**1. Introduction**

Simultaneous substitution in polycrystalline LaMnO3 on the La3+ and Mn3+ ions by magnetic Dy3+ and non-magnetic Zn ions, respectively, offers an adequate scenario for studies on the evolution of structure and magnetic properties due to competing effects. Low-doped regime in La1 � *<sup>x</sup>*Dy*x*Mn1 � *<sup>y</sup>*Zn*y*O3 manganites—(La(Dy) Mn(Zn)O3) means the amount of substitution (*x*,*y*) is kept in the 0*:*0–0*:*1 regime for both sites. For both *x* ¼ 0, *y* ¼ 0, the parent compound LaMnO3 is an insulator composed of ferromagnetic (*a*,*b*)-planes of Mn3+ ions with orbitals configuration {*t* 3 2*g*,*e*<sup>1</sup> *<sup>g</sup>*}, total spin *S* ¼ 2, oriented in basal plane, but antiferromagnetically (AF) coupled along the *c* axis [1]. This antiferromagnetic ground state structure (A-type) due to the Jahn-Teller (J-T) distortion of the Mn3+ ions [2–4] tends to disappear by oxygen excess, and the LaMnO(3 + <sup>δ</sup>) manganite becomes ferromagnetic. The magnetic A-type structure occurs because of the different orientations of the *e*<sup>1</sup> *<sup>g</sup>* orbitals within the (*a*,*b*) plane lead to FM superexchange, while covalent orientation of these orbitals along the *c* axis leads to AFM superexchange [5–7], which weakens the ferromagnetism within the (*a*,*b*) planes, but the AFM coupling along c axis remains unaltered. For LaMnO(3 + <sup>δ</sup>), the correlation between crystal structure and magnetism has been discussed in Ref. [8].

For *y* ¼ **0**, the magnetic and transport properties of La1 � *<sup>x</sup>*Dy*x*MnO3 compounds with nominal stoichiometry *x* ¼ **0***:***05**,**0***:***10** synthesized by sol-gel method have been studied by the authors in Ref. [9]. Although LaMnO3 and La1 � *<sup>x</sup>*Dy*x*MnO3 compounds were synthesized with the same method, they observed that in La1 � *<sup>x</sup>*Dy*x*MnO3 more La-site vacancies appear. This has been attributed to evaporation of La ions by chemical disorder. The La-site deficiencies, as mentioned, increase the FM double exchange (DE) interaction. Simultaneously, the ionic radius difference between La and Dy ions leads to local distortion, in addition to the J-T distortion caused by Mn3+ ions reducing the FM interaction between Mn3+ and Mn4+ ions. Furthermore, the large magnetic moment of Dy3+ (*μ***eff 10***:***83***μB*) randomly polarizes the magnetic Mn sublattice in favor of ferromagnetism. In slightly Dy-doped LaMnO3, the paramagnetic Dy ion can be represented as an impurity between the Mn-Mn spin pairs coupling to Mn ions through 3d and 4f electrons. At large Mn-Dy separation, the interaction between 3d and 4f electrons is smaller than (or just comparable) that between nearby Mn-Mn host ions [10–13], confirmed that through weak coupling between magnetic impurities and their nearest neighbor host ions, the local AFM order in the host spin system will be enhanced. Through small Dy doping, the interactions between Dy impurities are determined by host Mn spins. On the contrary, when the Dy concentration increases, the interaction between the Dy impurities increases, and the lattice becomes much more disordered. Thus, Dy can introduce magnetic disorder that can be important to understand the presence of ferromagnetic clusters above the ferromagnetic ordering.

For *x* ¼ **0**, a great deal of work has been conducted concerning the doping of the Mn site in LaMn1 � *<sup>y</sup>*Zn*y*O3 manganites with *y* in the **0***:***05**–**0***:***4** range [14–17]. Partial substitution of Mn by Zn2+ {3d10} nonmagnetic ions results in the simultaneous presence of Mn3+ and Mn4+ ions, triggering Zener's DE interaction. Thus, the transformation of Mn3+ into Mn4+ reduces the antiferromagnetism of the A-type structure, inducing 3-dimensional ferromagnetism [15]. Moreover, the Zn dilution of the Mn sublattice locally weakens magnetism and induces disorder. At the same time, the magnetic La(Dy) sublattice interacts with the local field imposed by the ferromagnetic of the Mn sublattice. Depending on the magnetic nature of the La(Dy) sublattice, the interaction can be FM or AFM; in our case, ferromagnetism is obtained.

