of critical slowing down for both the peaks *T*1 and *T*2.

insets of **Figures 10a(i)** and **b(i)**). Least‐square fit to these equation yields the following parameters (insets of **Figure 10**): interparticle interaction strength ( *T*0) = 162 K for *T*<sup>1</sup> (118 K for *T*2) and relaxation time constant *τ*<sup>0</sup> = 6.18 × 10−15 s for *T*<sup>1</sup> (4.4 × 10‐15 s for *T*2), critical exponent (*zν*) *=* 6.01 for *T*1 (7.14 for *T*2), and spin‐glass transition temperature (*T*SG) = 162.6 K for *T*<sup>1</sup> (119.85 K for *T*2). Since the values of *zν* for both the peaks *T*1 and *T*2 of Co2MnO4 nanoparticles lie well within the range (6–8) of a typical spin‐glass systems, one can conclude that Co2MnO4 exhibits spin‐glass‐like phase transition across 162.6 K just below the *T*<sup>C</sup> ∼ 176.4 K [89]. **Figure 11a** shows the magnetization relaxation of Co2MnO4 nanoparticles under ZFC and FC protocols with a temperature quench to 70 K at *H* = 250 Oe [89]. The magnetization relaxation during the third cycle appears as a continuation of first cycle (**Figures 11b** and **c**). Relaxation of ZFC magnetization with temperature quenching confirms the existence of memory effects in Co2MnO4 nanoparticles. A noticeable wait‐time (*t*wt) dependence of magnetization relaxation (*aging*) at 50 K in both *M*ZFC and *M*FC was noticed in these Co2MnO4 nanoparticles, which further

**Figure 10.** The real and imaginary components of the ac‐magnetic susceptibilities (*χ′(T)* and *χ″(T)*) of Co2MnO4 nano‐ particles measured at various frequencies. The insets a(i) and b(i) represent the Vogel‐Fulcher law whereas the insets

a(ii) and b(ii) represent the power law of critical slowing down for both the peaks *T*1 and *T*2.

supports the presence of the spin‐glass behavior observed in this system.

92 Magnetic Spinels- Synthesis, Properties and Applications

**Figure 11.** Magnetization relaxation *M*(*t*) under ZFC and FC protocols with a temperature quench to 70 K at *H* = 250 Oe. The continuation of the first and third relaxation process during (b) ZFC and (c) FC cycles.

The high‐temperature inverse magnetic susceptibility (1/*χ*ZFC versus *T*) data of Co2MnO4 nanoparticles (**Figure 12**) fit well with the Néel's expression for ferrimagnets:

**Figure 12.** The scattered data represent the high‐temperature inverse magnetic susceptibility (1/*χ*ZFC versus *T*) of Co2MnO4 nanoparticles and the solid line represents the best fit to the Néel's expression for ferrimagnets Eq (6).

The fit (red line in **Figure 12**) yields: *<sup>C</sup>* = 0.0349 emu K/g Oe, 0 = 4.5 × 10‐5 emu/g Oe, 0 = 5.76 × 104 g Oe K/emu, = 169.8 K, and the asymptotic Curie temperature *T*a = *C*/0 = 775.6 K [90, 91]. *T*a gives us information about the strength of antiferromagnetic exchange coupling between Mn3+ and Mn4+ at octahedral sites. Moreover, the effective magnetic moment *μ*eff calculated using expression: = eff 2 3B turnouts to be 8.13 μB.

## **5. Concluding remarks**

In this review, magnetic properties of bulk and nanoparticles of the Co‐based spinels Co3O4, Co2SnO4, Co2TiO4, and Co2MnO4 have been summarized. The fact that the observed magnetic properties of these spinels are so different is shown to result from the different occupation of the cations on the A‐ and B‐sites and their different electronic states at these sites. The richness of the properties of spinels thus results from these differences.

## **Acknowledgements**

The authors thank Prof. M. S. Seehra for his suggestions and guidance in organizing this chapter. Sobhit Singh acknowledges the support from the West Virginia University Libraries under OAAF program.

## **Author details**

Subhash Thota1\* and Sobhit Singh2

\*Address all correspondence to: subhashiitk@gmail.com


## **References**


The fit (red line in **Figure 12**) yields: *<sup>C</sup>* = 0.0349 emu K/g Oe, 0 = 4.5 × 10‐5 emu/g Oe, 0 = 5.76 × 104 g Oe K/emu, = 169.8 K, and the asymptotic Curie temperature *T*a = *C*/0 = 775.6 K [90, 91]. *T*a gives us information about the strength of antiferromagnetic exchange coupling between Mn3+ and Mn4+ at octahedral sites. Moreover, the effective magnetic moment *μ*eff

In this review, magnetic properties of bulk and nanoparticles of the Co‐based spinels Co3O4, Co2SnO4, Co2TiO4, and Co2MnO4 have been summarized. The fact that the observed magnetic properties of these spinels are so different is shown to result from the different occupation of the cations on the A‐ and B‐sites and their different electronic states at these sites. The richness

The authors thank Prof. M. S. Seehra for his suggestions and guidance in organizing this chapter. Sobhit Singh acknowledges the support from the West Virginia University Libraries

turnouts to be 8.13 μB.

eff 2

3B

of the properties of spinels thus results from these differences.

calculated using expression: =

94 Magnetic Spinels- Synthesis, Properties and Applications

**5. Concluding remarks**

**Acknowledgements**

under OAAF program.

Subhash Thota1\* and Sobhit Singh2

\*Address all correspondence to: subhashiitk@gmail.com

[2] D. W. Bruce, Functional Oxides, Wiley (2010).

1 Department of Physics, Indian Institute of Technology, Assam, India

2 Department of Physics & Astronomy, West Virginia University, Morgantown, USA

[1] A. Goldman, Magnetic Components for Power Electronics, Springer (Nov. 2001).

**Author details**

**References**


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#### **Electronic, Transport and Magnetic Properties of Cr-based Chalcogenide Spinels Electronic, Transport and Magnetic Properties of Cr-based Chalcogenide Spinels**

Chuan-Chuan Gu, Xu-Liang Chen and Zhao-Rong Yang Chuan-Chuan Gu, Xu-Liang Chen and Zhao-Rong Yang

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/110953

#### **Abstract**

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The Cr-based chalcogenide spinels with general formula ACr2X4 (A = Cd, Zn, Hg, Fe; X = S, Se) host rich physical properties due to coexistence of frustration as well as strong coupling among spin, charge, orbital and lattice degrees of freedom. In this chapter, recent advances on the study of electronic transport and magnetic properties of ACr2X4 are reviewed. After a short introduction of the crystal structure and magnetic interactions, we focus on the colossal magnetoresistance (CMR) in FeCr2S4, colossal magnetocapacitance (CMC) in CdCr2S4, negative thermal expansion (NTE) in ZnCr2Se4 and complex orbital states in FeCr2S4. It is hoped that this chapter will be beneficial for the readers to explore the interplay among different degrees of freedom in the frustrated system.

**Keywords:** Cr-based spinel, colossal magnetoresistance, colossal magnetocapacitance, negative thermal expansion, frustrated magnet, complex orbital states

## **1. Introduction**

Chromium-based chalcogenide spinels with general formula ACr2X4 (A = Cd, Zn, Hg, Fe; X = S, Se) have attracted special attention not only for pure academic interest, but also for potential applications [1–4]. On the one hand, the chromium-based chalcogenide spinels are typical strongly correlated electron materials. Due to strong coupling among spin, charge, orbital and lattice degrees of freedom, this system displays rich physical properties such as colossal magnetoresistance (CMR), colossal magnetocapacitance (CMC), gigantic Kerr rotation, and magnetoelectric effect [5–8]. On the other hand, the existence of frustration

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

(magnetic or orbital frustration) increases complexity of the system, yielding complex behaviors such as spin glass, orbital glasses, and spin nematic [9–11]. Depending on external perturbation from magnetic field, electric field, chemical substitution, or disorder, different quantum states are subtle balanced, increasing difficulty for understanding the intrinsic physics of this system. For example, the polycrystalline (PC) sample of FeCr2S4 displays orbital ordering around 9K, while single crystal (SC) sample shows orbital glass [12, 13]. CdCr2S4 single crystal exhibits multiferroic behavior with the evidence of relaxor ferroelectricity and CMC [6]. However, the emergence of ferroelectricity and CMC effect in these thio-spinels was found to be highly sensitive to the detail of sample preparation and chemical doping. Both multiferroicity and CMC effect are absent in PC samples [14].

In this chapter, recent progresses in the studies of Cr-based chalcogenide spinels are described. We will focus on the origin of several physical effects including CMR, CMC and NTE. The origin of complex spin and orbital states will also be covered.

## **2. Crystal structure and magnetic interactions in ACr2X4 (A= Cd, Zn, Hg, Fe; X = S, Se)**

The chromium-based spinels ACr2X4 (A = Cd, Zn, Hg, Fe; X = S, Se) have the cubic symmetry with space group *Fd*3′*<sup>m</sup>* (ℎ 7), as is shown in **Figure 1**. Each cubic cell has 8 molecular formulae, which possess 56 ions, including 8 A2+ ions, 16 Cr3+ ions and 32 X2− ions. The X2− anions form a close-packed face-centered cubic lattice with two-type coordinated interstice: tetrahedral and octahedral ones. In the normal type spinel, the A2+ ions occupy 1/8 of the tetrahedrally coordinated interstices and the B3+ions occupy 1/2 of the octahedrally coordinated interstices. Otherwise, it is defined as an inverse spinel type, in which the A2+ and B3+ cations exchange the sites. In some situations, the compound with the same chemical elements could be formed by normal and inverse type spinel simultaneously [15, 16].

**Figure 1.** Schematic structure of spinel ACr2X4. A2+ ions are in tetrahedral and Cr3+ ions in octahedral site.

In ACr2X4, if magnetic cations (such as Mn2+, Co2+, Fe2+) occupy the A site, the system usually displays a ferrimagnetic order with a net magnetization, due to the opposite spin direction of A and B sites. On the other hand, if A site is occupied by nonmagnetic ions (e.g., Zn2+, Cd2+, Hg2+), the Cr3+ ions form a network of corner-sharing tetrahedral known as the pyrochlore lattice [17]. The dominant frustration in this network that hinders a simple antiparallel spin pattern is tightly associated with the way the Cr-Cr atoms are separated. The different ground states as a function of lattice constants are driven by the dominating exchange interactions: at small Cr-Cr separation, strong direct antiferromagnetic (AFM) exchange dominates, indicative of strong geometrical frustration [18]; at larger Cr-Cr separations, 90° Cr3+-X2−-Cr3+ ferromagnetic and Cr3+-X2−-A2+-X2−-Cr3+ or AFM Cr3+-X2−-X2−-Cr3+ superexchange interactions come into play [1], with additional bond frustration dominanting in the sulfides and selenides.

## **3. Colossal magnetoresistance in FeCr2S4**

(magnetic or orbital frustration) increases complexity of the system, yielding complex behaviors such as spin glass, orbital glasses, and spin nematic [9–11]. Depending on external perturbation from magnetic field, electric field, chemical substitution, or disorder, different quantum states are subtle balanced, increasing difficulty for understanding the intrinsic physics of this system. For example, the polycrystalline (PC) sample of FeCr2S4 displays orbital ordering around 9K, while single crystal (SC) sample shows orbital glass [12, 13]. CdCr2S4 single crystal exhibits multiferroic behavior with the evidence of relaxor ferroelectricity and CMC [6]. However, the emergence of ferroelectricity and CMC effect in these thio-spinels was found to be highly sensitive to the detail of sample preparation and chemical doping. Both multiferroicity and CMC effect are absent in PC samples [14].

In this chapter, recent progresses in the studies of Cr-based chalcogenide spinels are described. We will focus on the origin of several physical effects including CMR, CMC and NTE. The

**2. Crystal structure and magnetic interactions in ACr2X4 (A= Cd, Zn, Hg, Fe;**

The chromium-based spinels ACr2X4 (A = Cd, Zn, Hg, Fe; X = S, Se) have the cubic symmetry

which possess 56 ions, including 8 A2+ ions, 16 Cr3+ ions and 32 X2− ions. The X2− anions form a close-packed face-centered cubic lattice with two-type coordinated interstice: tetrahedral and octahedral ones. In the normal type spinel, the A2+ ions occupy 1/8 of the tetrahedrally coordinated interstices and the B3+ions occupy 1/2 of the octahedrally coordinated interstices. Otherwise, it is defined as an inverse spinel type, in which the A2+ and B3+ cations exchange the sites. In some situations, the compound with the same chemical elements could be formed

**Figure 1.** Schematic structure of spinel ACr2X4. A2+ ions are in tetrahedral and Cr3+ ions in octahedral site.

7), as is shown in **Figure 1**. Each cubic cell has 8 molecular formulae,

origin of complex spin and orbital states will also be covered.

100 Magnetic Spinels- Synthesis, Properties and Applications

by normal and inverse type spinel simultaneously [15, 16].

**X = S, Se)**

with space group *Fd*3′*<sup>m</sup>* (ℎ

The presence of the CMR effect in mixed valence manganese oxides R3+1−*x*A2+*x*MnO3 (R is a rare earth and A is a divalent alkaline earth) in the vicinity of a paramagnetic (PM) to ferromagnetic (FM) transition has been the subject of much recent interest [19, 20]. This conductive behavior is described by the double-exchange (DE) model [21], which suggests that the conductivity is decided by the hopping of the electrons between hetrovalent Mn3+/Mn4+ pairs [22]. Later, another CMR material—FeCr2S4 has been reported by Ramirez et al. [5]. Since the magnetotransport behaviors of FeCr2S4 are quite similar to manganite perovskites, one might expect to apply the DE theory and Jahn-Teller (JT) polaron mechanism to explain the CMR effects in FeCr2S4. However, the X-ray diffraction (XRD) pattern and Mössbauer spectrum give direct evidences that there is no DE mechanism in FeCr2S4 [23].

