Cationic Mismatch Effect Induced by Double Substitution on the Structural and Magnetic Properties of La_0.5Ca_0.5MnO₃

Abstract

In this study, we aimed to induce controlled structural disorder through a double substitution approach in the La_0.5Ca_0.5MnO₃ compound by investigating La_0.5−xRe_xCa_0.5−yAe_yMnO₃ compounds with x = 0.05 and 0.1 and Re = Eu, Nd, Gd, Pr, and Ae = Ba and Sr. The y values are adjusted to maintain a constant average ionic radius (<r_A> = 1.198 Å) and an unchanged Mn^3+/Mn⁴⁺ ratio. These samples were synthesized using the sol–gel method. XRD analysis confirms structural stability despite the induced disorder, showing subtle lattice distortions. Magnetic measurements reveal that introducing low disorder annihilates the charge ordered (CO) state, enhances double-exchange interactions, and influences the ferromagnetic (FM) volume fractions. Moderate disorder strengthens AFM–CO state, triggering a first–order metamagnetic transition and reducing the Curie temperature value. Magnetic field-dependent magnetization data show disorder dependent magnetic behavior and suggest the presence of the Griffiths phase for all samples, confirming the role of structural disorder in tuning magnetic phase coexistence. Pr-based samples display a considerable magnetocaloric effect near their Curie temperature.

1. Introduction

Manganites, or manganese oxides, are of great interest thanks to their fascinating and relevant properties, such as charge-ordering (CO), orbital ordering, and magnetic phase transitions [1,2,3,4,5,6,7,8]. The present research aims to understand these properties in order to adopt these materials for technological applications (magnetic sensing, magnetic refrigeration, spintronics, hyperthermia, etc.) and investigate the potential use for multifunctional devices [1,2,3,4,5,6,7,8,9,10]. La_0.5Ca_0.5MnO₃ is one of the best known and most studied compounds in recent years. This compound exhibits two magnetic transitions as a function of temperature: a second-ordered transition to a ferromagnetic (FM) state around 220 K, followed by a first-ordered transition to an antiferromagnetic (AFM) state with CO at 150 K [5]. At low temperatures (below 150 K), magnetic phase separation (MPS) effects can be observed, with the FM and AFM regions coexisting in the material, contributing to complex magnetic behaviors. Similar studies have shown the same behavior with other compositions [11,12,13,14,15,16]. This compound also displays a magnetocaloric effect at low temperatures, where the magnetic entropy change manifests itself under the application of an external magnetic field. This effect is particularly marked around the transition to the FM state [15]. However, there are few works devoted exclusively to the effect of structural and magnetic disorder [4,11,15,16,17]. In other words, the double substitution approach remains insufficiently explored. This approach makes it possible to fix the value of the mean ionic radius at the A site <r_A> as well as the Mn^3+/Mn⁴⁺ ratio and thus isolate the effect of structural disorder σ², which was the objective of our previous works [15,16]. To do so, several compounds with critical composition were synthesized. These compositions were carefully adjusted in order to maintain a constant Mn³⁺/Mn⁴⁺ ratio (equal to 1) and a constant average ionic radius at A site. For perovskite manganites with general formula ABO₃, the values of <r_A> and σ² can be calculated by the following equations [18,19]:

<r_A> = ∑y_ir_i,

(1)

σ² = ∑y_ir_i² − <r_A>²,

(2)

where y_i is the occupation of the cation i having an ionic radius r_i [20]. In this study, we will investigate the effect of cationic disorder introduced by a double substitution with a fixed <r_A> value (<r_A> = 1.198 Å for La_0.5Ca_0.5MnO₃). The choice of compounds is not arbitrary, as it aims to control structural disorder to examine its impact on structural and magnetic properties. We have used europium and barium as substituents in La_0.5−xEu_xCa_0.5−yBa_yMnO₃ (with x = 0.05 and 0.1). Then, we introduced an additional magnetic disorder by replacing Eu³⁺ with Gd³⁺ and Nd³⁺ for x = 0.1 to achieve a high structural/magnetic disorder. Furthermore, a weak structural disorder will be introduced by using praseodymium and strontium substitution in La_0.5−xPr_xCa_0.5−ySr_yMnO₃ (x = 0.05 and 0.1). The study will reveal a strong correlation between the structural disorder and the magnetic behavior of the studied specimens.