### **2. Crystalline structure**

X-ray diffraction (XRD) patterns study of the samples of La1 � *<sup>x</sup>*Dy*x*Mn1 � *<sup>y</sup>*Zn*y*O3 family (synthesized by solid reaction method) with *x* ¼ 0*:*0,0*:*05,0*:*1 and *y* ¼ 0*:*0,0*:*05,0*:*1 for samples *x* ¼ 0,*y* ¼ 0*:*0 and *x* ¼ 0*:*0, *y* ¼ 0*:*05 exhibits a trigonal phase, while the other samples correspond to an orthorhombic phase. The effects on the crystal structure through simultaneous substitution on both La and Mn sites are complex. On the one hand, inclusion of Dy [18–20], with smaller ionic radius than La ions, and inclusion of Zn [16, 17], with a greater ionic radius than Mn ions, introduces distortions in the octahedra and, therefore, in the crystallographic structure. On the other hand, introduction of divalent Zn ions induces the change of Mn3+ for Mn4+ and the J-T distortion of the Mn3+ neighboring Zn2+ differs from one of the Mn3+ no-neighboring Zn2+ ions [17]. **Figure 1** shows the XRD pattern for *<sup>x</sup>* <sup>¼</sup> 0 due to different Zn substitution: *y* ¼ 0 (bottom panel), *y* ¼ 0*:*05 (middle panel), and *y* ¼ 0*:*1 (top panel).

*Low-Doped Regime Experiments in LaMnO3 Perovskites by Simultaneous… DOI: http://dx.doi.org/10.5772/intechopen.107309*

#### **Figure 1.**

*X-ray diffraction patterns for La1* � <sup>x</sup>*Dy*x*Mn1* � <sup>y</sup>*Zn*y*O3 (a) x* ¼ 0*:*0,*y* ¼ 0*:*1*; (b) x* ¼ 0*:*0 *y* ¼ 0*:*05*; and (c) x* ¼ 0 *y* ¼ 0*:*0*. Major Miller indices are indicated.*

X-ray diffraction data were refined by the Rietvel method—Fullproff program [21]. Information, such as phase structure, identification of planes, cell volumes, and cell densities were obtained. **Table 1** presents some crystallographic parameters corresponding to La1 � *<sup>x</sup>*Dy*x*Mn1 � *<sup>y</sup>*Zn*y*O3 samples.

**Figure 2** shows a structural phase transition for *x* ¼ 0*:*0 samples, when*y*>0*:*05 it is from triclinic to orthorhombic. This signals the high structural distortion introduced by Zn ions. Therefore, the sample *x* ¼ 0*:*0, *y* ¼ 0*:*1 relaxes the stress by symmetry breaking. As will be seen later, this behavior is also observed at Dy concentrations for *x* ¼ 0*:*05, 0.10 series, although for these samples, relaxation is achieved by octahedra tilting increases.


**Table 1.**

*Structural parameters for La1* � <sup>x</sup>*Dy*x*Mn1* � <sup>y</sup>*Zn*y*O3 samples. Values in white cells are from Ref. [22].*

#### **Figure 2.**

*Variation of unit cell parameter with Zn doping (*0*:*0<*y*<0*:*1*). (a) Cell parameter* a *(circle) and* b *(triangle); and (b) Cell parameter* c *(square). x* ¼ 0*:*0 *in all cases.*

Use of 3D reconstruction tools of structures (like *Visualization for Electronic Structural Analysis*) allows obtaining interatomic distances, Mn � O and angles, *θ<sup>i</sup>* in the Mn � O � Mn bonds (**Figure 3**). In the case of manganites, a distortion of structure is directly related to their magnetic properties. This phenomenon, known as the J-T effect, is a structural phase transition driven by the coupling between the orbital state and the vibronic configuration of the crystal lattice. The J-T coupling to the lattice manifests itself in changes in bond lengths Mn � O and *θ<sup>i</sup>* angles, as well as in orbital order [3, 4].

Regarding the measurements of structural distortion in perovskites with orthorhombic structure, two relations have been used to evaluate said distortion from the distances of the manganese with their neighboring oxygen Mn � O � Mn in the plane and with the apical oxygen ions. The octahedra distortion, *D*oct, can be calculated by [23, 24]:

*Low-Doped Regime Experiments in LaMnO3 Perovskites by Simultaneous… DOI: http://dx.doi.org/10.5772/intechopen.107309*

