Structural, magnetic, magnetocaloric and critical exponents of oxide manganite La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

Abstract

In this scientific paper, structural, magnetic, magnetocaloric and critical exponent’s properties of La_0.7Sr_0.3Mn_0.95Fe_0.05O₃ compound are briefly reviewed. The sample was synthesized by solid state reaction. X-ray powder diffraction analysis at room temperature showed that our sample is single phase without detection of any impurities. The refinement by the Rietveld method indicate that this compound crystallize in the orthorhombic structure with the space group Pnma. The variation of the magnetization versus temperature found that our perovskite has a single transition from the paramagnetic state (PM) to the ferromagnetic state (FM) with increasing temperature and the obtained Curie temperature is T_C = 311 K. The obtained value of | $\Delta {S}_{M}^{\text{MAX}}$| is about 2.3Jkg⁻¹ K⁻¹ under an applied magnetic field of 5 T. The achieved results show that our compound is a promising candidate for magnetic refrigeration. Also, to discover the nature of the paramagnetic-ferromagnetic phase transition, for the La_0.7Sr_0.3Mn_0.95Fe_0.05O₃we made an experimental study on the critical behaviour around the FM-PM transition. The value of the Curie temperature and the critical exponent’s β, γ and δ were determined using modified Arrott plots (MAP).

1 Introduction

The search for new magnetic materials for high performance magnetic entropy for applications has resulted in exponential growth in both scientific research in this field, and investment in such materials production. In addition, due to their potential applications for devices, colossal magnetoresistance (CMR) and magnetocaloric effect (MCE) in various perovskite oxide manganite’s has become a subject of considerable research interest, and the challenge of fully understanding the fundamental nature of the intense interplay between magnetic order, electronic transport, structural distortions and elastic properties in these materials. Manganite’s has been created a great deal of interest in the last century, thanks to their magnetic and electrical properties. For the base compound A_1−xB_xMnO₃(A = rare earth like Pr, La, Na….and B = divalent element like Sr, Ca, Ba…), which belong to perovskite structure, have been study, due to their crucial role in many applications such as magnetocaloric refrigeration [1, 2] and giant magnetoresistance [3]. For Lanthanum based materials and oxides, the substitution of La³⁺ions with alkaline earth metal ions (e.g. Sr²⁺, Ba²⁺, Ca²⁺, etc.) is a requirement for a low-cost solutions as they have excellent magnetic properties close to room temperature, in particular Collosal magnetoresistance (CMR), MC effect and semi-metallic properties close to disk heads and magnetic field sensor [4, 5]. Nano-magneto-caloric materials are adapted to practical nanometre-scale magnetic refrigeration equipment. As a result, researches concentrated on working on small magnetic materials (e.g. nanoparticles, thin film, nanowires, multilayer systems, etc.) and new magnetic materials production [6, 8]

The discovery of these physical–chemical properties, this way opens up an area of a fundamental and applied research. The variety of properties makes this type of materials candidate for using in magnetic cooling technology [9, 11].The magnetism in these materials comes essentially from manganese characterized by a high magnetic moment (S = 2 for Mn³⁺ and S = 3/2 for Mn⁴⁺).The nature of the paramagnetic-ferromagnetic transition is important to better understand the metal–insulator transition. In addition, several studies on critical behaviours and the universality class around the Curie temperature have known that critical exponents play important roles in elucidating mechanisms of interactions near T_C [12, 13].

Furthermore, many other properties have been discovered by doping Mn with a transition metal. The principal character of these compounds is the mixed valence of the manganese ions (Mn³⁺/Mn⁴⁺), that is the central reason of ferromagnetic character due to the double exchange between Mn³⁺ and Mn⁴⁺ [14, 16]. Besides all these properties, a lot of work was done about the substitution of the manganese by other 3d metal ions such as iron [17, 19].Therefore, the substitution of Fe³⁺ for Mn³⁺is not expected to change the tolerance factor, for that reason, the effect of the Jahn–Teller distortion may be neglected. Mössbauer spectroscopy is an effective way to examine octahedral symmetry at the Fe sites [20]. MCE in theseoxides is characterized by adiabatic temperature change (ΔT_ad) or isothermal magnetic entropy change (ΔS_M), which is a function of both magnetic field and temperature. Partial substitution of Mn by Fe was found to decrease the magnetization and Curie temperature, but the magnetic entropy shift values remained within the range appropriate for magnetic cooling.