The magnetization (*M*) in the temperature range from 4.2 to 400 K at the field *H* = 0.01 T is shown in **Figure 2(a)**. With decreasing temperature, *M* first increases slowly, and then increases abruptly near (173 K) due to the PM-FM transition. The Curie temperature *T*C is 168 K,

**Figure 2.** (a) Temperature dependence of the magnetization in field-cooled (FC) and zero-field-cooled (ZFC) sequences, respectively and (b) temperature dependence of the paramagnetic susceptibility *χ* as a plot of 1/*χ* versus temperature [24].

which is defined as the temperature corresponding to maximum of |d*M*/d*T*|. To clarify the magnetism in FeCr2S4, the temperature dependence of the PM susceptibility *χ* is shown in **Figure 2(b)** as a plot of 1/*χ* versus temperature. According to the physics of ferrimagnetism, the temperature dependence of the PM susceptibility *χ* can be described by Eq. (1) [25, 26]:

$$1 \mid \mathcal{X} = T \mid C + 1 \mid \mathcal{X}\_0 - \sigma \mid \left(T - \theta\right). \tag{1}$$

Here *χ*0, *C, σ* and *θ* are fitting parameters. The fit results of *χ* are shown as the solid line in **Figure 2(b)**, with 1/*χ*0 = 130(±2), *C* = 1.50(±0.02), *σ* = 3818(±50) and *θ* = 167(±3). Clearly, Eq. (1) fits the experimental result well except near *T*C, indicating a ferrimagnet state. At temperatures near and above *T*C, the system has strong short-range magnetic correlation, thus not in an ideal PM state.

The temperature-dependent resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0) from 4.2 K to 300 K under three different applied fields (0, 3 and 5 T) are shown in **Figure 3**. Both *ρ* and MRH display a peak near . The maximum of MR5 is 16%. The temperature corre-

**Figure 3.** Resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0), versus temperature for FeCr2S4. The inset shows the curve of ln *ρ* versus 1000/*T* [24].

sponding to the minimum resistivity in the *ρ*-*T* curve below *T*C is defined as *T*1 = 153 K. As seen from the inset of **Figure 3**, the curve of ln *ρ* versus 1000/*T* is linear at both > and *T* < *T*1, indicating a semiconductor like behavior in two regions. The fits by *ρ* = *ρ*0 exp(*E*/*k*B*T*) give the activation energies *E*L = 26 meV for *T* < *T*1, and *E*H = 47 meV for > , respectively. This implies that the conduction mechanisms are different for the two temperature regions. *<sup>E</sup>*H > *E*L indicates clearly that *E*H, the activated energy at temperatures above , does not arise from a simple thermally activated effect. In order to understand the discrepancy between *E*L and *E*H, the thermoelectric power (*S*) is fitted by the experimental data through *S* = (*k*B/*e*)(*a* + *ES*/*k*B*T*) [24, 27]. *ES* is obtained as 23 meV, which is approximately equal to 26 meV for *E*L, and much lower than 47 meV for *E*H. The discrepancy between *ES* and *E*H in manganite perovskites can be attributed to the presence of lattice or magnetic polarons. Since there is neither a structure transition nor a JT effect around *T*C in FeCr2S4, the polarons mainly exist in the form of magnetic polarons [28].

which is defined as the temperature corresponding to maximum of |d*M*/d*T*|. To clarify the magnetism in FeCr2S4, the temperature dependence of the PM susceptibility *χ* is shown in **Figure 2(b)** as a plot of 1/*χ* versus temperature. According to the physics of ferrimagnetism, the temperature dependence of the PM susceptibility *χ* can be described by Eq. (1) [25, 26]:

1/ / 1/ – / .

 cs

Here *χ*0, *C, σ* and *θ* are fitting parameters. The fit results of *χ* are shown as the solid line in **Figure 2(b)**, with 1/*χ*0 = 130(±2), *C* = 1.50(±0.02), *σ* = 3818(±50) and *θ* = 167(±3). Clearly, Eq. (1) fits the experimental result well except near *T*C, indicating a ferrimagnet state. At temperatures near and above *T*C, the system has strong short-range magnetic correlation, thus not in an ideal

The temperature-dependent resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0) from 4.2 K to 300 K under three different applied fields (0, 3 and 5 T) are shown in **Figure 3**. Both *ρ*

**Figure 3.** Resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0), versus temperature for FeCr2S4. The inset shows

 q

=+ - *TC T* <sup>0</sup> ( ) (1)

. The maximum of MR5 is 16%. The temperature corre-

c

PM state.

and MRH display a peak near

102 Magnetic Spinels- Synthesis, Properties and Applications

the curve of ln *ρ* versus 1000/*T* [24].

The sample at temperatures above is in a typical PM state, in favor of the existence of magnetic polarons [24]. As is known, a magnetic polaron is a carrier coupled by short-range magnetic correlation within a magnetic cluster at temperatures above . Thus, the effective mass of a magnetic polaron increases greatly with respect to that of a naked carrier, which means it has a lower mobility and a higher activated energy [29, 30]. In an ideal FM order, magnetic polarons will be delocalized from the self-trapped state and turn into naked carriers completely [29]. In consequence, *ρ* decreases drastically at this point, accompanied with the system changing completely to one of thermal-activated transport of naked carriers. However, *ρ* decreases gradually from to *T*1, and MR also expands to a broader temperature range below , indicative of the existence of magnetic polarons in this temperature range. Magnetic polarons will be delocalized gradually as the PM phase weakens. They then vanish completely at *T*1, denoting that magnetic order destroys the environment for magnetic polarons. Hence, *ρ* in the temperature range from to *T*1 can be described by a two-fluid model involving the coexistence of magnetic polarons and naked carriers. It could also explain that MR expands to a broader temperature range below , since the formation of magnetic polarons is inhibited by the enhancement of FM order at an external magnetic field.

To further investigate the evolution of magnetic polarons in FeCr2S4, nonmagnetic Cd is substituted for Fe. The XRD measurement for Fe1−*x*Cd*x*Cr2S4 reveals that the substitution of Fe by Cd produces no structural change [31]. The resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0), as a function of temperature are shown in **Figure 4**. Comparing with FeCr2S4, the Cd-containing sample has a higher zero-field resistivity. For *x* = 0.2, a peak is shown in both *ρ* and *MRH* near *T*C. Zero-field *ρ* reveals semiconductor-like behavior at temperatures for both *T* > *T*C and *T* far below *T*C, which is similar to the results of FeCr2S4. Upon substitution of Cd for Fe, both the zero-field *ρ* and *MRH* value increases monotonically, while the peak of the *MRH* curve shifts to lower temperatures. As mentioned above, it is believed that the conduction originates from Fe2+ narrow band at temperatures far below *T*C, and is dominated by the magnetic polarons in the temperature region above *T*C. For Fe1−*x*Cd*x*Cr2S4, there are two sided influences of the introduced Cd2+ on the conduction behavior. On the one hand, since the conduction originates from Fe2+ narrow band, the increase of Cd ions will decrease carrier density, resulting in the increase of *ρ*. As is mentioned above, the magnetic polaron hopping conduction *ρ* = *ρ*0*T* exp(*E*/*k*B*T*) should be considered for *T* > *T*C. On the other hand, the introduced Cd ions will induce both Coulomb and magnetic potential fluctuations, as a sequence, leading to the formation of a mobility edge. Thus, thermally activated behavior *ρ* = *ρ*0 exp(*E*/*k*B*T*) due to a mobility edge may be more appropriate to describe the conduction above *T*C [32, 33].

**Figure 4.** Resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0), versus temperature for Fe1−*x*Cd*x*Cr2S4 (0 < *x* ≤ 0.8) [31].

**Figure 5** shows the zero-field resistivity curves replotted as ln *ρ −* 1000/*T* and ln(*ρ*/*T*) *−* 1000/*T*, respectively. For *x* = 0.2, the curve of ln *ρ −* 1000/*T* is linear both at *T* > *T*C and at temperatures far below *T*C. The activation energy *E*, which is obtained from the fits to *ρ* = *ρ*0 exp(*E*/*k*B*T*), is 39 meV for the temperatures far below *T*C, and 50 meV for *T* > *T*C. As is known, the discrepancy of the activation energy for FeCr2S4 is described by a two-fluid model concerning the coexistence of magnetic polarons and naked carriers. As is shown in **Figure 5(a)**, magnetic polaron hopping conduction [*ρ* = *ρ*0*T* exp(*E*/*k*B*T*)] is more appropriate for the resistivity behavior at *T* > *T*C. Moreover, it gives more convincible description as compared to thermal-activated mechanism for higher Cd concentration, which implies that the magnetic polarons may be more stable in the high-Cd samples.

curve shifts to lower temperatures. As mentioned above, it is believed that the conduction originates from Fe2+ narrow band at temperatures far below *T*C, and is dominated by the magnetic polarons in the temperature region above *T*C. For Fe1−*x*Cd*x*Cr2S4, there are two sided influences of the introduced Cd2+ on the conduction behavior. On the one hand, since the conduction originates from Fe2+ narrow band, the increase of Cd ions will decrease carrier density, resulting in the increase of *ρ*. As is mentioned above, the magnetic polaron hopping conduction *ρ* = *ρ*0*T* exp(*E*/*k*B*T*) should be considered for *T* > *T*C. On the other hand, the introduced Cd ions will induce both Coulomb and magnetic potential fluctuations, as a sequence, leading to the formation of a mobility edge. Thus, thermally activated behavior *ρ* = *ρ*0 exp(*E*/*k*B*T*) due to a mobility edge may be more appropriate to describe the conduction above

**Figure 4.** Resistivity *ρ* and magnetoresistance *MRH* = [*ρ*(0) – *ρ*(*H*)]/*ρ*(0), versus temperature for Fe1−*x*Cd*x*Cr2S4 (0 < *x* ≤

**Figure 5** shows the zero-field resistivity curves replotted as ln *ρ −* 1000/*T* and ln(*ρ*/*T*) *−* 1000/*T*, respectively. For *x* = 0.2, the curve of ln *ρ −* 1000/*T* is linear both at *T* > *T*C and at temperatures far below *T*C. The activation energy *E*, which is obtained from the fits to *ρ* = *ρ*0 exp(*E*/*k*B*T*), is 39 meV for the temperatures far below *T*C, and 50 meV for *T* > *T*C. As is known, the discrepancy of the activation energy for FeCr2S4 is described by a two-fluid model concerning the coexistence of magnetic polarons and naked carriers. As is shown in **Figure 5(a)**, magnetic polaron hopping conduction [*ρ* = *ρ*0*T* exp(*E*/*k*B*T*)] is more appropriate for the resistivity behavior at *T* > *T*C. Moreover, it gives more convincible description as compared to thermal-activated mechanism for higher Cd concentration, which implies that the magnetic polarons may be

*T*C [32, 33].

104 Magnetic Spinels- Synthesis, Properties and Applications

0.8) [31].

more stable in the high-Cd samples.

**Figure 5.** Zero-field resistivity curves for Fe1−*x*Cd*x*Cr2S4 (0 < *x* ≤ 0.8) replotted as ln *ρ −* 1000/*T* (closed circle ●) and l ln(*ρ*/*T*) *−* 1000/*T* (solid square ■), respectively [31].

Direct evidence of the magnetic polarons could be best sought with electron spin-resonance spectroscopy (ESR) measurements [31]. Above *T*\* ~ 113 K, each spectrum consists of a single line with a Lorentzian line shape, and further decreasing temperature, some distortions occur. A similar behavior has been observed in manganese perovskites, which is attributed to the presence of the FM clusters embedded in PM matrix [34, 35]. In addition, as *T* is increased, the peak-to-peak line-width Δ*HPP* decreases in a broad temperature range [31]. *T*min (corresponding to the temperature where Δ*HPP* is minimum) is much higher than *T*\*, suggesting that the relaxation mechanism dominating in CdCr2S4 is different with that in the manganese. The analysis of ESR experiments in CMR materials has pointed out that linewidth Δ*HPP* will decrease exponentially upon warming if the magnetic polaron acts as a part in the relaxation mechanism, as a result of the motionally narrowed relaxation mechanism [36]. Thus in CdCr2S4, since magnetic polaron is more stable upon Cd substitution, it is plausible that the hopping of magnetic polarons will make contribution to the relaxation process, and certainly decrease the line-width Δ*HPP*. The decrease of line-width with increasing temperature obviously gives a direct evidence for the presence of magnetic polarons in CdCr2S4.

For a pure magnetic polaron system, the magnetic polaron forms by self-trapping in a ferromagnetically aligned cluster of spins at *T* < *TP* (*TP* denotes the temperature where polarons start forming). As the temperature is lowered toward *T*C, the polaron grows in size. According to the ML model [37], for a low carrier density ferromagnet, when *nξ* ≈ 1 is accomplished, magnetic polarons overlap, which leads to the carrier delocalization. Here *n* is the carrier density, and*ξ* is FM correlation length. It provides the temperature ratio of about *T*/*T*C ≤ 1.05– 1.1 [37]. Therefore, for a pure magnetic polaron system, the magnetic polarons are periodically spaced before overlapping, similar to a gas of magnetic polarons. When the system is in a PM state, no magnetic correlation occurs among the polarons to be considered as superparamagnetic. On the other hand, if the system is inhomogeneous, there may be magnetic correlation, which means magnetic polarons themselves are no longer isolated. Due to the correlation, the system could not stay in the superparamagnetic state, which results in the existence of some distortions in the resonance line [34]. Hence, it can be concluded that magnetic polarons first exist as a gas of polarons at temperatures *T* < *TP*, and then transform into correlated polarons at temperatures *T* < *T*\* (*TP* > *T*\* > *T*C).

## **4. Colossal magnetocapacitance in CdCr2S4**

Multiferroic materials that exhibit simultaneous magnetic and ferroelectric order as well as concomitant magnetoelectric coupling have attracted special interest in recent years [38–40]. CdCr2S4 was originally investigated as a FM semiconductor more than 40 years ago [41]. Recently, it was reported that SC CdCr2S4 exhibits multiferroic behavior with the evidence of relaxor ferroelectricity and CMC [6]. Soon after, similar magnetoelectric effect has also been revealed in other related thio-spinel compounds, that is, CdCr2Se4 and HgCr2S4 [42, 43]. However, the emergence of ferroelectricity and CMC effect in these thio-spinels was found to be highly sensitive to the detail of sample preparation and chemical doping. Annealing SC samples in vacuum or sulfur atmosphere led to a suppression of relaxation features, and no remanent electric polarization could be found at low temperatures [14]. In addition, multiferroicity and CMC effect are absent in undoped PC samples, but present in indium-doped PCs [14]. Accordingly, the question of whether the magnetoelectric effect in CdCr2S4 is intrinsic or not has been raised [44, 45]. In this section, the origin of CMC effect in the CdCr2S4system would be revealed systematically through the magnetic, dielectric and electric transport measurements of CdCr2S4 and Cd0.97In0.03Cr2S4 PC samples before and after annealing in cadmium vapor.