#### **Figure 3.**

*Unit cell of perovskite structure indicating the bond distances,* ð Þ� Mn*=*Zn O1 *and* Mn Zn � � � O1 *and bond angles, θ<sup>1</sup> and θ2. Atoms: O (red), Mn/Zn (black), and La/Dy (Green).*

$$\begin{split}D\_{\text{oct}} &= \mathbf{10} \times \frac{\left(\sum\_{i=1,\dots,6} \left| \langle \mathbf{M} \mathbf{n} - \mathbf{O}\_{i} \rangle - \langle \mathbf{M} \mathbf{n} - \mathbf{O} \rangle\_{\text{average}} \right| \right)}{\langle \mathbf{M} \mathbf{n} - \mathbf{O} \rangle\_{\text{average}}},\\ \mathbf{D}\_{\text{oct}} &= \mathbf{1}/\mathbf{6} \times \sum\_{i=1,\dots,6} \left[ \frac{\langle \mathbf{M} \mathbf{n} - \mathbf{O}\_{i} \rangle - \langle \mathbf{M} \mathbf{n} - \mathbf{O} \rangle\_{\text{average}}}{\langle \mathbf{M} \mathbf{n} - \mathbf{O} \rangle\_{\text{average}}} \right]^{2} \end{split} \tag{1}$$

where Mn � O*<sup>i</sup>* represents the bond distances between the manganese ion and each of the six oxygens of the octahedra that surround it. These distances will depend, among others, on the ionic radii and mainly on the doping of the ion in site *B*. **Figure 2** shows these distances of the manganese Mn � O2 in the plane and Mn � O1 with the apical oxygens.

Octahedra distortion, from the energetic point of view known as J-T distortion, is evaluated through the relation [25]:

$$
\lambda\_{l-T} = \sqrt{\frac{1}{3} \times \left( \sum \left( \langle \mathbf{M} \mathbf{n} - \mathbf{O}\_l \rangle - \langle \mathbf{M} \mathbf{n} - \mathbf{O} \rangle\_{\text{average}} \right)^2 \right)} \tag{2}
$$

Although Eqs. (1) and (2) are different ways of evaluating the distortion, both are dimensionless; their range is between [0, 1], and their behavior is similar. In the manganites studied herein, an inverse relationship between distortions and the magnetic moment of individuals or clusters has been observed for *T* >*Tc*. Where does this structure-magnetism relationship originate? Clearly, the J-T effect results in spontaneous splitting of the energy levels, reducing the total energy of the *Mn*<sup>3</sup><sup>þ</sup> also resulting in a spontaneous distortion of the octahedrons that increase their elastic

energy at the cost of a reduction in energy of certain electron orbitals, thus, resulting in a net reduction in energy.

The J-T distortions obtained through Eq. (2) showed anomalous behavior (**Figure 4**): Zn increases in the range of 0< *y*<0*:*05 increases the J-T distortion and for *y*>0*:*05, a reduction in the J-T distortion is observed (**Figure 4a**). This is due to the difference between the ionic radii of Zn and Mn ions [16]. However, when *x*>0*:*05, the accumulated strain of the system is relaxed via octahedral tilting—similar to the introduction of dislocation when the maximum stress tolerated is reached in a crystal [22]. Tilting as a relaxation mechanism is observed in **Figure 4b**, where greater tilting corresponds to samples with lower J-T distortion. The same anomalous behavior is observed by calculating octahedra distortions (Eq. (2)). As will be seen ahead,

#### **Figure 4.**

*(a) Jahn-Teller distortion versus Zn composition for* x *= 0.10 samples (squares) and* x *= 0.05 samples (circles); and (b) Jahn-Teller distortion vs. Octahedra tilting, ω, by using* 2*ω<sup>i</sup>* þ *θ<sup>i</sup>* ¼ 180° *[22].*

the activation energy that allows the magnetic exchange is accompanied by a charge exchange facilitated by these lattice distortions.

Local distortions affect directly the magnetic properties as a function of *T*, that is, exchange constants are proportional to the orthorhombic strain [8]. Also, magnetic moments and activation energies depend on distortion [22].

### **3. Local magnetism-electron paramagnetic resonance (EPR) analysis**

Electron paramagnetic resonance is an important technique to study the microscopic nature of local interactions in magnetic materials and, particularly, in manganites [26], which in many cases show short-range interactions for *T* >*Tc*. This technique contrasts with the magnetization and susceptibility techniques that provide global information about the exchange mechanisms and the possible spontaneous creation of clusters at high temperatures.

