**1. Introduction**

The recent developments in thin films and nanofabrication techniques of biosensors and related spintronic devices are the forefront of current research efforts, bridging material sciences, physics, chemistry, and engineering, to form a seamless integration of digital world into the soft or living systems. Magnetic functionalities may provide a sense of proximity, orientation, or displacement to this novel formulation of biomedical electronics.

High spin polarization is one of the requested and necessary properties of materials used as electrodes or spin pumping/spin analyzers elements in spintronics, including those used in medicine and this is by definition a characteristic of alloys with half-metallic properties [1, 2]. The property of half-metallic ferromagnetism initially discovered in Cu2MnAl compound [2] consists in a metallic behavior of one spin channel of electronic structure and a semiconducting one in the other, thus creating a material with hybrid properties between metals and semiconductors. As

a direct consequence, there will be always a 100% net spin polarization at the Fermi level due to the unique spin polarization of electrons in only one channel.

In materials in which the unit cell consists of two distinct sublattices with antiferromagnetic coupling between them, an internal spin partial compensation occurs and this particular property was referred as half-metallic ferrimagnetism [3, 4], which comparing to half-metallic ferromagnetism exhibits lower magnetic moments per formula unit (f.u) and weaker stray fields. Moreover, if the magnetic moments of the constituent sublattices fully compensate each other (with a net spin = 0 μB/f.u.), an alloy with a completely compensated ferrimagnetism (CCF) [5] resulted and the compound was classified as half-metallic completely compensated ferrimagnet (HM-CCFs) [6]. However, such a complete spin polarization of carriers occurs in the case of zero temperature and only in the absence of the spin-orbit interactions. Apart from this, HM-CCFs are intensively studied to develop new stable spin-polarized electrodes for biomedical in-vivo applications, junctions or integrated spin-transfer torque nano-oscillators for telecommunication.

A particular class of half-metallic materials is Spin Gapless Semiconductors (SGS). These compounds exhibit around Fermi level, in one spin channel a typical semiconducting band gap, while in the other (where in usual half-metallic compounds a metallic character is present), the negligible density of states are equivalent to a very narrow almost zero band gap. The above described characteristic of electronic structure, places SGSs at the boundary between half-metallic compounds and semiconductors.

In this particular case of half-metallicity, the materials act like topological insulators, where in particular high Curie temperature may coexist with high resistance. A combination of spin gapless semiconducting properties with completely compensated ferrimagnetism (0 μB total magnetic moment per f.u.) leads to spin gapless completely compensated ferrimagnetism (SG-CCF) [7].

Particularly, attractive classes of alloys exhibiting half-metallic properties, based on which may be developed biosensors, the new electrode materials with high spin polarization include alloys like Heusler compounds [2]. This class of materials, used in present as electrodes for magnetic tunnel junctions were discovered by Fritz Heusler, in 1903, who reported that Cu2MnAl alloy is ferromagnetic, even though, alone, none of constituent elements has magnetic properties [8]. These intermetallic alloys are described by two variants: the half-Heusler XYZ compounds, with C1b crystal structure and the full-Heusler X2YZ variants which typically crystallize in Cu2MnAl (cubic L21)-type structure; where X is a transition metal, Y may be a rare-metal or a transition metal, and Z is a main group element. Recently, it has been shown that in case of a full-Heusler compounds X2YZ, if the Y element is more electronegative than X, a structure with Hg2CuTi-prototype is observed. This is the so called as inverse Heusler structure, crystallizing in F43m space group [9], with X atoms placed in the 4a(0,0,0) and 4c(1/4,1/4,1/4) Wyckoff positions, Y in 4b(1/2,1/2,1/2) and Z in 4d(3/4,3/4,3/4), respectively. In this crystal structure, no octahedral symmetry Oh is adopted, and all atoms have tetrahedral symmetry Td.

The Slater-Pauling curve gives the interrelation between the total magnetic moment and the valence electron concentration in ferromagnetic/ferrimagnetic alloys [10, 11]. The original Slater-Pauling approach suggests the existence of different laws, due to the average over all atoms of the total magnetic moment and the number of valence electrons. For compounds with different kinds of atoms and ordered crystalline structures, it is more appropriate to consider all atoms of the unit cell, to find the magnetic moment per unit cell.