Upon doping and annealing, no impurity phases are detected [46]. The *M*-*T* curves under an external magnetic field of 1 T for all samples are shown in the inset of **Figures 6(b)** and **7(b)**. After annealing in cadmium vapor, the magnetic properties of PC CdCr2S4 and Cd0.97In0.03Cr2S4 are slightly changed. The Curie temperature *T*C is about 92.1 K for CdCr2S4 and 92.9 K for Cd0.97In0.03Cr2S4, respectively. After annealing, the increase of *T*C is less than 4 K. **Figures 6** and **7** display the temperature dependence of dielectric constant *ε′* and *ac*-conductivity *σ*′at two different frequencies in magnetic field of 0 T and 4.5 T for the as-prepared and annealed samples. Both *ε*′ and *σ*′ increase with temperature monotonously and do not show anomaly and magnetic field dependence in the whole measured temperature range, as seen from **Figures 6(a**, **b)** and **7(a**, **b)**. After annealing CdCr2S4 at 800°C (**Figure 6(c**, **d)**), *ε*′ displays a hump in the low temperature region and the hump temperature increases with frequency, implying a relaxor-like behavior of the dielectric property [14]. However, the magnetic field of 4.5 T still has no obvious effect on either *ε′* or *σ*′.

Electronic, Transport and Magnetic Properties of Cr-based Chalcogenide Spinels http://dx.doi.org/10.5772/110953 107

density, and*ξ* is FM correlation length. It provides the temperature ratio of about *T*/*T*C ≤ 1.05– 1.1 [37]. Therefore, for a pure magnetic polaron system, the magnetic polarons are periodically spaced before overlapping, similar to a gas of magnetic polarons. When the system is in a PM state, no magnetic correlation occurs among the polarons to be considered as superparamagnetic. On the other hand, if the system is inhomogeneous, there may be magnetic correlation, which means magnetic polarons themselves are no longer isolated. Due to the correlation, the system could not stay in the superparamagnetic state, which results in the existence of some distortions in the resonance line [34]. Hence, it can be concluded that magnetic polarons first exist as a gas of polarons at temperatures *T* < *TP*, and then transform into correlated polarons

Multiferroic materials that exhibit simultaneous magnetic and ferroelectric order as well as concomitant magnetoelectric coupling have attracted special interest in recent years [38–40]. CdCr2S4 was originally investigated as a FM semiconductor more than 40 years ago [41]. Recently, it was reported that SC CdCr2S4 exhibits multiferroic behavior with the evidence of relaxor ferroelectricity and CMC [6]. Soon after, similar magnetoelectric effect has also been revealed in other related thio-spinel compounds, that is, CdCr2Se4 and HgCr2S4 [42, 43]. However, the emergence of ferroelectricity and CMC effect in these thio-spinels was found to be highly sensitive to the detail of sample preparation and chemical doping. Annealing SC samples in vacuum or sulfur atmosphere led to a suppression of relaxation features, and no remanent electric polarization could be found at low temperatures [14]. In addition, multiferroicity and CMC effect are absent in undoped PC samples, but present in indium-doped PCs [14]. Accordingly, the question of whether the magnetoelectric effect in CdCr2S4 is intrinsic or not has been raised [44, 45]. In this section, the origin of CMC effect in the CdCr2S4system would be revealed systematically through the magnetic, dielectric and electric transport measurements of CdCr2S4 and Cd0.97In0.03Cr2S4 PC samples before and after annealing in cadmium vapor.

Upon doping and annealing, no impurity phases are detected [46]. The *M*-*T* curves under an external magnetic field of 1 T for all samples are shown in the inset of **Figures 6(b)** and **7(b)**. After annealing in cadmium vapor, the magnetic properties of PC CdCr2S4 and Cd0.97In0.03Cr2S4 are slightly changed. The Curie temperature *T*C is about 92.1 K for CdCr2S4 and 92.9 K for Cd0.97In0.03Cr2S4, respectively. After annealing, the increase of *T*C is less than 4 K. **Figures 6** and **7** display the temperature dependence of dielectric constant *ε′* and *ac*-conductivity *σ*′at two different frequencies in magnetic field of 0 T and 4.5 T for the as-prepared and annealed samples. Both *ε*′ and *σ*′ increase with temperature monotonously and do not show anomaly and magnetic field dependence in the whole measured temperature range, as seen from **Figures 6(a**, **b)** and **7(a**, **b)**. After annealing CdCr2S4 at 800°C (**Figure 6(c**, **d)**), *ε*′ displays a hump in the low temperature region and the hump temperature increases with frequency, implying a relaxor-like behavior of the dielectric property [14]. However, the magnetic field

at temperatures *T* < *T*\* (*TP* > *T*\* > *T*C).

106 Magnetic Spinels- Synthesis, Properties and Applications

**4. Colossal magnetocapacitance in CdCr2S4**

of 4.5 T still has no obvious effect on either *ε′* or *σ*′.

**Figure 6.** Temperature dependence of dielectric constant (upper frames) and *ac*-conductivity (lower frames) for the asprepared and annealed CdCr2S4 samples. Inset of (b) and (d) show temperature dependence of magnetization and resistivity in magnetic field of 0 and 4.5 T for annealed CdCr2S4, respectively [46].

**Figure 7.** Temperature dependence of dielectric constant (upper frames) and *ac*-conductivity (lower frames) for the asprepared and annealed Cd0.97In0.03Cr2S4 samples. Inset of (b) shows the temperature dependence of magnetization [46].

In contrast, for the Cd0.97In0.03Cr2S4 sample annealed at 380°C (**Figure 7(c**, **d)**), a strong upturn of *ε*′ is clearly observed with decreasing temperature near *T*C. *σ*′ has a similar temperature dependence as *ε*′. The external magnetic field of 4.5 T does not change the shape of *ε*′-*T* and *σ*′-*T* curves, but makes the upturn of *ε*′ and *σ*′ shifting toward higher temperatures. Magnetocapacitance, defined as MC = (*ε*′(4.5 T) − *ε*′(0 T))/*ε*′(0 T), reaches up to 290% at 1 kHz and 1950% at 600 kHz (**Figure 8(a)**). The sample annealed at 800°C has similar temperature dependence of *ε*′ and *σ*′ as the sample annealed at 380°C, while has a much higher *ε*′ and *σ*′, and a lower MC value (reaches up to 145% at 1 kHz and 104% at 600 kHz, see **Figure 8(c)**). A clear feature in **Figures 6(c**, **d)**, and **7(c**, **f)** is that the appearance of CMC effect is accompanied by the field-enhanced ac conductivity. The inset of **Figure 6(d)** shows the temperature dependence of DC-resistivity under 0 T and 4.5 T for the annealed CdCr2S4 sample. In accordance with the field independence of the *ac*-conductivity, the application of 4.5 T magnetic field has no evident influence on the DC-resistivity. Upon cooling, the DC-resistivity increases monotonously as a typical semiconductor behavior in the whole temperature range measured. However, as seen in **Figure 8(b**, **d)**, the temperature dependence of DC-resistivity for the annealed Cd0.97In0.03Cr2S4 samples is quite different from that of CdCr2S4. For annealed Cd0.97In0.03Cr2S4, the zero-field resistivity first increases with decreasing temperature. After reaching up to a maximum near *T*C, the resistivity decreases abruptly, indicating the occurrence of insulator-metal transition. Upon further cooling to the low temperature region, the resistivity increases again. Being correlated to the insulator-metal transition around *T*C, the external magnetic field of 4.5 T makes the resistivity peak moving to a higher temperature and dramatically depresses the peak value. Magnetoresistance, defined as MR = (*ρ*(0 T) − *ρ*(4.5 T))/*ρ*(0 T), reaches up to about 95% for the sample annealed at 380°C and 93% for the sample annealed at 800°C, much higher than the value of the most-investigated CMR material FeCr2S4, see the insets of **Figure 8(b**, **d)** [5, 31].

**Figure 8.** Temperature dependence of magnetocapacitance (upper frames) and resistivity (lower frames) for annealed Cd0.97In0.03Cr2S4. Insets of (b) and (d) display the magnetoresistance of the samples annealed at 380°C (left) and 800°C (right), respectively [46].

The appearance of CMC in the CdCr2S4 system is always accompanied by CMR. To confirm that the CMC can be described by a combination of CMR and Maxwell-Wagner effects, the impedance spectroscopy of Cd0.97In0.03Cr2S4 annealed at 380°C is fitted to a Maxwell-Wagner equivalent circuit. The impedance spectroscopy is converted from capacitance and dielectric loss tangent in the frequency range from 100 Hz to 600 kHz. The circuit consists of two subcircuits in series, each containing a resistor (*R*) and a capacitor (*C*) in parallel, as depicted in the inset of **Figure 9(a)**. *Z* is better described by using the Cole-Cole equation: *Z* = *R*/(1+ (*iωRC*)*<sup>n</sup>*), (0 ≤ *n* ≤ 1) [47, 48]. The fitting was performed with all parameters unlocked. Take the data under zero magnetic field for the Cd0.97In0.03Cr2S4 sample annealed at 380°C for example. The impedance spectroscopy can be fitted well in the temperature range from 79 K to 189 K, see the solid lines in **Figure 9(a)**. The temperature-dependent total resistance *R*1 + *R*2 derived from the fitting coincides with the temperature dependence of the measured DC resistance, as shown in **Figure 9(b)**.

1950% at 600 kHz (**Figure 8(a)**). The sample annealed at 800°C has similar temperature dependence of *ε*′ and *σ*′ as the sample annealed at 380°C, while has a much higher *ε*′ and *σ*′, and a lower MC value (reaches up to 145% at 1 kHz and 104% at 600 kHz, see **Figure 8(c)**). A clear feature in **Figures 6(c**, **d)**, and **7(c**, **f)** is that the appearance of CMC effect is accompanied by the field-enhanced ac conductivity. The inset of **Figure 6(d)** shows the temperature dependence of DC-resistivity under 0 T and 4.5 T for the annealed CdCr2S4 sample. In accordance with the field independence of the *ac*-conductivity, the application of 4.5 T magnetic field has no evident influence on the DC-resistivity. Upon cooling, the DC-resistivity increases monotonously as a typical semiconductor behavior in the whole temperature range measured. However, as seen in **Figure 8(b**, **d)**, the temperature dependence of DC-resistivity for the annealed Cd0.97In0.03Cr2S4 samples is quite different from that of CdCr2S4. For annealed Cd0.97In0.03Cr2S4, the zero-field resistivity first increases with decreasing temperature. After reaching up to a maximum near *T*C, the resistivity decreases abruptly, indicating the occurrence of insulator-metal transition. Upon further cooling to the low temperature region, the resistivity increases again. Being correlated to the insulator-metal transition around *T*C, the external magnetic field of 4.5 T makes the resistivity peak moving to a higher temperature and dramatically depresses the peak value. Magnetoresistance, defined as MR = (*ρ*(0 T) − *ρ*(4.5 T))/*ρ*(0 T), reaches up to about 95% for the sample annealed at 380°C and 93% for the sample annealed at 800°C, much higher than the value of the most-investigated CMR material

**Figure 8.** Temperature dependence of magnetocapacitance (upper frames) and resistivity (lower frames) for annealed Cd0.97In0.03Cr2S4. Insets of (b) and (d) display the magnetoresistance of the samples annealed at 380°C (left) and 800°C

The appearance of CMC in the CdCr2S4 system is always accompanied by CMR. To confirm that the CMC can be described by a combination of CMR and Maxwell-Wagner effects, the impedance spectroscopy of Cd0.97In0.03Cr2S4 annealed at 380°C is fitted to a Maxwell-Wagner equivalent circuit. The impedance spectroscopy is converted from capacitance and dielectric loss tangent in the frequency range from 100 Hz to 600 kHz. The circuit consists of two

FeCr2S4, see the insets of **Figure 8(b**, **d)** [5, 31].

108 Magnetic Spinels- Synthesis, Properties and Applications

(right), respectively [46].

**Figure 9.** (a) The complex impedance plot at 90, 130 and 170 K for the Cd0.97In0.03Cr2S4 sample annealed at 380°C. The solid line is the fitting result based on the equivalent circuit displayed in the inset. (b) Temperature dependence of the fitted resistance and measured DC resistance (multiplied by 0.59) [49].

The perfect match between the resistance derived from the impedance spectroscopy and the DC resistance strongly suggests that the annealed Cd0.97In0.03Cr2S4sample contains two components with different electrical response. These two components can be a sample and an electrode, or a grain and a grain boundary. In these cases, an applied bias voltage can change the capacitance and the ac conductance [50–52]. Moreover, Hemberger et al. have experimentally excluded any electrode effects on the magnetodielectric response and excluded any nonhomogeneous impurity distribution in their SC CdCr2S4 [42, 45]. Thus, CMC effect could not be attributed to the extrinsic Maxwell-Wagner effect. In phase-separated manganite, strong magnetodielectric effect is resulted from the scenario of phase separation [53–56]. The thermoelectric-power and ESR measurements reveal the existence of magnetic polarons in the annealed Cd0.97In0.03Cr2S4 sample [49]. As is discussed in the above section, magnetic polaron is similar as the presence of the FM clusters embedded in PM matrix, indeed a kind of phase separation in nature [24, 57, 58]. For the exchange interaction with localized spins, the energy of the conduction electron in the FM cluster is smaller than that in the PM host, which results in a nanoscale charge and phase separation [57, 58]. Upon cooling, magnetic polarons grow in size, as a consequence, their overlap induces larger metallic clusters and finally a percolative metallic filament. After the insulator-metal transition, the coexistence of FM metallic and PM insulating phases is replaced by a complete FM order founded in all the regions. The interfacial polarization or space-charge yielded by the mixture of insulating and metallic regions would cause a dielectric response, which is intrinsic to the material. Therefore, the dielectric response can be attributed to a combination of magnetoresistance and an intrinsic Maxwell-Wagner effect, as observed in the phase-separated manganite [53–56].