Reviewing previous research, several works centred on materials based on La_1−xSr_xMnO₃which showed different Curie temperature values [21, 22].The parent compound La_0.7Sr_0.3MnO₃exhibits a Curie temperature about 370 K [23]. In fact, Fe substitution in La_0.7Sr_0.3MnO₃ deserves precise interest due to magnetic properties of the iron. Leung et al. were among the first to study the effect of iron substitution, they studied the magnetic properties of the compound La_1−xPb_xMn_1−yFe_yO₃, and deduced the relationship between the antiferromagnetic interactions (AFM) Fe³⁺–O–Fe³⁺ and Fe³⁺–O–Mn³⁺ and the double exchange ferromagnetic interactions Mn³⁺–O–Mn⁴⁺[24].Damay et al. [25] found several orders of decrease in resistivity when applying a magnetic field in the Sm_0.7Sr_0.3Mn_1−xFe_xO₃(x = 0.03) series compared to x = 0.0.The insertion of Mn³⁺(${r}_{{\text{Mn}}^{3+}}$=0.720 Å) with the ferromagnetic ion Fe³⁺ (${r}_{{\text{Fe}}^{3+}}$ = 0.785Å) which have many results such as an increase in lengths of Mn–O, an increase in angles Mn–O–Mn, and as a result a weakening of the ferromagnetic state. The iron atom is placed in the centre of an octahedron, so there is the creation of an electrostatic field whose influence is the division of the levelled. Under the effect of the crystalline field the orbitals are destabilized. Consequently, degeneration has been lifted. 3d orbitals are divided into sub-levels t_2g and e_g.

To better illustrate the magnetic properties, in this work, we report on effect of 5% of Fe doping in La_0.7Sr_0.3MnO₃ on the structural, magnetic, magnetocaloric effect properties and critical exponents. This compound has been synthesized in the literature by several methods of elaboration [26]. The manganite was elaborated with the solid state reaction and characterized by X-ray diffraction (XRD) and magnetization measurements. The magnetocaloric effect was examined as well as the Arrott plot.

2 Experimental details

In this work, the sample was elaborated by solid state reaction at higher temperature, using oxides in form of powders. This process is used for the industrial powder production. Nevertheless, this technique may be ineffectual in controlling the grain size and morphology of the powder product. The precursors used are: La₂O₃, SrCO₃, MnO₂ and Fe₂O₃.

First, our precursors are weighted in the stoichiometric proportions desired by the reaction equation:

Then, the beginning materials were mixed in order to get a homogeneous mixture. The stoichiometric compound was then placed in alumina crucible and heated to a temperature of 700 °C for 20 h. Subsequently, the obtained powder was pressed into pellets and sintered at 900 °C, 1100 °C, and 1300 °C for 20 h with intermediate regrinding and re-pelletizing to acquire a better crystal. Finally, these pellets were sintered at 1400 °C for 4 h.

To check the structural and phase purity, we use X-ray powder diffraction using Cupper radiation (λ₁ = 1.54059 Å and λ₂ = 1.52442 Å). The magnetization measurements versus temperature M(T) in the range 0–450 K, and the isothermal magnetization curves in an applied magnetic field of up to 6 T were obtained using the BS1 magnetometer facility at Louis Neel Grenoble Laboratories. The MEC was estimated from isothermal magnetization measurements versus an applied field up to5T.

3 Results and discussion

3.1 Structural properties

The structural refinement of the diffractogram where performed by the Rietveld method [27] using FullProf code [28] (Fig. 1). The structure analysis showed that our compound crystallizes in the orthorhombic system with space group Pnma. Crystal structure parameters and χ² (the reliability factors) are summarized in Table 1. The positions atomics deduced from structural analysis are 4c(x, 0.25, z) for La/Sr, 4b(0, 0, 0.5) for Mn/Fe, 4c(x, 0.25, z) for oxygen ions occupied two different sites, namely O1 at 4c (x, 0.25, z), and O2 at 8d(x, y, z). A single phase was observed without any detectable impurities. It is noted that the lattice parameters and the volume of the unit cell only increased significantly when manganese was substituted by iron. The ionic radius of Mn³⁺ (0.645 Å) is equal to that of Fe³⁺[20], consequently, we have noticed that the substitution of manganese by 5% of iron allows a slight increases of the unit cell volume from 232.55 ų for x = 0 to 233.14 ų for x = 0.05 as well as for unit cells parameters. Our results are agreed to those obtained by Yanchevski et al. [29] and Huang et al. [30].

Fig. 1

XRD patterns for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

Table 1 Refined structural parameters for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

The tolerance factor of Goldschmidt [31] was calculated using:

$$t= \frac{{r}_{A}+ {r}_{O}}{\surd 2({r}_{B}+{r}_{O})}$$

(1)

with: r_A is the radius of the cation occupying site A, r_B is the radius of the cation occupying site B and r_O is the oxygen radius.