The EPR signal corresponds to *dχ*00*=dH*, where *χ = M/H* is the susceptibility. In the paramagnetic region, where *M* is linear with *H*, the double integral of the EPR intensity is proportional to the magnetization. From EPR measurements, we can build the dependence of the inverse of the temperature-dependent susceptibility, *<sup>χ</sup>*�<sup>1</sup>ð Þ *<sup>T</sup> .*To carry out the EPR measurements, a Bruker ESP-300 spectrometer was used in the radiation X-band with 9.408 GHz frequency and in a temperature range from 10 to 290 K. **Figure 5a** shows the resonant signals for manganite La0.9Dy0.1MnO3 in the temperature range 220<*T* < 290 *K*. The inset of **Figure 5a** is the integral of the EPR signal. It is observed that for high temperatures, the intensity of the EPR signal increases in all cases as the temperature decreases. For *T* > *TC*, it is found that the intensity of resonance line fits by the expression [28]:

$$I\_{\rm PM} = I\_0 \mathcal{e}^{\Delta E/k\_B T} \tag{3}$$

where *I*PM is the intensity extracted from the resonance line, *I*<sup>0</sup> is a fitting parameter, and Δ*E* is an activation energy.

**Figure 5c** shows the variation of the resonant field with temperature. A change in the value of *Hr* is observed for *T* >*Tc*. This local signal evidences an FM phase in the PM region [27, 29]. This local magnetism is strongly dependent on doping and oxygen content, as Oseroff et al. [28] show in their work on collective spin dynamics above *Tc* in manganites (La1 � *<sup>x</sup>*Ca*x*MnO3).

The peak-to-peak EPR linewidth, Δ*HPP*, can also be used to confirm the presence of short-range interacting magnetic entities. In magnetic resonance, the EPR linewidth is related to the relaxation mechanisms of the magnetic units, whether individual spins or spin-coupled systems. A decrease in Δ*HPP* as temperature decreases indicates PM behavior of the sample. However, in the case of La1*x*D*x*MnZnO manganites, an increase in Δ*H*PP is observed as temperature decreases, indicating the presence of short-range interactions. In **Figure 6a**, the arrows indicate the corresponding critical temperatures for each sample. Δ*H*PP increases as temperature decreases, indicating a greater range of the collective effects, approaching the FM phase. Tovar et al. [8] have found a direct dependence on temperature for the J-T distortion and the EPR linewidth.

The energy transferred in the relaxation process is related to jumps of polarons thermally activated between the Mn4+ and Mn3+ states. Therefore, the jump rate of the charge carriers will determine the half-life of the spin state and, therefore, determines

#### **Figure 5.**

*(a) EPR signal of La0.9Dy0.1MnO3 for different temperatures, Inset. Intensity obtained by integration of the EPR signal; (b) EPR signal intensity as a function of temperature, showing short-range interaction behavior for T* >181 K *for the sample La0.9Dy0.1Mn0.95Zn0.05O3; and (c) resonant field vs.* T *for LaMn0.9Zn0.1O3 [27].*

*Low-Doped Regime Experiments in LaMnO3 Perovskites by Simultaneous… DOI: http://dx.doi.org/10.5772/intechopen.107309*

#### **Figure 6.**

*(a) Temperature dependence on the resonance linewidth; the corresponding TC values of the x* ¼ 0*:*0*, y* ¼ 0*:*05 *(red) and x* ¼ 0*:*05*, y* ¼ 0*:*1 *(black) samples are indicated; and (b) linewidth as a function of temperature or the x* ¼ 0*:*0*, y* ¼ 0*:*05 *sample; red line corresponds to the fitting line to obtain the activation energy value as* E*<sup>a</sup> = 0.068 eV.*

the EPR linewidth and the conductivity. The dependence of the EPR linewidth as a function of temperature in the paramagnetic region can be evaluated by [30]:

$$
\Delta H\_{\rm PP}(T) = \frac{A}{T} e^{-\left(\frac{E\_a}{k\_B T}\right)}\tag{4}
$$

*Ea* values showed on **Table 2** are obtained by Eq. (4). Previous studies on relaxation modes in mixed-valence manganites have shown that the EPR predominant signal corresponds to Mn3<sup>þ</sup> � Mn<sup>4</sup><sup>þ</sup> relaxation and the internal relaxation of the ions through the lattice. Shengelaya et al. [31] showed that the relaxation, *R*, of the Mn<sup>4</sup><sup>þ</sup> (s) with the lattice can be negligible compared with the relaxation Mn3<sup>þ</sup> (σ) with the lattice (L),


**Table 2.**

*Activation energies as a function of Zn doping (*y*). White cells from Ref. [27].*

while the largest signal corresponds to the relaxation Mn3<sup>þ</sup> � Mn4<sup>þ</sup> and Mn4<sup>þ</sup> � Mn3þ. Thus, a "Bottleneck" is formed, corresponding to the charge transfer between the two magnetic subsystems (3+ and 4+), while a slower relaxation process, Mn3<sup>þ</sup> with the network occurs. A schematic representation proposed is presented in **Figure 7**.