In terms of two-orbital two-electron stabilizing interactions, within the framework of density functional theory, the states of each spin channel are occupied according to several aspects concerning ionic arguments, crystal structure of

**91**

Mn2CoAl.

to life science research.

*Zr-Based Heusler Compounds for Biomedical Spintronic Applications*

is the electron spin polarization P at Fermi level ( *<sup>F</sup>*

 *<sup>F</sup>* and ( ) <sup>↓</sup> ρ ε

*P*

ρε

ρε

Fermi energy. The states of opposite spin (majority and minority spin states or spin-up and spin-down states) are represented by arrows ↑ and ↓ . Depending on the magnetic characteristic of the material, the electron spin polarization vanishes in case of antiferromagnetic and paramagnetic compounds or has a finite value for ferrimagnetic and ferromagnetic alloys, below the Curie temperature. When either

For ternary 1:1:1 Heusler compounds, the Slater-Pauling rule was firstly reported by Kübler [12]. These compounds, with C1b structure have three atoms per unit cell and follow the Slater-Pauling 18-electron-rule (Mt = Zt - 18), where Mt is the total magnetic moment per the formula unit, Zt is the total number of valence electrons, and 18 represents the number of occupied states in the spin bands. A Slater-Pauling 24-electron-rule (Mt = Zt - 24) was found for the 2:1:1 family of full-Heusler compounds with L21 structure (Cu2MnAl-prototype) [13]. The present work deals only with ternary 2:1:1 full-Heusler compounds with Hg2CuTi type structure. Even though the origin of the band gap in the latter 2:1:1 full-Heusler compounds is different than that of the ternary 1:1:1 Heusler compounds, the corresponding Slater-Pauling rule is similar: 18-electron-rule (Mt = Zt - 18). This Slater-Pauling 18-electron-rule was recently explained for Ti2-based full-Heusler

Many Co2, Mn2, Ti2, and Sc2 – Heusler compounds reported in literature are ferromagnetic [15–18], ferrimagnetic half-metals [19], or spin gapless semiconductors [20]. Among them, Mn2CoAl full-Heusler compound crystallizing in Hg2CuTiprototype was extensively studied: theoretically investigated, the structure was experimentally verified by XRD and the electron transport characteristics where obtained by a Physical Properties Measurement System (PPMS) on samples cut from ingots. The total magnetic moment was experimentally measured using a Magnetic Properties Measurement System (MPMS) [20]. Zirconium has a Pauling electronegativity value lower than those of all d-elements and hence Zr-based Heusler materials are supposed to crystallize in Hg2CuTi type structure, similar to

Zirconium-based Heusler compounds were selected because they exhibit low toxicity and are corrosion resistant, being therefore susceptible of convenient preparation and processing in the field of electronic biomedical sensors ranging from healthcare and medical diagnosis, food safety, and environmental monitoring

primitive cell, lattice parameter, approximations made for the exchange and correlation interaction, energy threshold set between the core and valence states, and also Brillouin zone integration mesh. Based on ionic arguments, the most electropositive element transfers the valence electrons to the most electronegative element. The purpose is to obtain stable closed shell ions. In addition, strongly dependent by the atomic arrangement of atoms and environment, hybridization occurs whenever the sum of metallic radii (12-coordinated) of two first-neighbors exceeds the

A particularly useful measure to describe the electronic properties of a material

( ) ( ) ( ) ( ) ↑ ↓ ↑ ↓ <sup>−</sup> <sup>=</sup> <sup>+</sup>

 ρε

 ρε

*<sup>F</sup>* equals zero, the electrons around Fermi level are fully spin

*F F F F*

ε

*<sup>F</sup>* denote the spin projected density of states around

), given by Eq. (1)

(1)

*DOI: http://dx.doi.org/10.5772/intechopen.93372*

interatomic distance.

where ( ) <sup>↑</sup> ρ ε

 *<sup>F</sup>* or ( ) <sup>↓</sup> ρ ε

compounds [4, 14].