According to the electrical neutrality law of our compound:

$$0.7 {\text{La}}^{3+} 0.3 {\text{Sr}}^{2+} 0.65{\text{Mn}}^{3+} 0.3{\text{Mn}}^{4+} 0.05{Fe}^{3+}{O}_{3}^{2-}$$

so:

$${r}_{A}=0.7 {r}_{{\text{La}}^{3+}}+0.3 {r}_{{\text{Sr}}^{2+}}$$

$${r}_{B}=0.65 {r}_{{\text{Mn}}^{3+}}+0.3 {r}_{{\text{Mn}}^{4+}}+0.05 {r}_{{\text{Fe}}^{3+}}$$

Accordingly, the calculation of the tolerance factor (t = 0.92) shows that the structure of our sample is orthorhombic, what is confirmed with Rietveld refinement.

The average crystallite size was estimated from X-ray diffraction using Debye–Scherrer formula [32]:

$$D= \frac{K\lambda }{\beta\cos(\theta )}$$

(2)

where K, λ, β, and θ are the grain shape factor, the X-ray wavelength, the full width at half maximum (FWHM) of the diffraction peak and the Bragg diffraction angle, respectively. The value of the effective crystallite size is 24 nm.

To draw the unit cell, we used “Diamond “program (Fig. 2), in order to determine distances Mn–O₁ and Mn–O₂ and the inter-atomic angles Mn–O–Mn. The results obtained are listed in Table 2.

Fig. 2

Crystal structure of La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

Table 2 Interatomic distances Mn–O and angles Mn–O–Mn for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

3.2 Magnetic properties

Figure 3 indicates the magnetization of La_0.7Sr_0.3Mn_0.95Fe_0.05O₃as a function of temperature for an applied field of 0.05 T. The compound reveals a transition from a ferromagnetic state at low temperature to a paramagnetic state followed by a rapid increase of magnetization around the Curie Temperature (T_C). The value of this temperature is determined at the inflection point of M(T), obtained from the minimum of dM/dT, and it is found equal to 311 K, which is low than that reported by Brik et al. [33], T_C = 343 K. This difference between the two values is probably due to the experimental conditions: elaboration method and temperatures.

Fig. 3

Magnetization versus temperature under an applied field of 0.05 T and The dM/dT curve

Moreover, some studies on the magnetic measurements indicates that the Curie temperature decrease with increasing the Fe content [33,34,35]. The observed decrease in magnetization and T_C with doping iron could be correlated with the fact that Fe³⁺ ions do not engage in the ferromagnetic double exchange (DE) interaction with Mn³⁺ ions, but instead promote the antiferromagnetic interactions Fe³⁺–O–Mn³⁺, Mn⁴⁺–O–Fe³⁺ and Fe³⁺–O–Fe³⁺ super-exchange (SE) interactions [36].

We plotted, (Fig. 4), the inverse of the susceptibility in the paramagnetic state, deduced from the M (T) curves at an applied field of 0.05 T. The Weiss temperature and the Curie constant were so determined using the Curie–Weiss formula:

$$\chi = \frac{C}{T- {\theta }_{\omega }}$$

(3)

where C is the Curie constant and ${\theta }_{\omega }$ is the Weiss temperature.

Fig. 4

The inverse of susceptibility of the sample La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

Figure 4 shows a deviation of χ⁻¹(T) from the linearity around T_C. We obtained the estimated values of the Curie constant and the paramagnetic Curie temperature ${\theta }_{\omega }$. The experimental effective magnetic moment μ_eff(exp.)were deduced from the estimated Curie constant and compared with the theorical value μ_eff(cal.) (Table 3). The difference between the experimental and calculated values is due to the presence of ferromagnetic clusters in the paramagnetic state [37].

Table 3 Magnetic data of La_0.7Sr_0.3Mn_0.95Fe_0.05O₃: The Curie temperature T_C, the Curie–Weiss temperature, the experimental effective paramagnetic moment and theoretical effective paramagnetic moment

The magnetization curve M(H) at T = 5 K is shown in Fig. 5. Our sample is obviously ferromagnetic at this temperature and almost saturated at an applied field of 6 T. The saturation magnetization for our sample is about 3.3 μ_B. Important the magnetic properties of the ordering of cations in the A-sublattice of perovskite can be explained by chemical phases. The separation takes into account the compression effect, which is the result of the action of chemicals and external pressure (surface tension) [38].