## **5. Negative thermal expansion in ZnCr2Se4**

Recently, ZnCr2Se4 has been observed to display NTE and a large magnetostriction [2]. To study the very origin of NTE, a set of experimental techniques is utilized to probe the spin-lattice correlation in ZnCr2Se4. **Figure 10(a)** shows the temperature dependence of lattice constant *a*. With decreasing temperature, *a* first decreases rapidly and then manifests a NTE behavior below about *T*E = 60 K. Upon further cooling below 20 K, splitting of several peaks in XRD spectra is observed. **Figure 10(b)** presents the magnetization versus *T* at low-applied magnetic field of 100 Oe. A fitting of the inverse susceptibility 1/*χ* according to the PM Curie-Weiss (CW) law 1/*χ* = (*T* – ΘCW0)/*C* is shown in **Figure 10(c)**. A large positive CW temperature ΘCW0 = 85 K and the coefficient*C* = 3.74 are obtained. The large positive CW temperature implies a dominant FM exchange interaction; however, the compound shows an AFM ordering at low temperatures. On the other hand, both the constant *g*-factor and linear behavior of peak-to-peak linewidth (Δ*HPP*) in the ESR spectrum evidence a well-defined PM state at least above 100 K [59]. Thus, the inverse susceptibility should be described by the PM CW law down to this temperature. However, it departs from the linear behavior at a temperature as high as about 180 K, see **Figure 10(c)**. Recalling the fitting process in **Figure 10(c)**, a constant CW temperature ΘCW0 has been assumed, that is, a constant magnetic exchange interaction *J*. In addition, the nearest neighbor FM Cr-Se-Cr and other neighbor AFM Cr-Se-Zn-Se-Cr super-exchange interactions depend strongly on the lattice constant [1]. It means that the total *J* may change since a decreases dramatically upon cooling. Accordingly, the traditional CW behavior should be modified within the present case. In specific, one should take a variable ΘCW (or *J*) as a function of *T* or *a* into account.

In AFM spinel oxides, the CW temperature changes exponentially with the lattice parameter [60]. Naturally, an empirical description of ΘCW(*T*) = ΘCW0 – *Θ*\*e−*<sup>T</sup>*/*<sup>β</sup>* is postulated. The fitting of the inverse susceptibility above 100 K using the modified CW behavior 1/*χ*= (*T* – ΘCW(*T*))/*C* is exhibited in **Figure 11(a)**. The parameters are *Θ* = 226 and *β* = 45. Furthermore, a remarkable deviation below 100 K in blue short-dashed line indicates the appearance of the effective internal field originating from FM clusters. Next, based on the obtained *Θ* and *β*, ΘCW(T) is extrapolated to low temperatures as exhibited in **Figure 11(b)**. It shows a derivation at about 180 K from the nearly constant value. With further lowering temperature, it decreases faster and faster and below *T* ≈ 45 K, ΘCW(T) even becomes negative. These features may interpret qualitatively the fact that ZnCr2Se4 is dominated by ferromagnetic exchange interaction but orders at low temperatures antiferromagnetically. Since the exchange integral and the CW temperature are linked by *J*(*T*) ∝ ΘCW(T) [*J*(*a*) ∝ ΘCW(*a*)], we will use *J*(*T*) [*J*(*a*)] instead in the following discussion. Given that *J* is changeable, magnetic exchange and lattice elastic energies can link effectively with each other via magnetoelastic coupling. The free energy *F* in a magnetoelastic system is expressed as:

polarization or space-charge yielded by the mixture of insulating and metallic regions would cause a dielectric response, which is intrinsic to the material. Therefore, the dielectric response can be attributed to a combination of magnetoresistance and an intrinsic Maxwell-Wagner

Recently, ZnCr2Se4 has been observed to display NTE and a large magnetostriction [2]. To study the very origin of NTE, a set of experimental techniques is utilized to probe the spin-lattice correlation in ZnCr2Se4. **Figure 10(a)** shows the temperature dependence of lattice constant *a*. With decreasing temperature, *a* first decreases rapidly and then manifests a NTE behavior below about *T*E = 60 K. Upon further cooling below 20 K, splitting of several peaks in XRD spectra is observed. **Figure 10(b)** presents the magnetization versus *T* at low-applied magnetic field of 100 Oe. A fitting of the inverse susceptibility 1/*χ* according to the PM Curie-Weiss (CW) law 1/*χ* = (*T* – ΘCW0)/*C* is shown in **Figure 10(c)**. A large positive CW temperature ΘCW0 = 85 K and the coefficient*C* = 3.74 are obtained. The large positive CW temperature implies a dominant FM exchange interaction; however, the compound shows an AFM ordering at low temperatures. On the other hand, both the constant *g*-factor and linear behavior of peak-to-peak linewidth (Δ*HPP*) in the ESR spectrum evidence a well-defined PM state at least above 100 K [59]. Thus, the inverse susceptibility should be described by the PM CW law down to this temperature. However, it departs from the linear behavior at a temperature as high as about 180 K, see **Figure 10(c)**. Recalling the fitting process in **Figure 10(c)**, a constant CW temperature ΘCW0 has been assumed, that is, a constant magnetic exchange interaction *J*. In addition, the nearest neighbor FM Cr-Se-Cr and other neighbor AFM Cr-Se-Zn-Se-Cr super-exchange interactions depend strongly on the lattice constant [1]. It means that the total *J* may change since a decreases dramatically upon cooling. Accordingly, the traditional CW behavior should be modified within the present case. In specific, one should take a variable ΘCW (or *J*) as a function of *T* or

In AFM spinel oxides, the CW temperature changes exponentially with the lattice parameter

the inverse susceptibility above 100 K using the modified CW behavior 1/*χ*= (*T* – ΘCW(*T*))/*C* is exhibited in **Figure 11(a)**. The parameters are *Θ* = 226 and *β* = 45. Furthermore, a remarkable deviation below 100 K in blue short-dashed line indicates the appearance of the effective internal field originating from FM clusters. Next, based on the obtained *Θ* and *β*, ΘCW(T) is extrapolated to low temperatures as exhibited in **Figure 11(b)**. It shows a derivation at about 180 K from the nearly constant value. With further lowering temperature, it decreases faster and faster and below *T* ≈ 45 K, ΘCW(T) even becomes negative. These features may interpret qualitatively the fact that ZnCr2Se4 is dominated by ferromagnetic exchange interaction but orders at low temperatures antiferromagnetically. Since the exchange integral and the CW temperature are linked by *J*(*T*) ∝ ΘCW(T) [*J*(*a*) ∝ ΘCW(*a*)], we will use *J*(*T*) [*J*(*a*)] instead in the following discussion. Given that *J* is changeable, magnetic exchange and lattice elastic energies can link

is postulated. The fitting of

[60]. Naturally, an empirical description of ΘCW(*T*) = ΘCW0 – *Θ*\*e−*<sup>T</sup>*/*<sup>β</sup>*

effect, as observed in the phase-separated manganite [53–56].

**5. Negative thermal expansion in ZnCr2Se4**

110 Magnetic Spinels- Synthesis, Properties and Applications

*a* into account.

**Figure 10.** (a) Temperature dependent lattice parameter *a* versus *T* for ZnCr2Se4. (b) Low temperature dependence of the magnetization *M* at 100 Oe. (c) A Curie-Weiss fitting of the inverse susceptibility [59].

**Figure 11.** (a) A fitting of the inverse susceptibility above 100 K in red solid line using 1/*χ* = (*T* – ΘCW(*T*))/*C* taking a temperature or lattice constant *a* dependent CW temperature into account. The short-dashed blue line is an extension of the fitting to low temperatures. (b) ΘCW versus *T* and the red dashed line indicates ΘCW = 0 at 45 K [59].

$$F(T) = -J\left(T\right)\sum\_{y} \overline{S\_i} \cdot \overline{S\_j} + \frac{1}{2} N o \sigma^2 \Delta^2 \left(T\right) - T \cdot S\left(T\right) \tag{2}$$

where *N* is the number of the ion sites, *ω* is the averaged vibrational angular frequency, and is the averaged strain relative to the equilibrium lattice constant. The first term is exchange energy (*E*ex) as a function of *J*, the second is lattice elastic energy (*E*el) related mainly to the lattice parameter *a* (or equivalent *T*), and the last is the entropy. From the above equation, if the system stays at an ideal PM state, then *E*ex = 0. So *E*ex and *E*el will show no coupling.

When the system stays in FM state with a changeable *J*, there may exist a competition between *E*ex and *E*el since the former is negative while the latter always is positive. Indeed, it has been concluded above that *J* decreases exponentially [**Figure 11(a)**] and some FM clusters form gradually below 100 K. Therefore, the concomitant decrease of *J* and *a* causes an increasing *E*ex but decreasing *E*el in the FM clusters. At some critical point, a totally compensation between them may present. If a further decreases upon cooling, the variation of *E*ex would gradually exceed that of *E*el in magnitude. Especially when *J* drops sharply with respect to *a*, say here at *T*E, a tiny decrement of *a* will give rise to a dramatic increment of *E*ex, whereas *E*el keeps nearly constant. The state in a system subjected to stimuli, such as cooling, always tends to develop toward one that can lower *F*. In this sense, it is favorable to lowering *F* by expanding the lattice parameter *a* to increase *J* (*J*> 0), and thereby to decrease *E*ex due to its negative value, at the same time at a cost of small increases of *E*el in magnitude. This means that a NTE of the lattice originating from the FM clusters with an exponentially changeable *J* is expected. It is noted that when applying a magnetic field to the system in the NTE temperature region, magnitude of NTE enhances [2]. This is because the size or population of the FM clusters increases when applying a magnetic field. On the contrary, when an AFM ordering appears, *J* becomes negative and the condition to stimulate NTE is not met any more. Normal thermal expansion upon cooling results in a simultaneous decreasing of *E*ex and *E*el, which is consistent to lowering *F*. In fact, a normal expansion feature is observed below *T*<sup>N</sup> [2]. It should be noted that the existence of NTE evidences in turn that *J* is changeable [2, 61]. If *J* keeps constant in a FM cluster, *E*ex will be almost constant and a normal thermal expansion of the lattice alone can give rise to a decrease of *E*el and of *F* sufficiently.

The thermal expansion data for ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) SC samples is represented as the function of *δ* = [*L*(*T*) − *L*0]/*L*0 from 4 K to 300 K in **Figure 12(a)**, where *L*0 is the length of the sample at room temperature. For ZnCr2Se4, as *T* is lowered, *δ* first decreases monotonically and reaches a minimum at *T*m~ 50 K. Then *δ* begins to increase, followed by a steep downturn upon further cooling across *T*N. For the S-doped samples, the striction below *T*<sup>N</sup> becomes gentler, while the temperature region of the NTE is expanded. As seen from the inset of **Figure 12(a)**, *T*<sup>N</sup> moves to lower temperatures with increasing S content while *T*<sup>m</sup> shifts oppositely. To further probe the nature of spin-lattice coupling in the complex magnetic state, the field dependence of both magnetization and magnetostriction *δ* at 5 K for all the ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) samples are illustrated in **Figure 12(b**, **c)**. *δ* is defined as *δ* = [*L*(*H*) − *L*(0)]/*L*(0), and *L*(0) is the length of the sample at zero field. Due to strong spin-lattice coupling, a one-to-one correlation between *M*-*H* and *δ*-*H* is clearly reflected in **Figure 12(b**, **c)**. At both of the characteristic fields of *H*C1 and *H*C2, *δ* also displays an anomaly. Being associated to domain reorientation, hysteresis is also observed below *H*C1 as the magnetic field returns to zero, see **Figure 12(b**, **c)**. For *x* = 0.05 and 0.10, field dependence of magnetization is still inconsistent with the magnetostriction data. With increasing S content, the hysteresis behavior below *H*C1 wanes in both *M*-*H* and *δ*-*H*, and completely vanishes at *x* =

0.10 [9]. In addition, the magnetization and magnetostriction data are both suppressed by an order of magnitude.

energy (*E*ex) as a function of *J*, the second is lattice elastic energy (*E*el) related mainly to the lattice parameter *a* (or equivalent *T*), and the last is the entropy. From the above equation, if the system stays at an ideal PM state, then *E*ex = 0. So *E*ex and *E*el will show no coupling.

When the system stays in FM state with a changeable *J*, there may exist a competition between *E*ex and *E*el since the former is negative while the latter always is positive. Indeed, it has been concluded above that *J* decreases exponentially [**Figure 11(a)**] and some FM clusters form gradually below 100 K. Therefore, the concomitant decrease of *J* and *a* causes an increasing *E*ex but decreasing *E*el in the FM clusters. At some critical point, a totally compensation between them may present. If a further decreases upon cooling, the variation of *E*ex would gradually exceed that of *E*el in magnitude. Especially when *J* drops sharply with respect to *a*, say here at *T*E, a tiny decrement of *a* will give rise to a dramatic increment of *E*ex, whereas *E*el keeps nearly constant. The state in a system subjected to stimuli, such as cooling, always tends to develop toward one that can lower *F*. In this sense, it is favorable to lowering *F* by expanding the lattice parameter *a* to increase *J* (*J*> 0), and thereby to decrease *E*ex due to its negative value, at the same time at a cost of small increases of *E*el in magnitude. This means that a NTE of the lattice originating from the FM clusters with an exponentially changeable *J* is expected. It is noted that when applying a magnetic field to the system in the NTE temperature region, magnitude of NTE enhances [2]. This is because the size or population of the FM clusters increases when applying a magnetic field. On the contrary, when an AFM ordering appears, *J* becomes negative and the condition to stimulate NTE is not met any more. Normal thermal expansion upon cooling results in a simultaneous decreasing of *E*ex and *E*el, which is consistent to lowering *F*. In fact, a normal expansion feature is observed below *T*<sup>N</sup> [2]. It should be noted that the existence of NTE evidences in turn that *J* is changeable [2, 61]. If *J* keeps constant in a FM cluster, *E*ex will be almost constant and a normal thermal expansion of the lattice alone can give rise to

The thermal expansion data for ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) SC samples is represented as the function of *δ* = [*L*(*T*) − *L*0]/*L*0 from 4 K to 300 K in **Figure 12(a)**, where *L*0 is the length of the sample at room temperature. For ZnCr2Se4, as *T* is lowered, *δ* first decreases monotonically and reaches a minimum at *T*m~ 50 K. Then *δ* begins to increase, followed by a steep downturn upon further cooling across *T*N. For the S-doped samples, the striction below *T*<sup>N</sup> becomes gentler, while the temperature region of the NTE is expanded. As seen from the inset of **Figure 12(a)**, *T*<sup>N</sup> moves to lower temperatures with increasing S content while *T*<sup>m</sup> shifts oppositely. To further probe the nature of spin-lattice coupling in the complex magnetic state, the field dependence of both magnetization and magnetostriction *δ* at 5 K for all the ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) samples are illustrated in **Figure 12(b**, **c)**. *δ* is defined as *δ* = [*L*(*H*) − *L*(0)]/*L*(0), and *L*(0) is the length of the sample at zero field. Due to strong spin-lattice coupling, a one-to-one correlation between *M*-*H* and *δ*-*H* is clearly reflected in **Figure 12(b**, **c)**. At both of the characteristic fields of *H*C1 and *H*C2, *δ* also displays an anomaly. Being associated to domain reorientation, hysteresis is also observed below *H*C1 as the magnetic field returns to zero, see **Figure 12(b**, **c)**. For *x* = 0.05 and 0.10, field dependence of magnetization is still inconsistent with the magnetostriction data. With increasing S content, the hysteresis behavior below *H*C1 wanes in both *M*-*H* and *δ*-*H*, and completely vanishes at *x* =

a decrease of *E*el and of *F* sufficiently.