Furthermore, the intensity of the EPR signal is proportional to the static magnetic susceptibility, *χe*, it is possible to explain the bottleneck regime due to the coupling of the spins (s) and (σ) as:

$$\chi\_{\rm S} = \chi\_{\rm S}^{\rho} \frac{1 + \lambda^{\prime} \chi\_{\sigma}^{\rho}}{1 - \lambda^{\prime 2} \chi\_{\sigma}^{\rho} \chi\_{\rm S}^{\rho}} \tag{5}$$

where *χ<sup>o</sup>* <sup>S</sup> and *χ<sup>o</sup>* <sup>σ</sup> are the ion susceptibilities without exchange of Mn4<sup>þ</sup> and Mn<sup>3</sup>þ, respectively, and λ is the dimensionless coupling constant.

$$
\dot{\lambda}' = \frac{-\text{zf}}{\text{ng} \, \text{g} \, \text{g} \, \text{}\_{\sigma} \text{}^2 \, \text{}^{\text{(}\text{)}} \tag{6}
$$

with *<sup>n</sup>* being the number of spins per cm<sup>3</sup> and *<sup>g</sup>*s,*g<sup>σ</sup>* being the g-factors of the Mn<sup>4</sup><sup>þ</sup> and Mn<sup>3</sup><sup>þ</sup> ions, respectively. For *T* ≫ *TC*, the EPR signal intensity drops faster than predicted by Eq. (5), associated with a transition from the bottleneck to an isothermal regime: *Rσ*<sup>L</sup> ≫ *Rσ*s, where the relaxation, *Rσ*s, is *T* independent [31].

For manganites, the contribution of each coexistent phase has been evaluated by means of the EPR technique. In this case, FM clusters also contribute to the magnetization of the material, so that the total magnetization is the result of the PM and FM contributions above *TC* by [32]:

#### **Figure 7.**

*A block diagram showing the energy flow paths for the Mn4+ and Mn3+ spin subsystems and the lattice. The relaxation rates R<sup>σ</sup>S*, *RS<sup>σ</sup> represent relaxation between the subsystems. The thickness of the arrows is a measure of the magnitude of the particular relaxation rate [31].*

*Low-Doped Regime Experiments in LaMnO3 Perovskites by Simultaneous… DOI: http://dx.doi.org/10.5772/intechopen.107309*

**Figure 8.** *(°) IPM*ð Þ *T , (solid line) M=H T*ð Þ *at 3.5 kG and (•) IFM*ð Þ *T vs. T for La0.75Ca0.25MnO3. Adapted from Ref. [32].*

$$M(H,T) = \varkappa(T)\chi\_{\rm PM}(T)H + [1-\varkappa(T)]M\_{\rm FM}(H,T) \tag{7}$$

where *x* and 1ð Þ � *x* are the fractions of PM and FM signals, respectively. The intensity of ESR lines are:

$$I\_{\rm PM}(T) \propto \pi(T) \chi\_{\rm PM}(T) \text{ and } I\_{\rm FM}(T) \propto [1 - \pi(T)] \mathcal{M}\_{\rm FM}(T) \tag{8}$$

For *T* ≫ *Tc*, the EPR signal consists only of a PM line; then *x T*ð Þ ≫ *Tc* = 1, and *M H*ð Þ , *T =H* ¼ *χ*PM, while *x T*ð Þ <*Tc* = 0 and *M H*ð Þ , *T =H* = *χ*FM.As Eq. (8) shows, it is possible to find the fraction of the FM phase in the samples by subtracting the EPR intensity from the magnetic susceptibility (**Figure 8**). The inset shows the fraction as a function of temperature.

Dormann and Jaccarino [33] proposed the following Huber approximation for a coupled system (clusters) in the PM state:

$$
\Delta H\_{\rm pp}(T) \propto [\chi\_s(T)/\chi\_{\rm EPR}(T)]\Delta H\_{\rm pp}(\infty) \tag{9}
$$

where *<sup>χ</sup>s*ð Þ¼ *<sup>T</sup> <sup>C</sup>=<sup>T</sup>* is the susceptibility of the individual ions M3<sup>þ</sup> and M<sup>4</sup>þ; Δ*H*ppð Þ ∞ corresponds to spin-only interactions (Δ*H*ppð Þ¼ ∞ 2600 G reported by Causa et al. [34] for perovskites with A = La) and *χ*EPRð Þ *T* the PM signal of the coupled system.

$$\mathbf{C} = \mathbf{N}\_A \mu\_{\rm eff}^2 \mu\_B^2 / \Im k\_B \tag{10}$$