Fig. 5

Magnetization versus an applied field at 5 K

3.3 Magnetocaloric properties

In Fig. 6, we plotted the evolution of magnetization versus the applied magnetic field at different temperatures [260, 376 K] with a step of 4 K around Curie temperature. This figure shows an increase of magnetization when the applied magnetic field is less than 0.5 T and saturates above 1 T. The saturation magnetization increases when the temperature decreases, which confirms the ferromagnetic behaviour at low temperatures. This comportment is typical of a soft magnetic material.

Fig. 6

Isothermal magnetization curves measured at different temperatures

The curves for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃continued to rise and did not saturate even at 5 T. In order to understand the nature of transition we plotted Arrott curves M² versus $\left( {\frac{{\mu _{{0H}} }}{M}} \right)$. The plots exhibited a positive slope around T_C which confirms that our sample exhibit second order ferromagnetic to paramagnetic phase transition [39,40,41,42,43,44,45,46].

To investigate the magnetocaloric properties, the magnetic entropy change (MCE, ΔS_M) was calculated. The magnetic entropy change,(–ΔS_M), caused by the increase in the magnetic field was determined using the following equation according to the classical thermodynamic theory based on the relation of Maxwell [47]:

$$ \Delta S_{M} (T)_{{\Delta H}} = \int_{{H_{1} }}^{{H_{2} }} {\left( {\frac{{\partial M\left( {T,H} \right)}}{{\partial T}}} \right)} _{H} {\text{d}}H $$

(4)

The numerical integration of the latter formula at different field and temperature conditions gives the values of ΔS_M:

$$\Delta {S}_{M}= {\sum }_{i}\frac{{M}_{i+1}-{M}_{i}}{{T}_{i}-{T}_{i+1}} \Delta {H}_{i}$$

(5)

where M_i and M_i+1 are experimental values of magnetization at T_i and T_i+1 temperature, respectively, under an applied field H_i. Figure 7 illustrates the magnetic entropy change |${\Delta S}_{M}$| versus temperature at different applied magnetic field from 1 to 5 T. Predictably, the magnetic entropy change increased with the magnetic field applied, and reaches the maximum value around T_C. The maximum of entropy changes from 0.46 J Kg⁻¹ K⁻¹ at an applied field of 1 T to 2.13 JKg⁻¹ K⁻¹ at an applied field of 5 T.The small value of magnetic entropy change can be related to second order magnetic phase transition. As a rule, materials with first order transitions typically exhibit a much greater magnetocaloric effect than those with second order transitions.

Fig. 7

Temperature dependence of magnetic entropy change for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃

Nevertheless, the value of the device studied stems from the ability to adjust its properties and check the structural factors, as well as the facility to synthesize these materials with good chemical stability.

In Table 4, the MCE values obtained in comparison with some others reported in the literature were listed. To calculate the relative cooling power (RCP) the following formula was adopted [47, 48]:

Table 4 Maximum entropy change $\left|{\Delta S}_{M}^{\text{MAX}}\right|$, RCP values and magnetic field change for La_0.7Sr_0.3Mn_0.95Fe_0.05O₃ in comparison with the literature

$${\text{RCP}}= \left|{\Delta S}_{M}^{\text{MAX}}\right| \times {\delta T}_{\text{FWHW}}$$

(6)

${\delta T}_{\text{FWHW}}$ is the full width at half maximum of the magnetic entropy and $\left|{\Delta S}_{M}^{\text{MAX}}\right|$ is the maximum entropy changes. While iron doping reduces T_C and $\left|{\Delta S}_{\text{Max}}^{M}\right|$ relatively, the observed properties of the investigated method are promising and open the way for investigations of materials that are useful for magnetic cooling (Fig. 8)..

Fig. 8

a Arrott plot curves M² versus μ₀H/M for the mean field model, b Arrott plots for the trictritical model, c Arrott curves for the 3D-Heinsenberg model, and d Arrott curves for the 3D-Ising model

3.4 Critical behaviour

To investigate the critical behaviour of manganese oxide around the FM-PM transition second order magnetic phase transition we used different techniques given a wide range critical exponents: α (associated to the critical magnetization at Curie temperature), β (associated to the spontaneous magnetization), and δ (associated to initial susceptibility) [49,50,51].Firstly, these critical exponents defined to apply in the DE model for the long-range mean field theory [11, 52, 53]. Furthermore, the interpretation of some important experimental results on critical exponents and the universality of manganite’s is still controversial [11, 49,50,51,52,53,54,55].In this work we study the critical behaviour of the sample La_0.7Sr_0.3Mn_0.95Fe_0.05O₃oxide using modified Arrott-Plots (MAP).In addition, according to Banerjee, the positive slope indicates a second order phase transition [56]. Arrott and Noakes proposed a strong tool, the MAPs, to use the following empirical relation to evaluate magnetic data [39]:

$${\left(\frac{H}{M}\right)}^{\frac{1}{\gamma }}= \frac{T -{T}_{C}}{{T}_{1}}+ {\left(\frac{M}{{M}_{1}}\right)}^{\frac{1}{\beta }}$$

(7)

where ${T}_{1}$ and ${M}_{1}$ are constants characterizing the compound.