112 Magnetic Spinels- Synthesis, Properties and Applications

**Figure 12.** (a) The thermal expansion plotted as *δ* = [*L*(*T*) − *L*0]/*L*0 for SC ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) from 5 K to 300 K, where *L*0 is the length of the sample in a paramagnetic state at 300 K. The inset shows the enlarged view of the lowtemperature region. (b) Magnetic field dependence of magnetization; (c) Magnetostriction plotted as *δ* = [*L*(*H*) − *L*(0)]/ *L*(0) at 5 K for SC ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1), where *L*(0) is the length of each ZnCr2(Se1−*x*S*x*)4 (0 ≤ *x* ≤ 0.1) sample at zero field. (d) The variable CW temperature plotted as ΘCW (*T*) versus *T* [9].

To investigate the NTE and magnetostriction in S-substituted samples, the inverse susceptibility was analyzed by the same method as is proposed above, which is shown in **Figure 12(d)** [59]. For ZnCr2Se4, ΘCW (*T*) drops dramatically and changes sign at 43 K, close to the onset temperature of NTE. The substitution of S for Se drives ΘCW0 to lower temperature on account of an enhancement of the AFM exchange interaction, while the temperature corresponding to the sign change in ΘCW (*T*) is increased. It could explain why the temperature region of the NTE is extended in ZnCr2(Se1−*x*S*x*)4 (0 < *x* ≤ 0.1) samples. The substitution of sulfur for selenium not only enhances the AFM exchange interaction, but also leads to a Cr-Cr bond disorder [9]. The bond disorder frustrates the spins and finally leads to a spin-glass state. In a spin-glass state, since the spin arranges or freezes randomly upon cooling to lower temperature, the magnetic exchange and lattice elastic energy are decoupled. Note that, in the S-substituted samples, potential striction or shrinkage of the lattice can still be observed upon cooling across *T*N, which implies that a partial long-range AFM ordering still manifests and coexists with the spin-glass state.

## **6. Complex orbital states in spinel FeCr2S4**

Due to strong frustration, the spinel FeCr2S4 not only shows the fascinating CMR effect, but also displays complex orbital states [12, 13]. Recently, it was reported to display the orbital glass state in SC samples, while it displays orbital ordering in PC ones [12, 13]. In FeCr2S4, the Fe2+ ion is tetrahedrally coordinated by the sulfur ions, with an electronic configuration 3 2 3 and *S* = 2, is a typical JT active. Thus, it might induce long-range orbital order at low temperatures [62, 63]. In addition, the diamond lattice formed by Fe ions is geometrically frustrated for the orbital degrees of freedom [12, 13]. Thus, Fichtl et al. proposed two possible explanations to interpret the discrepancy of different orbital states in FeCr2S4 [12]. One is that the orbital glass state is attributed to geometric frustration in the SC, and broken in the PC by marginal disorder. Alternatively, the orbital ordering in the SC is suppressed by small disorder (such as chlorine defects from the growth process). To verify the role of disorder in these two possibilities, the physical properties of some SC and doped PC FeCr2S4 are presented in detail next.

**Figures 13(a)** and **14** display the magnetization as a function of temperature obtained in ZFC and FC processes with *H* = 0.005 T. All samples display clear anomalies around 65–75 K and irreversibility between ZFC and FC curves. The cusp-like anomaly was early correlated to an abrupt increase of magnetic anisotropy below *T*<sup>m</sup> ~ 70 K, and recently attributed to a spinreorientation transition associated with the onset of short-range orbital ordering [64, 65]. Moreover, the PC FeCr2S4 displays a step-like anomaly in the magnetization around *T*OO ~ 9 K in **Figure13(a)**. For the other samples, the transition is replaced by a smooth temperature dependence, which is shown in the insets of **Figure 14**. The step-like anomaly for PC and smooth temperature dependence for other ones can be related to the orbital-ordering (OO) transition and orbital glass state, respectively [66]. A similar temperature-dependent magnetization between SC and doped PC samples suggests that the orbital order might also be frozen in these samples. Temperature dependence of specific heat for PC FeCr2S4 is shown in **Figure 13(b)**. It displays a well-defined λ-type anomaly around 9 K, indicative of the OO transition, which is consistent with the step-like transition in magnetization [12, 13]. For the other samples, the λ-type anomaly is entirely inhibited and becomes a broad hump, see **Figure 14(e)**. In addition, as *T* is lowered below 2 K, the heat capacity approaches zero following a strict *T*<sup>2</sup> -dependence in the insets of **Figure 14(e)**. In contrast, the specific heat of PC deviates from the linear behavior in low temperatures below 2 K, shown in the inset of **Figure 13(b)**. The earlier reports pointed out that the phonon and magnon contribution to the specific heat of SC could be ignorable as compared to the orbital contribution at ultra-low temperatures [12, 13]. Thus, the existence of the orbital glass state in both SC and doped samples is plausible, since heat capacity of orbital order suppressed by random fields obeys the *T*<sup>2</sup> -dependence predicted by the theoretical calculation [67]. Clearly, all the results reveal that the orbital moment has been frozen into the orbital glass state in the SC and doped PC samples.

For a different orbital state, the orientation of the orbital is coupled to the elastic response of the ionic lattice via electron-phonon interaction, and therefore a different orbital state is accompanied by a different charge distribution [68]. The resistivity curves in the function of ln *ρ*-1000/*T* and ln *ρ*-(1000/*T*)1/4 are shown in **Figures 13(c)** and **15**, respectively. The conduction mechanism for PC FeCr2S4 has been studied in detail in the previous section. In the low temperatures below 37 K, the resistivity could be better described by a semiconductor-like behavior. Upon warming, a curvature emerges, which might be related to the formation of short-range orbital order state [12]. For the other samples, the Mott's variable-range hopping is more appropriate to fit the feature of resistivity. As we know, for variable-range hopping, it is necessary that the system exists random potential fluctuations, being related to the degrees of disorder [32]. Hence, the presence of random potential could be the reason for the emergence of orbital glass state [12, 13].

**6. Complex orbital states in spinel FeCr2S4**

114 Magnetic Spinels- Synthesis, Properties and Applications

strict *T*<sup>2</sup>

Due to strong frustration, the spinel FeCr2S4 not only shows the fascinating CMR effect, but also displays complex orbital states [12, 13]. Recently, it was reported to display the orbital glass state in SC samples, while it displays orbital ordering in PC ones [12, 13]. In FeCr2S4, the

Fe2+ ion is tetrahedrally coordinated by the sulfur ions, with an electronic configuration

and *S* = 2, is a typical JT active. Thus, it might induce long-range orbital order at low temperatures [62, 63]. In addition, the diamond lattice formed by Fe ions is geometrically frustrated for the orbital degrees of freedom [12, 13]. Thus, Fichtl et al. proposed two possible explanations to interpret the discrepancy of different orbital states in FeCr2S4 [12]. One is that the orbital glass state is attributed to geometric frustration in the SC, and broken in the PC by marginal disorder. Alternatively, the orbital ordering in the SC is suppressed by small disorder (such as chlorine defects from the growth process). To verify the role of disorder in these two possibilities, the physical properties of some SC and doped PC FeCr2S4 are presented in detail next. **Figures 13(a)** and **14** display the magnetization as a function of temperature obtained in ZFC and FC processes with *H* = 0.005 T. All samples display clear anomalies around 65–75 K and irreversibility between ZFC and FC curves. The cusp-like anomaly was early correlated to an abrupt increase of magnetic anisotropy below *T*<sup>m</sup> ~ 70 K, and recently attributed to a spinreorientation transition associated with the onset of short-range orbital ordering [64, 65]. Moreover, the PC FeCr2S4 displays a step-like anomaly in the magnetization around *T*OO ~ 9 K in **Figure13(a)**. For the other samples, the transition is replaced by a smooth temperature dependence, which is shown in the insets of **Figure 14**. The step-like anomaly for PC and smooth temperature dependence for other ones can be related to the orbital-ordering (OO) transition and orbital glass state, respectively [66]. A similar temperature-dependent magnetization between SC and doped PC samples suggests that the orbital order might also be frozen in these samples. Temperature dependence of specific heat for PC FeCr2S4 is shown in **Figure 13(b)**. It displays a well-defined λ-type anomaly around 9 K, indicative of the OO transition, which is consistent with the step-like transition in magnetization [12, 13]. For the other samples, the λ-type anomaly is entirely inhibited and becomes a broad hump, see **Figure 14(e)**. In addition, as *T* is lowered below 2 K, the heat capacity approaches zero following a


from the linear behavior in low temperatures below 2 K, shown in the inset of **Figure 13(b)**. The earlier reports pointed out that the phonon and magnon contribution to the specific heat of SC could be ignorable as compared to the orbital contribution at ultra-low temperatures [12, 13]. Thus, the existence of the orbital glass state in both SC and doped samples is plausible,

predicted by the theoretical calculation [67]. Clearly, all the results reveal that the orbital

For a different orbital state, the orientation of the orbital is coupled to the elastic response of the ionic lattice via electron-phonon interaction, and therefore a different orbital state is accompanied by a different charge distribution [68]. The resistivity curves in the function of ln *ρ*-1000/*T* and ln *ρ*-(1000/*T*)1/4 are shown in **Figures 13(c)** and **15**, respectively. The conduction

since heat capacity of orbital order suppressed by random fields obeys the *T*<sup>2</sup>

moment has been frozen into the orbital glass state in the SC and doped PC samples.

3 2 3


**Figure 13.** (a) Temperature dependence of ZFC (red circle) and FC (blue circle) magnetization in *H* = 0.005 T for PC FeCr2S4. The inset shows an enlarged view at low temperatures. (b) The specific heat plotted as *CP*/*T* versus *T* for PC FeCr2S4. The inset shows an enlarged view at temperatures below 2 K. (c) Resistivity curves in the function of ln *ρ −* 1000/*T* (blue triangle) and ln *ρ*-(1000/*T*) 1/4 (red circle) for PC FeCr2S4. The solid lines are a guide to eyes [10].

**Figure 14.** Temperature dependence of magnetization at 0.005 T for (a) SC FeCr2S4, (b) FeCr1.9Al0.1S4, (c) FeCr1.95Ga0.05S4 and (d) Fe1.05Cr1.95S4. The insets show enlarged views of the magnetization at low temperatures. (e) The specific heat in the function of *CP*/*T* versus *T* for SC FeCr2S4 (red circle), FeCr1.9Al0.1S4 (blue circle), FeCr1.95Ga0.05S4 (violet triangle) and Fe1.05Cr1.95S4 (olive triangle). The insets show enlarged views below 2 K. The solid lines are a guide to eyes [10].

In conclusion, complex orbital states in FeCr2S4 are driven by the coexistence of strong electronphonon coupling and geometrical frustration. The different orbital states in PC and SC FeCr2S4 reveal the exquisite balance between frustration and strong coupling among different degrees of freedom. The magnetism, heat capacity and resistivity properties of all the samples give clear evidence that the disorder in SC and doped samples raises random potential up, freezes the orbital order and finally results in orbital glass state.

**Figure 15.** Resistivity curves in the function of ln *ρ −* 1000/*T* (blue triangle) and ln *ρ −* (1000/*T*) 1/4 (red circle) for (a) SC FeCr2S4, (b) FeCr1.9Al0.1S4, (c) FeCr1.95Ga0.05S4 and (d) Fe1.05Cr1.95S4. The solid lines are a guide to eyes [10].

### **7. Conclusion**

Due to the presence of frustration as well as strong coupling among spin, charge, orbital and lattice degrees of freedom, Cr-based chalcogenide spinels display rich physical effects and complex ground states. There is still some open questions such as the nature of spin nematic, correlation between orbital state and magnetic structure, which should be addressed in future under the conditions of high pressures and high magnetic fields.

#### **Acknowledgements**

This work is financially supported by the National Natural Science Foundation of China under Grant nos. U1332143 and 11574323.

## **Author details**

Chuan-Chuan Gu, Xu-Liang Chen and Zhao-Rong Yang\*

\*Address all correspondence to: zryang@issp.ac.cn

High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China

### **References**

In conclusion, complex orbital states in FeCr2S4 are driven by the coexistence of strong electronphonon coupling and geometrical frustration. The different orbital states in PC and SC FeCr2S4 reveal the exquisite balance between frustration and strong coupling among different degrees of freedom. The magnetism, heat capacity and resistivity properties of all the samples give clear evidence that the disorder in SC and doped samples raises random potential up,

freezes the orbital order and finally results in orbital glass state.

116 Magnetic Spinels- Synthesis, Properties and Applications

**Figure 15.** Resistivity curves in the function of ln *ρ −* 1000/*T* (blue triangle) and ln *ρ −* (1000/*T*)

under the conditions of high pressures and high magnetic fields.

Chuan-Chuan Gu, Xu-Liang Chen and Zhao-Rong Yang\*

High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China

\*Address all correspondence to: zryang@issp.ac.cn

**7. Conclusion**

**Acknowledgements**

**Author details**

Grant nos. U1332143 and 11574323.

FeCr2S4, (b) FeCr1.9Al0.1S4, (c) FeCr1.95Ga0.05S4 and (d) Fe1.05Cr1.95S4. The solid lines are a guide to eyes [10].