2. Materials and Methods

First, we calculated the <r_A> value for the pristine compound La_0.5Ca_0.5MnO₃ by using Equation (1) and found that <r_A> = 1.198 Å. After that, the y values were adjusted for fixed x values to maintain a constant <r_A> for all our compounds (<r_A> = 1.198 Å) and an unchanged Mn^3+/Mn⁴⁺ ratio (Mn^3+/Mn⁴⁺ = 1). All the studied compounds in this work have been synthesized using the sol–gel method [21,22]. We have selected high-purity precursors (99.9%, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) to guarantee the quality of the final materials. All the precursors were dissolved in a nitric acid solution at 60 °C. Then, we added citric acid and ethylene glycol to achieve the solution homogeneity. Next, the solution was heated to 130 °C until the formation of a viscous gel. After that, this gel was transformed into ash by further heating it up to 300 °C. Then, the obtained ash was ground and then calcined at 600 °C for 5 h in order to decompose the residual organic matter. The obtained powders were pressed into pellets that underwent several cycles of grinding, pelletizing and sintering at 600 °C, 800 °C and 1000 °C. These compounds are referred as L0, LE1, LE2, LG, LN, LP1, and LP2 for La_0.5Ca_0.5MnO₃, La_0.45Eu_0.05Ca_0.483Ba_0.017MnO₃, La_0.4Eu_0.1Ca_0.466Ba_0.034MnO₃, La_0.4Nd_0.1Ca_0.4817Ba_0.0183MnO₃, La_0.4Gd_0.1Ca_0.4624Ba_0.0376MnO₃, La_0.45Pr_0.05Ca_0.4854Sr_0.0146MnO₃, and La_0.4Pr_0.1Ca_0.4715Sr_0.0285MnO₃, respectively. These compounds were characterized using X-ray diffraction at room temperature by using a Cu-Kα radiation source (Bruker D8 advance, Grenoble, France), energy dispersive X-ray (EDX) spectroscopy, and an extraction magnetometer (Grenoble, France).

3. Results and Discussion

The EDX spectroscopy data for L0 and LG samples, presented in Figure 1, confirm the presence of all the elements used during the synthesis, without contamination or unwanted elements. A detailed structural analysis [15,16,23,24] was performed using FullProf software (version June 2015) to assess the effect of cationic disorder on structural properties. All the studied samples crystallized in the orthorhombic system with Pnma space group, indicating the absence of any structural transition induced by substitution. We have presented, in Figure 2, the refined diffractograms of the L0 and LP2 compounds. We have gathered all the refinement parameters as well as the values of cationic disorder in

Table 1. Structural parameters and cationic mismatch for our studied samples.

Sample	a (Å)	b (Å)	c (Å)	σ2 (10−4 Å2)
L0	5.3954(4)	7.6593(2)	5.3983(4)	3.2
LP1	5.4144(3)	7.6714(2)	5.4147(2)	6.2
LP2	5.4161(3)	7.6771(2)	5.4154(3)	6.9
LE1	5.4008(6)	7.6664(3)	5.4010(6)	21.8
LE2	5.4218(3)	7.6254(3)	5.4088(3)	40.2
LN	5.3973(10)	7.6650(4)	5.3973(9)	17.0
LG	5.3996(7)	7.6633(3)	5.3989(7)	51.0

.

It can be observed that the increase in cationic disorder does not affect the stability of the crystal structure. As shown in Table 1, the lattice parameters of each compound undergo slight modifications, indicating the presence of MnO₆ octahedra deformations. It is evident that cationic disorder enhances the MnO₆ octahedra distortions. These distortions can be observed through the crystal structure of L0, LP2, and LG samples obtained by VESTA software (Version 3.5.8) in Figure 3.