Then a linear relation between ${M}^{\frac{1}{\beta }}$ and can be sought by proper choice of β and γ. Thus by choosing the critical parameters of a given universality class, a linear relation means that the compound belongs to that class.

Figure 8a-d show the variation of modified Arrott plots ${M}^{\frac{1}{\beta }}$ versus ${\left(\frac{H}{M}\right)}^{\frac{1}{\gamma }}$ for different models: mean field theory (β = 0.5; γ = 1); the 3D-Ising model (β = 0.325; γ = 1.241); the tricritical mean- field model (β = 0.25; γ = 1), and the 3D-Heisenberg model(β = 0.365; γ = 1.336).

The scaling hypothesis offers a basis for characterizing a second order phase transition by the values of the critical exponent β, γ and δ for spontaneous magnetization, initial magnetic susceptibility and critical isothermal magnetization, respectively [56]. The magnetic parameters are given in relation to these exponents by the following relationships:

• Spontaneous magnetization under T_C at the zero-applied field limit is given by Eq. 7:

  $$ M_{S} \left( T \right) = M_{0} \left( { - \varepsilon } \right)^{\beta } \,T < T{{\text{c}}} $$

  (8)

• The initial susceptibility is given over above T_C by Eq. 8:

  $$ \chi _{0}^{{ - 1}} \left( T \right) = \left( {\frac{{h_{0} }}{{M_{0} }}} \right)\varepsilon ^{\gamma } T > T{\text{c}} $$

  (9)

• At T_C, magnetization M is based on magnetic field H using Eq. 9:

  $$ M = D_{0} H^{{\frac{1}{\alpha }}} ;\quad T = T{\text{c}} $$

  (10)

Where ε is the reduced temperature $\varepsilon =(T-{T}_{C})/{T}_{C}$, ${M}_{0}$, ${h}_{0}$ and D are critical amplitudes.

Using the adjust of ${M}^{\frac{1}{\beta }}$ versus $\left(\frac{{\mu }_{0}H}{M}\right)$ near T_C, we can deduce the values of β and γ. The obtained curves are parallel to each other in high field region, then that at T_C we have straight line and the α value are directly determined by the linear fit of magnetization. In order to deduce M_S(T) (Spontaneous magnetization) and χ₀⁻¹(T) (inverse initial susceptibility), we investigate the extrapolation of linear part of MAPs in range of the high magnetic field in intersect with (H/M)^1/γ and M^1/β (Fig. 9). On the other way they can be calculated using the Widom relation with β and γ [56]:

Fig. 9

The fits of spontaneous magnetization and initial inverse of susceptibility versus temperature

$$\alpha =1+ \frac{\gamma }{\beta }$$

(11)

The obtained values using MAP are: β = 0.54; γ = 1.13; α = 3.07. The results show that the critical exponents are consistent with the mean field model which is confirmed with the relative slope RS = S(T)/S(T_C) in the high field region around T_C, Fig. 10.

Fig. 10

Relative slope RS versus temperature

4 Conclusion

In summary, we have elaborated and investigated structural, magnetic, magnetocaloric and critical exponents of the manganite oxide La_0.7Sr_0.3Mn_0.95Fe_0.05O₃. The sample was elaborated by solid state reaction. Using Rietveld refinement, the compound crystallized in the orthorhombic structure with Pnma space group. Magnetic measurement shows that the sample exhibits a transition from paramagnetic to ferromagnetic state with decreasing temperature. The substitution of manganese with 5% of iron does not cause a structural transition, but modify the crystallographic parameters, and decreases the T_C value. The magnetocaloric study indicates that the |${\Delta S}_{M}^{\text{MAX}}$|reaches its maximum value at an applied magnetic field 5 T near T_C. The RCP value of doped compound was found to be 127.9 J Kg⁻¹ at ΔH = 5 T, which is suitable for potential application in magnetic refrigeration and heat storage near T_C). Finally, the critical exponents α, β, and γ were evaluated from modified Arrott plots. They are consistent with those of mean field model.