( ) <sup>↑</sup> ρ ε

polarized.

#### *Zr-Based Heusler Compounds for Biomedical Spintronic Applications DOI: http://dx.doi.org/10.5772/intechopen.93372*

*Magnetic Materials and Magnetic Levitation*

and semiconductors.

a direct consequence, there will be always a 100% net spin polarization at the Fermi

level due to the unique spin polarization of electrons in only one channel. In materials in which the unit cell consists of two distinct sublattices with antiferromagnetic coupling between them, an internal spin partial compensation occurs and this particular property was referred as half-metallic ferrimagnetism [3, 4], which comparing to half-metallic ferromagnetism exhibits lower magnetic moments per formula unit (f.u) and weaker stray fields. Moreover, if the magnetic moments of the constituent sublattices fully compensate each other (with a net spin = 0 μB/f.u.), an alloy with a completely compensated ferrimagnetism (CCF) [5] resulted and the compound was classified as half-metallic completely compensated ferrimagnet (HM-CCFs) [6]. However, such a complete spin polarization of carriers occurs in the case of zero temperature and only in the absence of the spin-orbit interactions. Apart from this, HM-CCFs are intensively studied to develop new stable spin-polarized electrodes for biomedical in-vivo applications, junctions or

integrated spin-transfer torque nano-oscillators for telecommunication.

completely compensated ferrimagnetism (SG-CCF) [7].

unit cell, to find the magnetic moment per unit cell.

A particular class of half-metallic materials is Spin Gapless Semiconductors (SGS). These compounds exhibit around Fermi level, in one spin channel a typical semiconducting band gap, while in the other (where in usual half-metallic compounds a metallic character is present), the negligible density of states are equivalent to a very narrow almost zero band gap. The above described characteristic of electronic structure, places SGSs at the boundary between half-metallic compounds

In this particular case of half-metallicity, the materials act like topological insulators, where in particular high Curie temperature may coexist with high resistance. A combination of spin gapless semiconducting properties with completely compensated ferrimagnetism (0 μB total magnetic moment per f.u.) leads to spin gapless

Particularly, attractive classes of alloys exhibiting half-metallic properties, based on which may be developed biosensors, the new electrode materials with high spin polarization include alloys like Heusler compounds [2]. This class of materials, used in present as electrodes for magnetic tunnel junctions were discovered by Fritz Heusler, in 1903, who reported that Cu2MnAl alloy is ferromagnetic, even though, alone, none of constituent elements has magnetic properties [8]. These intermetallic alloys are described by two variants: the half-Heusler XYZ compounds, with C1b crystal structure and the full-Heusler X2YZ variants which typically crystallize in Cu2MnAl (cubic L21)-type structure; where X is a transition metal, Y may be a rare-metal or a transition metal, and Z is a main group element. Recently, it has been shown that in case of a full-Heusler compounds X2YZ, if the Y element is more electronegative than X, a structure with Hg2CuTi-prototype is observed. This is the so called as inverse Heusler structure, crystallizing in F43m space group [9], with X atoms placed in the 4a(0,0,0) and 4c(1/4,1/4,1/4) Wyckoff positions, Y in 4b(1/2,1/2,1/2) and Z in 4d(3/4,3/4,3/4), respectively. In this crystal structure, no octahedral symmetry Oh is adopted, and all atoms have tetrahedral symmetry Td. The Slater-Pauling curve gives the interrelation between the total magnetic moment and the valence electron concentration in ferromagnetic/ferrimagnetic alloys [10, 11]. The original Slater-Pauling approach suggests the existence of different laws, due to the average over all atoms of the total magnetic moment and the number of valence electrons. For compounds with different kinds of atoms and ordered crystalline structures, it is more appropriate to consider all atoms of the

In terms of two-orbital two-electron stabilizing interactions, within the framework of density functional theory, the states of each spin channel are occupied according to several aspects concerning ionic arguments, crystal structure of

**90**

primitive cell, lattice parameter, approximations made for the exchange and correlation interaction, energy threshold set between the core and valence states, and also Brillouin zone integration mesh. Based on ionic arguments, the most electropositive element transfers the valence electrons to the most electronegative element. The purpose is to obtain stable closed shell ions. In addition, strongly dependent by the atomic arrangement of atoms and environment, hybridization occurs whenever the sum of metallic radii (12-coordinated) of two first-neighbors exceeds the interatomic distance.