To better understand the cationic mismatch effect, the evolution of the cationic disorder values has been plotted in Figure 4. One can observe that the LP1 and LP2 samples exhibit low disorder values (close to that of parent compound L0) compared to other substituted specimens. We should notice that the LG sample is the most disordered sample in this study.

Figure 5 shows the evolution of magnetization as a function of temperature in field-cooled mode under an applied magnetic field of 0.05 T. This figure clearly shows the difference between the magnetization measurements of each compound. First, the parent compound exhibits two magnetic transitions, the first from the paramagnetic (PM) state to the FM state at Curie temperature T_C = 250 K, followed by a transition to a CO–AFM state at T_CO = 120 K, indicating that this compound is characterized by the MPS phenomenon. Moreover, another transition can be observed near 50 K for the pristine compound as well as the LG sample, and such a transition may reflect the presence of a glassy state below 50 K. When a slight structural disorder is introduced by using praseodymium and strontium (LP1 and LP2 compounds), the T_C value remains close to that of the parent compound (L0), with absence of the transition to the CO state. Additionally, the magnetization value significantly increases, indicating that the introduction of a slight cationic disorder stabilizes the FM state, which favors double-exchange interactions and suppresses CO. The observed changes for the LP1 and LP2 samples are ascribed to the cooperative effect of both Pr³⁺ and Sr²⁺ ions. In fact, the substitution by both ions shifts the composition of L0 towards that of the Pr_0.5Sr_0.5MnO₃ sample, where no CO is observed at low temperature, except for an A–type AFM structure [3]. Both Pr_0.5Sr_0.5MnO₃ [3] and La_0.5Ca_0.5MnO₃ [5] display AFM behavior at low temperature. However, both the LP1 and LP2 samples are FM at low temperature despite having an intermediate composition between Pr_0.5Sr_0.5MnO₃ and La_0.5Ca_0.5MnO₃, which highlights the contribution of structural disorder. As the cationic disorder increases (becoming nearly seven times stronger than that in the parent compound), the transition to the CO state remains absent. However, the Curie temperature T_C sharply decreases, reaching 97 K for the LN compound (based on neodymium and barium), and continues to decrease until reaching 72 K for the LG compound, which exhibits the highest disorder. It can also be observed that the low-temperature magnetization value is higher than that of the parent compound L0, but significantly lower than the values reported for LP1 and LP2. This could be attributed to the important effect of structural disorder.

Figure 6 illustrates the variation in the magnetic transition temperature T_C as a function of cationic disorder, clearly showing the decrease in T_C due to the cationic disorder effect. The discontinuity in T_C is remarkable when σ² shifts from 7 × 10⁻⁴ to 17 × 10⁻⁴ Ų. We believe that this disorder range should be further investigated in order to check if there is a critical σ² value where FM starts to weaken.

The variations in the inverse of PM susceptibility is shown in Figure 7. The results for the LP2 sample are not shown because they are similar to those of LP1. According to the Curie–Weiss law, the inverse of PM susceptibility can be expressed as

$${\displaystyle \frac{1}{\chi }}={\displaystyle \frac{T-{\theta }_p}{C_p}},$$

(3)

where C_p and θ_p are the Curie constant and the Weiss PM temperature, respectively. A deviation from linearity is observed for all samples, supporting the presence of some FM interactions in the PM phase (a manifestation of MPS phenomenon). The deviation achieves reduced when a higher magnetic field is applied as can be seen for the LP1 sample, which indicates the presence of Griffiths phase [14,15,23]. The presence of such a phase is very important since it is a possible origin of colossal magnetoresistance [13]. One can notice that disordered samples display stronger deviation from the Curie–Weiss law, which demonstrates that the Griffiths phase can be controlled by simply modifying the cationic disorder. Therefore, inducing a cationic mismatch may yield a colossal magnetoresistive effect near Tc. Thus, the magnetotransport properties of our studied specimens should be investigated in order to shed some light on their magnetoresistive potential. The different magnetic transition temperatures, the Curie constant and the theoretical and experimental effective moment values for all samples are gathered in

Table 2. The magnetic transition temperature, the Curie constant, the theoretical and experimental effective moment values, and the calculated percentage of FM fraction for all samples.