Due to the presence of frustration as well as strong coupling among spin, charge, orbital and lattice degrees of freedom, Cr-based chalcogenide spinels display rich physical effects and complex ground states. There is still some open questions such as the nature of spin nematic, correlation between orbital state and magnetic structure, which should be addressed in future

This work is financially supported by the National Natural Science Foundation of China under

1/4 (red circle) for (a) SC


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#### **Structure-Property Correlations and Superconductivity in Spinels Structure-Property Correlations and Superconductivity in Spinels**

Weiwei Xie and Huixia Luo Weiwei Xie and Huixia Luo

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120 Magnetic Spinels- Synthesis, Properties and Applications

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65943

#### **Abstract**

In this chapter, alternative views based on the structure have been presented in the spinel superconducting compounds, including the only oxide spinel superconductor, LiTi2 O4 , and non-oxide superconductors, CuIr2 S4 and CuV2 S4 . Inspection of the atomic arrangements, electronic structures and bonding interactions of spinel superconductor, LiTi2 O4 shows that LiTi2 O4 can be interpreted as Li-doped TiO2 , which is similar with doping Cu into TiSe2 to induce superconductivity. Different from LiTi<sup>2</sup> O4 , the electronic structures of CuIr2 S4 and CuV2 S4 indicate a distinctive way to understand them in the structural viewpoint. The *d*<sup>6</sup> electron configuration and the octahedral coordination of Ir in CuIr<sup>2</sup> S4 can be analogous to the *d*<sup>6</sup> in perovskites, which sometimes host a metal-insulator transition. However, the superconductivity in CuV2 S4 may be induced from the suppression of charge density waves. This kind of structural views will help chemists understand physical phenomena obviously more straightforward, though not sufficient, as clearly shown by the competition between each other, such as superconductivity and other structural phase transition (CDWs), oxidation fluctuation or magnsetism.

**Keywords:** superconductivity, chemical bonding, crystal structural analysis

## **1. Introduction**

Superconducting phenomenon incorporates the exact zero electrical resistance and expulsion of magnetic flux fields occurring in many solid state materials when cooling below a certain critical temperature [1]. The expulsion of the magnetic flux fields, known as Meissner effect, and zero electric resistance has tremendous applications in the fields of transportation, electricity, and so on [2]. The "ideal" superconducting materials potentially could solve the most energy problems human being is facing. Back to the discovery

and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of superconductivity in mercury in 1911, a century has passed by. However, the mechanisms of superconductivity are still undergoing extraordinary scrutiny. The conventional pictures arising from the Bardeen-Cooper-Scrieffer (BCS) theory merge the electron-phonon coupling to generate a pairing mechanism between electrons with the opposite crystal momenta that induce a superconducting state [3,4]. Derived from the BCS theory, the qualitative correlation between the superconducting critical temperature (*Tc* ) and the density of states (DOS) at the Fermi level, *N*(EF ), is *kTc* = 1.13 ħ ω exp(−1/*N*(*EF* )V), where V is a merit of the electron-phonon interaction and ω is a characteristic phonon frequency, similar to the Debye frequency [5]. According to the expression, a large density of states at Fermi level *N*(*EF* ) or electron-phonon interaction V or both leads to a higher *Tc* superconductor. Later, Eliashberg and McMillan extended the BCS theory and gave a better correspondence between experiment and prediction [6].

Until now, BCS theory is still in an even more dominant position to determine whether a superconductor will be classified as BCS-like or not. As more high temperature superconductors were discovered, more new "universal" mechanisms were sought for. However, neither BCS nor other exotic mechanisms established a relationship with the real chemical systems. Thus, the question appears whether the general statements of BCS theory can be associated with distinct chemical meanings, such as specific bonding situations, and whether the physical phenomenon of superconductivity can be interpreted from the viewpoint of chemistry.

## **2. Electron counting rules in chemistry and superconductors**

Empirical observations of the range of electron counts to specific structural compounds are widely used in chemistry to help determine and find out the empirical rules to stabilize the compounds with specific structural frameworks, such as Wades-Mingo polyhedral skeletal rules for boron cluster compounds [7], 14e rules for DNA-like helix Chimney Ladders phases [8] and Hume-Rothery rules for multi-shelled clustering γ-brass phases [9, 10]. The electronic structure calculation and the bonding schemes allow us to determine a structure's preferred electron count for most compounds, for example, take Hume-Rothery rules in complex clustering compounds. The stability ranges of complex intermetallic alloys (CMAs) are frequently identified by specific valence electron-to-atom (*e*/*a*) ratios, such as 1.617 e-/a for transition-metal-free γ-brass systems, which are generally called Hume-Rothery rules and validated by the presence of pseudogaps at the corresponding Fermi level in the calculated electronic structures [10]. Moreover, a distinctive way to count electrons is applied for the transition-metal-rich systems, such as Chimney Ladders phases, endohedral gallides superconductors, and so on [11]. For example, Ga-cluster superconductor, ReGa5 , containing 11 bonding orbitals in the cluster would be fully occupied by 22e- (Re: 7e- from 5*d* and 6*s* orbitals + 5Ga: 3e- from 4*s* and 4*p* orbitals) and the Fermi level of ReGa5 should be located in a gap or pseudo gap in the DOS [11]. Briefly, small values of density of states, *N*(*EF* ), are corresponding to the stable electronic structures in the reciprocal space and chemical compounds in the real chemistry system [12]. As we mentioned in early section, *N*(*EF* ) exists the close relationship with the superconducting critical temperatures: the larger values of *N*(*EF* ) in DOS, the higher *Tc* is likely to appear in the solid state materials. An empirical electron counting method, although this follows a different, less chemical-based electron counting process, was generated by Matthias [13]. It states that the number of valence electrons in a superconductor has lost nothing of its fundamental importance to the value of *Tc* . For the transition-metal-rich compounds with simple crystal structures, the maximum in *Tc* is seen to occur at approximately 4.7 and 6.5 valence electrons per atom [14]. The particular impressive example is the *Tc* dependence on the average number of valence electrons in A15 phases, for example, take Nb3 Ge. The valence electron concentration is calculated as follows: (5 e-/Nb × 3 Nb + 4 e-/Ge × 1 Ge)/4 = 4.75 e-/atom [15]. Similarly, 4.6 e-/atom work for (Zr/Hf)<sup>5</sup> Sb2.5Ru0.5 [16, 17]. Therefore, to increase the *Tc* in superconductivity is at a high risk of destabilizing the compounds. From the chemistry viewpoints, BCS-like superconductors need to balance the structural stability and superconducting property and result in the limited *Tc* [18]. Circumventing the inherent conflict of structural stability and superconducting critical temperatures in BCS-like superconductors would be analogous to the thermoelectric materials with a phonon glass with electron-crystal properties [19].

of superconductivity in mercury in 1911, a century has passed by. However, the mechanisms of superconductivity are still undergoing extraordinary scrutiny. The conventional pictures arising from the Bardeen-Cooper-Scrieffer (BCS) theory merge the electron-phonon coupling to generate a pairing mechanism between electrons with the opposite crystal momenta that induce a superconducting state [3,4]. Derived from the BCS theory, the quali-

of the electron-phonon interaction and ω is a characteristic phonon frequency, similar to the Debye frequency [5]. According to the expression, a large density of states at Fermi

Later, Eliashberg and McMillan extended the BCS theory and gave a better correspondence

Until now, BCS theory is still in an even more dominant position to determine whether a superconductor will be classified as BCS-like or not. As more high temperature superconductors were discovered, more new "universal" mechanisms were sought for. However, neither BCS nor other exotic mechanisms established a relationship with the real chemical systems. Thus, the question appears whether the general statements of BCS theory can be associated with distinct chemical meanings, such as specific bonding situations, and whether the physical phenomenon of superconductivity can be interpreted from the view-

Empirical observations of the range of electron counts to specific structural compounds are widely used in chemistry to help determine and find out the empirical rules to stabilize the compounds with specific structural frameworks, such as Wades-Mingo polyhedral skel-

phases [8] and Hume-Rothery rules for multi-shelled clustering γ-brass phases [9, 10]. The electronic structure calculation and the bonding schemes allow us to determine a structure's preferred electron count for most compounds, for example, take Hume-Rothery rules in complex clustering compounds. The stability ranges of complex intermetallic alloys (CMAs) are frequently identified by specific valence electron-to-atom (*e*/*a*) ratios, such as 1.617 e-/a for transition-metal-free γ-brass systems, which are generally called Hume-Rothery rules and validated by the presence of pseudogaps at the corresponding Fermi level in the calculated electronic structures [10]. Moreover, a distinctive way to count electrons is applied for the transition-metal-rich systems, such as Chimney Ladders phases, endohedral gallides

11 bonding orbitals in the cluster would be fully occupied by 22e- (Re: 7e- from 5*d* and 6*s*

corresponding to the stable electronic structures in the reciprocal space and chemical com-

in a gap or pseudo gap in the DOS [11]. Briefly, small values of density of states, *N*(*EF*

superconductors, and so on [11]. For example, Ga-cluster superconductor, ReGa5

pounds in the real chemistry system [12]. As we mentioned in early section, *N*(*EF*

orbitals + 5Ga: 3e- from 4*s* and 4*p* orbitals) and the Fermi level of ReGa5

= 1.13 ħ ω exp(−1/*N*(*EF*

) and the density of

superconductor.

, containing

) exists the

), are

should be located

)V), where V is a merit

rules for DNA-like helix Chimney Ladders

tative correlation between the superconducting critical temperature (*Tc*

**2. Electron counting rules in chemistry and superconductors**

), is *kTc*

) or electron-phonon interaction V or both leads to a higher *Tc*

states (DOS) at the Fermi level, *N*(EF

122 Magnetic Spinels- Synthesis, Properties and Applications

between experiment and prediction [6].

etal rules for boron cluster compounds [7], 14e-

level *N*(*EF*

point of chemistry.

In the past several decades, several new classes of high temperature superconductors were discovered, whose critical temperatures are way above the ones of conventional superconductors [20–23]. These discoveries give physicists hope to keep looking for the new mechanisms for superconductivity. Different from metallic superconductors, more chemistry terms can be applied for the high temperature superconductors, such as oxidation numbers, Zintl phases, valence-electron-precise systems, and so on [24, 25].

## **3. Inducing superconductivity by the suppression of charge density waves**

In the semiconductor BaBiO3 compound, the bonding interaction can be described by the formula (Ba2+)(Bi4+)(O2-)3 , Bi has the unusual oxidation state, +IV [26, 27]. At room temperature, it has the doubled perovskite unit cell and the structure distorted to monoclinic rather than being cubic. It contains two types of Bi atoms in different sized coordinated polyhedral, so the formula of BaBiO3 can be modified as (Ba2+)2 (Bi3+)(Bi5+)(O2-)6 . Now the complex structural distortion can be interpreted as the relocalization of two electrons at the Bi3+ ion with the "long pair" configuration [28]. Contradictory, the two Bi atoms show slightly different in the oxidation states (+3.9 versa +4.1) from the band structure calculation [29]. Another argument was arisen that the structural distortion, as well as the non-equivalent Bi atoms, caused by the charge density waves (CDWs) [30]. Suppression of the charge density waves in Bi oxides may induce the superconductivity. It is achieved by doping Pb4+, which has closed electron configuration and prefers a regularly coordinated environment to stabilize the structure. BaPb*<sup>x</sup>* Bi1-*<sup>x</sup>* O3-δ shows no CDWs but the superconducting transition when cooling to 13 K [31]. Another way to stabilize the regular structure is increasing the Bi5+ ions, which also has the closed electron configuration. To obtain this, K was used to partially replace Ba and K*<sup>x</sup>* Ba1-*<sup>x</sup>* BiO3 in cubic perovskite structure shows the superconducting transition around 30 K [26].

## **4. Superconductivity hosted in the specific structural frameworks**

High temperature superconductivity in ThCr2 Si2 -type iron pnictides led to numerous investigations in these compounds in the past decade [32]. However, the structure of ThCr2 Si2 -type materials hosting superconductivity could be traced back to the quaternary superconductors, LnNi2 B2 C (Ln = Ho, Er, Tm, Y and Lu) [33]. In LnNi2 B2 C, we could treat the B-C-B as a single chemical unit based on the short bonding distance and strong bonding interaction between B and C [34]. Therefore, the ionic formula of LnNi2 B2 C can be treated as Ln3+(Ni0 )2 (B2 C)3- [34]. In the viewpoint of chemistry, the large *N*(*EF* ) in LnNi2 B2 C was mainly arisen from the slight orbital distortion of B-C-B fragments. Moreover, the structure could be considered to represent the first member of a homologous series (LnC)n(Ni2 B2 ), in which the LnC block adopts to a NaCl-type packing, which naturally drove us to investigate the (LnC)2 (Ni2 B2 ), written as (LnC)(NiB), in which the ionic formula could be written as Ln3+(Ni0 )(BC)3- [33]. (BC)3- is isoelectronic with CO, and the B-C interaction rapidly changes from bonding to antibonding in addition to the dispersionless band from Ln orbital below Fermi level in LnNiBC may be the important factor to kill the superconductivity [34].

However, the "exotic" quantum mechanism for superconductivity is undergoing an unclear status even though the phenomenon has been discovered for more than a century. Superconductivity is still unpredictable currently. Condensed matter physicists try to predict superconductors based on analyzing the superconductivity through "*k*-space" pictures based on Fermi surfaces and particles interactions, that is, electron-phonon coupling [35]. Thus, there are few predictive rules from physics aspect, one of which, perhaps the most widely used, is that in intermetallic compounds of a known superconducting structure type, one can count electrons and expect to find the best superconductivity or the highest critical temperature (*Tc* ) at ~4.7 or ~6.5 valence electrons per atom—Matthias rules mentioned above [14]. However, the chemists' viewpoint is from real space such as chemical compositions and atomic structures, which play critical roles in superconductivity, rather than reciprocal space [11]. One of the chemical views to increase the occurrence of new superconducting materials is to posit that it carries out in structural families. The well-known examples are found in ThCr2 Si2 -type such as BaFe2 As2 and LnNi2 B2 C systems and perovskites like bismuth oxides, which are fairly favored by superconductivity [32]. Laves phase compounds are previously well-investigated families for hosting superconductivity among alloys [36]. Here, we analyze the structural relationship between diamond framework and spinels from a molecular perspective, then apply this connection for interpretation and prediction of other possible new superconductors adopting to spinels and their derived structures.