A particularly useful measure to describe the electronic properties of a material is the electron spin polarization P at Fermi level ( *<sup>F</sup>* ε), given by Eq. (1)

$$P = \frac{\rho\_\uparrow \left(\varepsilon\_F\right) - \rho\_\downarrow \left(\varepsilon\_F\right)}{\rho\_\uparrow \left(\varepsilon\_F\right) + \rho\_\downarrow \left(\varepsilon\_F\right)}\tag{1}$$

where ( ) <sup>↑</sup> ρ ε *<sup>F</sup>* and ( ) <sup>↓</sup> ρ ε *<sup>F</sup>* denote the spin projected density of states around Fermi energy. The states of opposite spin (majority and minority spin states or spin-up and spin-down states) are represented by arrows ↑ and ↓ . Depending on the magnetic characteristic of the material, the electron spin polarization vanishes in case of antiferromagnetic and paramagnetic compounds or has a finite value for ferrimagnetic and ferromagnetic alloys, below the Curie temperature. When either ( ) <sup>↑</sup> ρ ε *<sup>F</sup>* or ( ) <sup>↓</sup> ρ ε *<sup>F</sup>* equals zero, the electrons around Fermi level are fully spin polarized.

For ternary 1:1:1 Heusler compounds, the Slater-Pauling rule was firstly reported by Kübler [12]. These compounds, with C1b structure have three atoms per unit cell and follow the Slater-Pauling 18-electron-rule (Mt = Zt - 18), where Mt is the total magnetic moment per the formula unit, Zt is the total number of valence electrons, and 18 represents the number of occupied states in the spin bands. A Slater-Pauling 24-electron-rule (Mt = Zt - 24) was found for the 2:1:1 family of full-Heusler compounds with L21 structure (Cu2MnAl-prototype) [13]. The present work deals only with ternary 2:1:1 full-Heusler compounds with Hg2CuTi type structure. Even though the origin of the band gap in the latter 2:1:1 full-Heusler compounds is different than that of the ternary 1:1:1 Heusler compounds, the corresponding Slater-Pauling rule is similar: 18-electron-rule (Mt = Zt - 18). This Slater-Pauling 18-electron-rule was recently explained for Ti2-based full-Heusler compounds [4, 14].

Many Co2, Mn2, Ti2, and Sc2 – Heusler compounds reported in literature are ferromagnetic [15–18], ferrimagnetic half-metals [19], or spin gapless semiconductors [20]. Among them, Mn2CoAl full-Heusler compound crystallizing in Hg2CuTiprototype was extensively studied: theoretically investigated, the structure was experimentally verified by XRD and the electron transport characteristics where obtained by a Physical Properties Measurement System (PPMS) on samples cut from ingots. The total magnetic moment was experimentally measured using a Magnetic Properties Measurement System (MPMS) [20]. Zirconium has a Pauling electronegativity value lower than those of all d-elements and hence Zr-based Heusler materials are supposed to crystallize in Hg2CuTi type structure, similar to Mn2CoAl.

Zirconium-based Heusler compounds were selected because they exhibit low toxicity and are corrosion resistant, being therefore susceptible of convenient preparation and processing in the field of electronic biomedical sensors ranging from healthcare and medical diagnosis, food safety, and environmental monitoring to life science research.

The information about the experimental preparation and electronic structure of Zr-based Heusler compounds with true half-metallic properties are still scarce. Therefore, to understand the properties of potential zirconium-based Heusler compounds, in the beginning, theoretical investigations can be performed via density functional theory (DFT). Self-consistent calculations using a "muffin-tin" model and various approximations to describe the exchange and correlation interactions can lead to valuable information about the energetically favorable crystalline structure, electronic configuration, or magnetic properties by means of the total energy minimization.

This chapter gives a comprehensive overview of the key electronic structures and magnetic properties usually found in half-metallic zirconium-based full-Heusler compounds.