Sample	TC (K)	θp (K)	CP/µ0 (µB K T−1)	${\mathit{\mu }}_{\mathit{e}\mathit{f}\mathit{f}}^{\mathit{e}\mathit{x}\mathit{p}}$ (µB)	${\mathit{\mu }}_{\mathit{e}\mathit{f}\mathit{f}}^{\mathit{t}\mathit{h}}$ (µB)
L0	250	218	7.82	5.81	4.41
LP1	215	227	9.37	4.49	4.56
LP2	220	225	7.97	6.47	5.98
LN	97	156	5.63	4.92	4.56
LE1	90	179	8.55	6.17	5.98
LE2	85	210	10.11	7.40	4.41
LG	72	100	7.00	5.49	5.07

. It is possible to calculate the experimental effective PM moment ${\mu }_{eff}^{exp}$ by

$$C_p={\displaystyle \frac{{\mu }_0}{3k}}{({\mu }_{eff}^{\exp })}^2,$$

(4)

where µ₀ is the vacuum permeability and k is the Boltzmann constant. Furthermore, we can notice that the theoretical effective moment ${\mu }_{eff}^{the}$ is higher than the experimental effective moment values for all samples, which suggests the presence of short-range FM interactions in the PM region.

In order to understand the impact of cationic mismatch on magnetic behavior at low temperature, we have illustrated, in Figure 8, the magnetization isotherms recorded at 45 K for all the studied samples. One can notice that none of the isotherms reach saturation, with the presence of a metamagnetic transition (field-induced transition from AFM to FM state) for the L0, LG, LN, LE1, and LE2 samples. The presence of metamagnetic transition is direct evidence of the presence of AFM domains inside these samples, which means that a high disorder does not suppress CO domains, it just weakens FM interactions. But with low cationic disorder (which is case of the LP1 and LP2 samples), the isotherms display saturated behavior even for low field values, with the absence of a metamagnetic transition, which indicates the annihilation of the CO–AFM state. Thus, while CO seems to be destroyed by weak disorder in favor of FM domains, strong disorder highly weakens FM domains, leading to the improvement of super exchange interactions, which promote the development of CO domains.

To better understand the observed magnetic transition, we have illustrated in Figure 9 the Arrott plots above the magnetic transition temperature Tc, with the selected temperatures above Tc. Arrott plots are effective ways to detect the presence of metamagnetic behavior in phase-separated manganites [11,15,16,25]. The presence of isotherms with negative slopes is a signature of a first-ordered metamagnetic transition from the AFM to the FM state as the applied magnetic field increases.

Both the LP1 and LP2 samples exhibit only positive slopes, suggesting that the PM–FM transition is of second-order. However, as the cationic disorder increases, a first-order transition appears (plots with negative slope), along with the occurrence of a second-order FM–PM transition in LN, LE1, LE2, and LG. The presence of such behavior supports the persistence of AFM domains above Tc for these samples. The metamagnetic transition is responsible for such behavior, confirming the presence of the MPS phenomenon in these highly disordered specimens. Thus, structural disorder appears to be an effective way to control the concentration of the different coexisting phases, which is crucial for technological applications.