## **5. Calculation details**

#### **5.1. Tight-binding, linear Muffin-Tin orbital-atomic spheres approximation (TB-LMTO-ASA)**

Calculations of the electronic structures were performed by TB-LMTO-ASA using the Stuttgart code [37–39]. Exchange and correlation were treated by the local density approximation (LDA) [40]. In the ASA method, space is filled with overlapping Wigner-Seitz (WS) spheres [41]. The symmetry of the potential is considered spherical inside each WS sphere, and a combined correction is used to take into account the overlapping part, and the overlap of WS spheresis limited to no larger than 16%. The empty spheres are necessary, and the overlap between empty spheres is limited to no larger than 40%.The convergence criterion was set to 0.1 meV.A mesh of ~100 *k* points [42] in the irreducible edge of the first Brillouin zone was used to obtain all integrated values, including the density of states (DOS) and Crystal Orbital Hamiltonian Population (COHP) curves [43].

#### **5.2. WIEN2k**

**4. Superconductivity hosted in the specific structural frameworks**

gations in these compounds in the past decade [32]. However, the structure of ThCr2

Si2

materials hosting superconductivity could be traced back to the quaternary superconductors,

chemical unit based on the short bonding distance and strong bonding interaction between

orbital distortion of B-C-B fragments. Moreover, the structure could be considered to repre-

electronic with CO, and the B-C interaction rapidly changes from bonding to antibonding in addition to the dispersionless band from Ln orbital below Fermi level in LnNiBC may be the

However, the "exotic" quantum mechanism for superconductivity is undergoing an unclear status even though the phenomenon has been discovered for more than a century. Superconductivity is still unpredictable currently. Condensed matter physicists try to predict superconductors based on analyzing the superconductivity through "*k*-space" pictures based on Fermi surfaces and particles interactions, that is, electron-phonon coupling [35]. Thus, there are few predictive rules from physics aspect, one of which, perhaps the most widely used, is that in intermetallic compounds of a known superconducting structure type, one can count electrons and expect to find the best superconductivity or the highest critical temperature (*Tc*

at ~4.7 or ~6.5 valence electrons per atom—Matthias rules mentioned above [14]. However, the chemists' viewpoint is from real space such as chemical compositions and atomic structures, which play critical roles in superconductivity, rather than reciprocal space [11]. One of the chemical views to increase the occurrence of new superconducting materials is to posit

favored by superconductivity [32]. Laves phase compounds are previously well-investigated families for hosting superconductivity among alloys [36]. Here, we analyze the structural relationship between diamond framework and spinels from a molecular perspective, then apply this connection for interpretation and prediction of other possible new superconduc-

Calculations of the electronic structures were performed by TB-LMTO-ASA using the Stuttgart code [37–39]. Exchange and correlation were treated by the local density approximation

that it carries out in structural families. The well-known examples are found in ThCr2

**5.1. Tight-binding, linear Muffin-Tin orbital-atomic spheres approximation** 

B2

B2

B2

C systems and perovskites like bismuth oxides, which are fairly

B2

) in LnNi2


C can be treated as Ln3+(Ni0

C, we could treat the B-C-B as a single

C was mainly arisen from the slight

), in which the LnC block adopts

(Ni2 B2

) 2 (B2

)(BC)3- [33]. (BC)3- is iso-

Si2 -type

C)3- [34].

), written as

)

Si2 -type

High temperature superconductivity in ThCr2

124 Magnetic Spinels- Synthesis, Properties and Applications

B and C [34]. Therefore, the ionic formula of LnNi2

important factor to kill the superconductivity [34].

In the viewpoint of chemistry, the large *N*(*EF*

C (Ln = Ho, Er, Tm, Y and Lu) [33]. In LnNi2

sent the first member of a homologous series (LnC)n(Ni2

to a NaCl-type packing, which naturally drove us to investigate the (LnC)2

(LnC)(NiB), in which the ionic formula could be written as Ln3+(Ni0

LnNi2 B2

such as BaFe2

As2

**5. Calculation details**

**(TB-LMTO-ASA)**

and LnNi2

B2

tors adopting to spinels and their derived structures.

The electronic structures (density of states and band structure) of intermetallics were calculated using the WIEN2k code with spin orbital coupling, which has the full-potential linearized augmented plane wave method (FP-LAPW) with local orbitals implemented [44, 45]. For the treatment of the electron correlation within the generalized gradient approximation, the electron exchange-correlation potential was used with the parameterization by Perdew et al. (i.e. the PBE-GGA) [46]. For valence states, relativistic effects were included through a scalar relativistic treatment, and core states were treated fully relativistic [47]. The structure used to calculate the band structure was based on the single crystal data. The conjugate gradient algorithm was applied, and the energy cutoff was 500 eV. Reciprocal space integrations were completed over a 9 × 9 × 9 Monkhorst-Pack *k*-points mesh with the linear tetrahedron method. With these settings, the calculated total energy converged to less than 0.1 meV per atom.

#### **5.3. Materials projects**

The electronic structures of partial hypothetical compounds were predicted and calculated using the Materials Projects, which have been treated in the electron correlation within the generalized gradient approximation. The structure used to calculate the band structure was based on the single crystal data. The conjugate gradient algorithm was applied, and the energy cutoff was 520 eV. Reciprocal space integrations were completed over a 104 Monkhorst-Pack *k*-points mesh with the linear tetrahedron method.

## **6. Hierarchical structural interpretation of existing superconductors with spinels**

Spinels, generally formulated as A2+(B3+)2 O4 , crystallize in the cubic crystal system, with the oxide anions arranged in a cubic close-packed lattice and the cations A and B occupy the octahedral and tetrahedral sites in the lattice [48, 49]. An alternative tantalizing way to view the spinel structure is to treat spinels as void-filled cubic Laves phases, both of which exhibit some close relationships with the diamond structure. In the cubic Laves phase, MgCu2 , the Mg atom sites (Wyckoff designation 8*a*) arrange precisely into a three-dimensional (3D) diamond network. Within the voids, Cu atoms (Wyckoff designation 16*d*) form a 3D framework of vertex-sharing tetrahedra, as emphasized in **Figure 1** (Left). Thus, the Mg and Cu sites become A and B, respectively, in spinels. Furthermore, in spinels, the O atoms on 32*e* (*x, x, x*)

**Figure 1.** The structural relationship between the MgCu2 -type, cubic Laves phase structure and the spinel-type, MgAl2 O4 . *Left*: MgCu2 -type (Mg, green; Cu, purple); *right*: Spinel type MgAl2 O4 (Mg, green; Al, purple and O, red).

sites forming isolated tetrahedral were inserted into the B4 tetrahedra and center around 8*b* (½, ½, ½) sites in **Figure 1** (Right). The formation of the complete cubic unit cell from the cubic Laves phase to the spinels A8 B16O32 is, therefore, shown in **Figure 1**.

#### **6.1. Li-doped "TiO2 ": superconductivity in spinel LiTi2 O4**

Superconductivity in Li1−*<sup>x</sup>* Ti2+*<sup>x</sup>* O4 was first reported in 1973, much earlier than the discovery of high-*Tc* cuprate superconductors. The superconducting transition temperature (*Tc* ) of LiTi2 O4 is around 11 K [50]. As the first oxide superconductor with a relatively high critical temperature, LiTi2 O4 remains widely intriguing for scientists. The most frequent questions arose are why LiTi2 O4 adopts to a unique structure type, which is different from other high temperature superconducting materials, such as perovskites or cuprates. However, Li-doped TiO2 and LiTi2 O4 can be treated as the analogy between Cu-doped TiSe2 and Cu0.08TiSe2 in a certain way [51]. TiSe2 adopts to the trigonal-layered structure (1T) (S.G. P-31*m*) with charge density waves observed around 220 K, and with doping Cu, the superconductivity in Cu*<sup>x</sup>* TiSe2 appears and the charge density wave was suppressed. Similarly, for both rutile- and anatase-TiO2 , Ti and O atoms form distorted Ti@O6 octahedra; thus, there exist empty voids in the structure shown in **Figure 2a** and **b**. Based on the electronic structures of TiO2 in **Figure 3a** and **b**, both polymorphic TiO2 compounds are well-known *n*-type semiconductors with ~2eV gaps above Fermi levels [52]. Through doping with Li atom, which can be considered as the nearly free electron in solid state chemistry, the empty voids in TiO2 are occupied by the Li atoms, and the Fermi levels start lifting up and shifting to the peak in the DOS.

To confirm our assumptions, the electronic structures of LiTi<sup>2</sup> O4 are calculated using TB-LMTO-ASA with Crystal Orbital Hamilton Population (COHP) codes. In **Figure 4** (left), the DOS

sites forming isolated tetrahedral were inserted into the B4


Ti2+*<sup>x</sup>* O4

O4

**Figure 1.** The structural relationship between the MgCu2

126 Magnetic Spinels- Synthesis, Properties and Applications

and LiTi2

for both rutile- and anatase-TiO2

O4

O4

To confirm our assumptions, the electronic structures of LiTi<sup>2</sup>

in a certain way [51]. TiSe2

TiSe2

Laves phase to the spinels A8

Superconductivity in Li1−*<sup>x</sup>*

**6.1. Li-doped "TiO2**

ery of high-*Tc*

Li-doped TiO2

conductivity in Cu*<sup>x</sup>*

structures of TiO2

to the peak in the DOS.

voids in TiO2

Cu0.08TiSe2

O4

cal temperature, LiTi2

tions arose are why LiTi2

of LiTi2

*Left*: MgCu2

(½, ½, ½) sites in **Figure 1** (Right). The formation of the complete cubic unit cell from the cubic

high temperature superconducting materials, such as perovskites or cuprates. However,

P-31*m*) with charge density waves observed around 220 K, and with doping Cu, the super-

there exist empty voids in the structure shown in **Figure 2a** and **b**. Based on the electronic

*n*-type semiconductors with ~2eV gaps above Fermi levels [52]. Through doping with Li atom, which can be considered as the nearly free electron in solid state chemistry, the empty

ASA with Crystal Orbital Hamilton Population (COHP) codes. In **Figure 4** (left), the DOS

are occupied by the Li atoms, and the Fermi levels start lifting up and shifting

in **Figure 3a** and **b**, both polymorphic TiO2

**": superconductivity in spinel LiTi2**

B16O32 is, therefore, shown in **Figure 1**.

**O4**

remains widely intriguing for scientists. The most frequent ques-

can be treated as the analogy between Cu-doped TiSe2

appears and the charge density wave was suppressed. Similarly,

O4

adopts to a unique structure type, which is different from other

adopts to the trigonal-layered structure (1T) (S.G.

, Ti and O atoms form distorted Ti@O6 octahedra; thus,

cuprate superconductors. The superconducting transition temperature (*Tc*

O4

is around 11 K [50]. As the first oxide superconductor with a relatively high criti-

was first reported in 1973, much earlier than the discov-


(Mg, green; Al, purple and O, red).

tetrahedra and center around 8*b*

compounds are well-known

are calculated using TB-LMTO-

)

O4 .

and

**Figure 2.** The structure and space group connections between two types of TiO2 and Lix TiO2 . (a) The crystal structure of rutile-TiO2 . The rutile-TiO2 adopts to the primitive tetragonal structure with space group P42 /*mnm*. Each Ti atom surrounded by 6 O atoms forms the octahedral coordination. (b) The schematic picture showing the possible phase transitions when doping Li into TiO2 . (c) The space group and sub-space group relationship among TiO2 and LiTi2 O4 .

qualitative features obtained by this calculation state that are 2–6 eV below the Fermi level (*EF* ) arise primarily from valence 4*s* and 3*d* orbitals from Ti and 2*p* orbitals from O, whereas the Li 2*s* band is broadly distributed from −6 to −2 eV. The contribution of Li 2*s* electrons to the DOS curve, as shaded in **Figure 4** in black, shows it just contributes one free electron to the system rather than making any change to the DOS features of TiO2 in the diamond-like framework. The integrated DOS till the broad band gap around 1 eV below Fermi level results in the same electron counts as TiO2 . Comparing with the DOS of rutile- and anatase-TiO2 in **Figure 3**, the difference between LiTi<sup>2</sup> O4 and TiO2 is the up-lift 1 e- per formula of the Fermi level. The Fermi level for LiTi2 O4 falls just above the topmost peak of the largely Ti 3*d* bands. Therefore, we employed Local Spin Density Approximation (LSDA) to see if a magnetic moment would spontaneously develop, but the converged result yielded zero magnetic moment. This result of the unstable electronic structure gives a strong indication of the occurrence of superconductivity. The "bond energy" term is evaluated by the crystal orbital Hamilton populations

**Figure 3.** The band structures and density of states (DOS) of (a) anatase-TiO2 with ~2eV indirect band gap and (b) rutile-TiO2 with ~2eV direct band gap (generated from *Materials Projects*).

**Figure 4.** Electronic structure of spinel LiTi2 O4 . Partial DOS curves, –COHP curves and band structure of "LiTi2 O4 " obtained from non-spin-polarization (LDA). (+ is bonding/ – is anti-bonding).

(COHP) curves [53]. These curves illustrated in **Figure 4** (Middle) show that the band gap around 1eV below Fermi level corresponds to the non-bonding for the compound, similar in rutile- and anatase-TiO2 . Interestingly, there is no atomic interaction between Li and O or Li and Ti, which confirmed our claims discussed above—Li just acts as the electron-donator to change the Fermi level as well as balance the charge, and empty sphere to fill the volume, rather than giving the impact on the electronic structure including changing the atomic interactions. In –COHP, the Fermi level is located on the Ti-O anti-bonding and Ti-Ti bonding interactions, the sum of the anti-bonding and bonding effects is close to zero, which indicates the possibility of the stabilization of the compound. The strong Ti–O antibonding interactions at the Fermi level, contributing the unstable factors in the electronic structure is significant relative with the superconductivity in spinel LiTi2 O4 . Meanwhile, in the band structure of spinel LiTi2 O4 , the Fermi level locates on the saddle points around U and W points in the Brillouin zone, which is a strong evidence for the unstable electronic structure.The structural connection might also be noted from the links between the space groups in **Figure 2**. If we divided the unit cell of the spinel structure into two along ½(*a* + *b*) and ½(*a* - *b*), the cubic structure will become tetragonal, and space group will decrease from F*d*-3m to I41 /*amd*s. Furthermore, the distortion of *a* and *b* decreases the symmetry from tetragonal to orthorhombic and the space group will become I*mma* instead of I41 /*amd*s. On the other side, I*mma* is also the direct subgroup of P42 /*mnm* (rutile-TiO2 ). In summary, the structural transformation could be treated as the transition of a continuously doping Li process. When the amount of doped Li is small, the Li*x* TiO2 keeps in I41 /*amd*s. As *x* increases, the orthorhombic structure appears. When *x* is close to 0.5, the spinel phase is more favored than other phases [54].

Since the discovery of the superconductivity in spinel LiTi2 O4 , much effort has been put into finding more spinel oxide superconductors. The studies of spinel oxide superconductors endeavored for the physics community for many years. The alternative view on the spinel superconductor, LiTi2 O4 , could be considered as the electron-doping in transition metal dichalcogenides, similar with Cu-doped TiSe2 . Li-doped anatase-TiO2 crystallizes in tetragonal structure with the space group of I41 /*amd*s. With doping more electrons into the system, the structural transitions happen from tetragonal to orthorhombic to cubic. The superconductivity was arisen when doping Li to ~1/2 per f.u. and the structure adopting to the cubic spinel. Similar structural transitions from tetragonal I41 /*amd* to F*d*-3*m* occur in another spinel superconductor, CuIr2 S4 [55].

#### **6.2. Superconductivity in non-oxide spinel CuIr<sup>2</sup> S4 and CuV2 S4**

(COHP) curves [53]. These curves illustrated in **Figure 4** (Middle) show that the band gap around 1eV below Fermi level corresponds to the non-bonding for the compound, similar

O4

obtained from non-spin-polarization (LDA). (+ is bonding/ – is anti-bonding).

**Figure 3.** The band structures and density of states (DOS) of (a) anatase-TiO2

with ~2eV direct band gap (generated from *Materials Projects*).

128 Magnetic Spinels- Synthesis, Properties and Applications

TiO2

Li and Ti, which confirmed our claims discussed above—Li just acts as the electron-donator

. Interestingly, there is no atomic interaction between Li and O or

. Partial DOS curves, –COHP curves and band structure of "LiTi2

O4 "

with ~2eV indirect band gap and (b) rutile-

in rutile- and anatase-TiO2

**Figure 4.** Electronic structure of spinel LiTi2

CuIr2 S4 in the cubic structure with the space groupshows metallic properties at room temperature [56]. As the temperature decreases, CuIr2 S4 undergoes a transition from a metal to an insulator around 230 K, which is also associated with a structural change from cubic to tetragonal [57]. Interestingly, a pseudogap is situated just above in the calculated density of states (DOS). In **Figure 5** (left), the DOS shows that ~6 eV range below the Fermi level (*EF* ) arises from all of the valence Cu, Ir and S orbitals. The contribution of Cu 4*s* and 3*d* electrons to the DOS curve, as shaded in **Figure 5** in black, states the filled-up *d* electrons are delocalized and hybridized with 5*d* electrons from Ir as well as 3*p* electrons from S, which is quite different from LiTi2 O4 . To further confirm our assumptions, the bonding/anti-bonding interactions (–COHP) in CuIr2 S4 are calculated. Unlike the –COHP in LiTi2 O4 , which was dominated by Ti-O and Ti-Ti interactions, Ir-S and Cu-S interactions play the most important roles in the structural stabilization and superconducting properties in CuIr2 S4 . The band gap in LiTi2 O4 corresponds to the non-bonding boundary in LiTi2 O4 ; however, the 0–1 eV below the Fermi

**Figure 5.** Electronic structure of spinel CuIr2 S4 . Partial DOS curves, –COHP curves and band structure of "CuIr2 S4 " obtained from non-spin-polarization (LDA). (+ is bonding/ – is anti-bonding, *EF* for 53e– is set to zero).

level in CuIr2 S4 is on the mixed status of Ir-S anti-bonding and Cu-S bonding interactions. The Fermi level at anti-bonding interactions indicates the instability of electronic structure of CuIr2 S4 and the possible occurrence of superconductivity. The integrated DOS of CuIr2 S4 gives 53e- per f.u., whereas the band gap just above Fermi level corresponds to 54e- per f.u., which can be expressed with the hypothetical compound "CuIr2 S4 (1e-)" according to the Zintl-Klemm concept. The ionic formula of CuIr2 S4 can be interpreted as Cu2+(Ir3+)2 (S2-)4 (1e-), the electron configuration of Ir3+ becomes 5*d*<sup>6</sup> . Or Cu+ (Ir4+)(Ir3+)(S2-)4 (1e-) with two kinds of electron configurations of Ir, 5*d*<sup>6</sup> and 5*d*<sup>5</sup> . The coordinated environment of Ir3+ is octahedral (*Oh* ), thus, the *d* orbital will split into *e*<sup>g</sup> and *t* 2g.

It has been well known even in textbooks that molecular transition metal complexes have a gap between the *e*<sup>g</sup> and *t*2g type in *d* orbitals, which is determined by the α and π boning of the coordinated ligands. However, the band gap between the *e*<sup>g</sup> and *t*2g in *d* bands in certain solids is dependent on more complex orbital considerations. Take perovskite LaCoO3 for example, the band gap is very small, close to 0 eV, but the iso-electronic LaRhO3 has ~1.6 eV band gap. Similarly, in CuIr2 S4 , the band gap between *e*<sup>g</sup> and *t*2g is so small that the 5*d*<sup>6</sup> and 5*d*<sup>5</sup> configurations can coexist [58]. Moreover, at higher temperatures, a whole series of transformations take place triggered by thermal excitation of electrons from the valence to the conduction band. In CuIr2 S4 compound, the two possible oxidation state fluctuations of Cu+ /Cu2+ and Ir3+/Ir4+ could be related to superconductivity. The presence of a metal-insulator (M-I) transition on cooling or under pressure has been of particular interest in the heavy metal chalcogenide spinel systems to make superconductors. Based on the decreased lattice parameters, CuRh2 S4 and CuRh2 Se4 can be treated as the compressed and expanded format of CuIr2 S4 [59].

Another representative non-oxide spinel superconductor is CuV2 S4 [60]. Unlike CuIr2 S4 , the superconductivity in CuV2 S4 is induced by suppressing the CDWs rather than the metalinsulator transition in CuIr2 S4 [61]. Also, according to the Zintl-Klemm concept, the ionic formula of CuV2 S4 can be written as Cu2+(V3+)(V3+)(S2-)4 . From the electronic structural calculations of CuV2 S4 in **Figure 6**, a ~0.3 eV band gap is located at 0.6 eV below the Fermi level. The integrated DOS shows the gap responds to the 42e- (45e- for Fermi level). The band gap above Fermi level corresponds to 54e-, just as "CuIr2 S4 (1e)." The band structure indicates the similarity betweenCuV2 S4 (early transition metal, V) and LiTi2 O4 (early transition metal, Ti) and the difference between CuV<sup>2</sup> S4 (early transition metal, V) and CuIr2 S4 (late transition metal, Ir). By analogy with Jahn-Teller distortion ideas, the partially occupied bands are subject to the geometrical distortions related to a lowering of the total energy and usually termed as the instability of the Fermi surface (CDWs). A band gap may open at the Fermi level to create a semiconductor or insulator as the structure changes. From the chemistry viewpoint, the highest occupied conduction band is filled to make insulators. For example, in MoS<sup>2</sup> , the charge density waves were observed in the localized unit of S-Mo-S rather than a localized

level in CuIr2

CuIr2 S4 S4

**Figure 5.** Electronic structure of spinel CuIr2

130 Magnetic Spinels- Synthesis, Properties and Applications

configurations of Ir, 5*d*<sup>6</sup>

gap between the *e*<sup>g</sup>

and 5*d*<sup>5</sup>

Cu+

the *d* orbital will split into *e*<sup>g</sup>

eV band gap. Similarly, in CuIr2

the conduction band. In CuIr2

is on the mixed status of Ir-S anti-bonding and Cu-S bonding interactions.

(Ir4+)(Ir3+)(S2-)4

and *t*2g type in *d* orbitals, which is determined by the α and π boning of

. The coordinated environment of Ir3+ is octahedral (*Oh*

S4

can be interpreted as Cu2+(Ir3+)

. Partial DOS curves, –COHP curves and band structure of "CuIr2

for 53e–

compound, the two possible oxidation state fluctuations of

S4 gives

(1e-), the

S4 "

), thus,

for

has ~1.6

(1e-)" according to the Zintl-

is set to zero).

(1e-) with two kinds of electron

2 (S2-)4

and *t*2g in *d* bands in certain

and *t*2g is so small that the 5*d*<sup>6</sup>

The Fermi level at anti-bonding interactions indicates the instability of electronic structure of

and the possible occurrence of superconductivity. The integrated DOS of CuIr2

53e- per f.u., whereas the band gap just above Fermi level corresponds to 54e- per f.u., which

S4

It has been well known even in textbooks that molecular transition metal complexes have a

, the band gap between *e*<sup>g</sup>

/Cu2+ and Ir3+/Ir4+ could be related to superconductivity. The presence of a metal-insulator

transformations take place triggered by thermal excitation of electrons from the valence to

configurations can coexist [58]. Moreover, at higher temperatures, a whole series of

solids is dependent on more complex orbital considerations. Take perovskite LaCoO3

example, the band gap is very small, close to 0 eV, but the iso-electronic LaRhO3

. Or Cu+

can be expressed with the hypothetical compound "CuIr2

obtained from non-spin-polarization (LDA). (+ is bonding/ – is anti-bonding, *EF*

S4

 and *t* 2g.

the coordinated ligands. However, the band gap between the *e*<sup>g</sup>

S4

S4

and 5*d*<sup>5</sup>

Klemm concept. The ionic formula of CuIr2

electron configuration of Ir3+ becomes 5*d*<sup>6</sup>

**Figure 6.** Electronic structure of spinel CuV2 S4 . Partial DOS curves,–COHP curves and band structure of "CuV2 S4 " obtained from non-spin-polarization (LDA). (+ is bonding/ – is anti-bonding, *EF* for 45e– is set to zero).

atom. A series of superconductors were reported by suppression of the charge density waves in MoS2 , just like CuV2 S4 [58].

Based on the above considerations, one of the most interesting areas from both chemical and physical points of view is identification of the factors that determines whether a particular solid is a conductor of electricity or a specific structure type is favored to hold the conducting properties and how well they do it. Furthermore, how external events such as pressure and temperature may affect a system to transit from one regime to the other. Are there any surprises associated with the transition between metal and insulator? Indeed, one of the consequences of the discovery of this series of superconducting copper and bismuth oxides has been unraveling of the possible connection with the metal-insulator transition. But what are the rules associated with the generation of this state of affairs, and what are the factors which compete with them and which lead to the superconductivity and how can we use this to make new superconductors? Recently, the superconductivity was observed in the non-superconducting CuIr2 Se4 spinel by partial substitution of Pt for Ir [62].

## **7. Concluding remarks**

The understanding of superconductivity from the viewpoint of chemistry offers a relatively straightforward approach to the real space rather than thinking in reciprocal space from a physical viewpoint. This chemical thinking is obviously basic, though not sufficiently comprehensive, as clearly shown by the competition between superconductivity and other structural phase transition (CDWs), oxidation fluctuation or magnetism. In this work, the introduced ideas are coming from the chemistry and carried some way into physics, alternatively, using chemical concepts to explain some physical phenomenon. A few questions arise about chemical trivial materials, such as how to make an indirect band gap a direct one. Several empirical rules can be used for chemists to design new superconductors.


But many CDW instabilities are triggered by lowering the temperature and occur in a range of systems, which cover a wide range of chemical types, including metal oxides and sulfides and molecular metals. The surprise of superconductivity may be observed by suppressing the CDWs.

## **Acknowledgements**

atom. A series of superconductors were reported by suppression of the charge density waves

Based on the above considerations, one of the most interesting areas from both chemical and physical points of view is identification of the factors that determines whether a particular solid is a conductor of electricity or a specific structure type is favored to hold the conducting properties and how well they do it. Furthermore, how external events such as pressure and temperature may affect a system to transit from one regime to the other. Are there any surprises associated with the transition between metal and insulator? Indeed, one of the consequences of the discovery of this series of superconducting copper and bismuth oxides has been unraveling of the possible connection with the metal-insulator transition. But what are the rules associated with the generation of this state of affairs, and what are the factors which compete with them and which lead to the superconductivity and how can we use this to make new superconductors? Recently, the superconductivity was observed in the non-supercon-

The understanding of superconductivity from the viewpoint of chemistry offers a relatively straightforward approach to the real space rather than thinking in reciprocal space from a physical viewpoint. This chemical thinking is obviously basic, though not sufficiently comprehensive, as clearly shown by the competition between superconductivity and other structural phase transition (CDWs), oxidation fluctuation or magnetism. In this work, the introduced ideas are coming from the chemistry and carried some way into physics, alternatively, using chemical concepts to explain some physical phenomenon. A few questions arise about chemical trivial materials, such as how to make an indirect band gap a direct one. Several

**1.** Matthias' rule to make diamond-related α-Mn type new superconductors: α-Mn framework can be treated as defected 2 × 2 × 2 diamond structure shown in Xie's yet unpublished work. The space group of α-Mn is I-43*m*, which is the direct subgroup of F*d*-3*m*. Re-rich binary compounds are favored by α-Mn structure. By tuning the electron counts to 6.5e- per atom, α-Mn type Re-rich compounds are highly likely to be

**2.** Searching for the new pyrochlore-type superconductors: In a brief discussion of the

**3.** It is not straightforward to predict the metallic or insulating properties, even harder to predict the M-I transition including the accompanying superconductivity sometimes.

compounds can be synthesized to examine the superconducting properties.

spinels and pyrochlores structures show the similarities just like cubic Laves phases and

In. Pyrochlores can be treated as the superlattice of spinels according to the connection

O4

Re2 O7

In structures, it is suggested that

, in the pyrochlore-type structure

. Moreover, more non-oxide pyrochlore

spinel by partial substitution of Pt for Ir [62].

empirical rules can be used for chemists to design new superconductors.

structural chemistry of both cubic Laves phase and Ni2

in the lattice parameters. The superconductor, Cd<sup>2</sup>

can be conducted the similar research to LiTi2

in MoS2

ducting CuIr2

, just like CuV2

Se4

**7. Concluding remarks**

superconductors.

Ni2

S4 [58].

132 Magnetic Spinels- Synthesis, Properties and Applications

W. Xie thanks Louisiana State University for the start-up funding support and also acknowledges very helpful discussions with Professor Robert Cava (Princeton University) and Professor Gordon Miller (Iowa State University). W. Xie appreciates Yuze Gao for editing the references.

## **Author details**

Weiwei Xie<sup>1</sup> \* and Huixia Luo2

\*Address all correspondence to: weiweix@lsu.edu

1 Department of Chemistry, Louisiana State University, Baton Rouge, USA

2 Department of Chemistry, Princeton University, Princeton, USA

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