Since the LP1 and LP2 samples possess an FM ground state and present the highest Curie temperature value, it is important to explore the magnetocaloric potential of these specimens. Figure 10 shows the variations in magnetic entropy change (ΔS_M) with temperature for our studied samples, determined from isothermal magnetization measurements according to the following relation:

$$\Delta S_M\left(T\right)={{\displaystyle \int }}_0^H{\displaystyle \frac{\partial M}{\partial T}}dH.$$

(5)

We can observe two extrema in the magnetic entropy change for L0. The first maximum is negative and appears around T_C. The presence of a negative peak is generally characteristic of FM samples, as it results from the FM–PM transition (order–disorder transition) with increasing temperature. However, the second maximum located near T_CO is positive, indicating the existence of a magnetic transition from the CO–AFM state to the FM state (order–order transition). For the Pr-based compounds, only negative ΔS_M values can be observed, indicating a unique transition from the FM to the PM state. However, we note the absence of the positive ΔS_M characterizing the pristine compound, which confirms the annihilation of long-range CO. In addition, we can observe an increase in the maximum value of the magnetic entropy change when the applied field value is increased due to the enhancement of FM tendencies. It is possible to evaluate the relative cooling power (RCP) by

$$RCP=-\Delta S_M^{Max}·\delta T^{FWHM},$$

(6)

with $\Delta S_M^{Max}$ being the maximum ΔS_M value and $\delta T^{FWHM}$ being the full width at half maximum of ΔS_M peak. The values of $-\Delta S_M^{Max}$, RCP, and $\delta T^{FWHM}$ for the LP1 and LP2 samples are listed in

Table 3. Magnetocaloric parameters under several magnetic field values for LP1 and LP2 compounds.

Sample	LP1			LP2
µ0H (T)	$-\Delta S_M^{Max}$ (J K−1 kg−1)	$\delta T^{FWHM}$ (K)	RCP (J kg−1)	$-\Delta S_M^{Max}$ (J K−1 kg−1)	$\delta T^{FWHM}$ (K)	RCP (J kg−1)
1	1.48	10.05	14.87	0.88	33	29.04
2	2.24	33.09	74.12	1.75	48.37	84.65
3	2.84	48.82	138.64	2.48	50.94	126.33
4	3.29	62.04	204.11	3.1	58.94	182.71
5	3.68	74.26	273.28	3.63	69.52	252.36
6	4.12	85.04	350.38	4.16	73.79	306.97

. The weakening of AFM–CO interactions induced by substitution significantly contributes to the observed increase in cooling capacity values for Pr-based compounds compared to L0 [15]. Indeed, the substitution disrupts the AFM–CO domains which transform into the FM state, leading to an increase in the RCP value. Compared to the parent compound, the substitutions have a positive impact on the cooling capacity, as can be noticed from Figure 10. Thus, weak structural disorder presents an effective way to enhance the magnetocaloric effect through the destabilization of CO–AFM domains in manganites, leading to their conversion to the FM state.

4. Conclusions

In this study, we have investigated the impact of cationic disorder on the structural and magnetic properties of La_0.5Ca_0.5MnO₃. Compounds of formulas La_0.5−xEu_xCa_0.5−yBa_yMnO₃ (x = 0.05; 0.1), La_0.5−xPr_xCa_0.5−ySr_yMnO₃ (x = 0.05; 0.1), and La_0.4Re_0.1Ca_0.5−yBa_yMnO₃ (Re = Nd and Gd) were synthesized using the sol–gel method with high-purity precursors. Structural refinements using FullProf software confirm that increasing cationic disorder does not destabilize the structure but induces subtle lattice distortions. Magnetization measurements reveal a strong influence of disorder on phase transitions. Introducing a low level of disorder suppresses the CO state, enhances the FM phase, and stabilizes double-exchange interactions. With increasing disorder, the Curie temperature T_C decreases, along with reinforcement of the AFM–CO state in favor of FM state. The inverse of PM susceptibility testifies to the presence of Griffiths phase, indicating the presence of FM clusters just above T_C. Isothermal magnetization curves at 45 K reveal a first-order metamagnetic transition for highly disordered specimens. However, a low level of disorder stabilizes the FM state, eliminating the first-ordered metamagnetic transition. These findings suggest that tuning cationic disorder allows for precise control over MPS in La_0.5Ca_0.5MnO₃. A considerable magnetocaloric effect was recorded for Pr-based specimens.