Structural study and large magnetocaloric entropy change at room temperature of La_1−x□_xMnO₃ compounds

Abstract

In this study, our central focus is to investigate the magnetocaloric characteristics of a La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) series prepared by a sol–gel technique published in Prog. Mater. Sci., 93, 2018, 112–232. The crystallographic study revealed that our compounds crystallize in a rhombohedral structure with R3̄c. Ferromagnetic (FM) and paramagnetic (PM) characters were detected from the variation in magnetization as a function of magnetic fields at different temperatures. The second order transition was verified from the Arrott plots (M² vs. (μ₀H/M)), where the slopes have a positive value. In order to verify the second order, we traced the variation of magnetization vs. temperature at different magnetic fields for x = 0.2. This revealed a ferromagnetic (FM)–paramagnetic (PM) transition when temperature increases. Relying on the indirect method while using the Maxwell formula, we determined the variation in the entropy (−ΔS_M) as a function of temperature for different magnetic fields for the three samples. We note that all the studied systems stand as good candidates for magnetic refrigeration with relative cooling power (RCP) values of around 131.4, 83.38 and 57.26 J kg⁻¹ with magnetic fields below 2 T, respectively. Subsequently, the magnetocaloric effect was investigated by a phenomenological model for x = 0.2. The extracted data confirm that this phenomenological model is appropriate for the prediction of magnetocaloric properties. The study also demonstrated that this La_0.8□_0.2MnO₃ system exhibits a universal behaviour.

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1. Introduction

Today, materials that have better properties have long drawn the interest and attention of researchers.¹ For this reason, there is a spate of interest in manganites because of their promising properties such as the colossal magnetoresistance (CMR), magnetocaloric effect of exchange (EME), Griffiths phase.^2–8 Perovskite-lanthanum manganites proved to be potential candidates for magnetic refrigeration at different temperature ranges.^9–12 Nanomaterials are expected to bring new features to the magnetocaloric effect (MCE) and magnetic properties compared to bulk materials.^13,14

We note that there are numerous complex physical phenomena of manganites such as the charge ordering (CO). Swain et al. have shown that this phenomenon exists in nanomaterials. This is due to the planar defects and surface spin disorder, i.e., the deformation within a nanomaterial disturbs the AFM arrangement of the spins in the nucleus. Consequently, the state of the charge order is suppressed. However, for a bulk material the deformation is small as compared to a nanomaterial and that it has no impact on the AFM core and therefore, the appearance of the charge ordering (CO). More the suppression of the charge ordering (CO) in the materials can be due to the eruption of the spatial symmetry.¹⁵ The charge ordering (CO) can be demonstrated from the electrical measurements. In the system Pr_0.5Ca_0.5MnO₃,¹⁶ the suppression of CO is explained by the melting of long-range charge ordering behavior due to surface spin disorder and induced lattice strain effects in PCMO manganite system.

Electric field controlled magnetism is an exciting area of condensed matter physics. It allows the exploration of device applications with ultra-low energy consumption compared to the conventional current-controlled or magnetic field-controlled devices. Numerous studies were performed by Swain et al. to demonstrate the electric field-controlled magnetoresistance (MR) in a three layer structure composed of La_0.67Sr_0.33MnO₃ (LSMO) (40 nm)/SrTiO₃ (10 nm)/LSMO (10 nm) grown via the pulsed laser deposition technique on a 500 μm thick BaTiO₃ (001) monocrystalline substrate (BTO). The jumps observed in the temperature-dependent magnetization curve around the structural phase transitions of BTO ensure the magnetoelectric coupling mediated by the stress between the LSMO and BTO layers. A significant change in the MR of this structure in the applied electric fields shows no dependence on polarity. Results are linked to magnetoelectric coupling mediated by network constraint in ferromagnetic/ferroelectric LSMO BTO heterostructures.¹⁷

Today, a new technology called magnetic cooling offers several advantages, including higher cooling efficiency, lower power consumption, lower noise level, much compactness, and higher safety for the environment. This new technology rests on a phenomenon called “magnetocaloric effect” (MCE). Recent discoveries in materials science disclosed that colossal ECM values can be observed in many materials (manganites, ferrites, amorphous alloys, intermetallic compounds, etc.).¹⁸ The magnetocaloric effect (MCE) is a basic character of magnetic materials. It is the response of the material to the application or suppression of magnetic fields. Relying upon the isothermal magnetic data, the magnetic entropy change (ΔS_M) can be assessed through the use of the standard Maxwell relation:¹⁹

According to Maxwell's relation, we get

The extremums of the −ΔS_M of our compounds are reported in the vicinity of T_C, where is the experimental value obtained from the M(T) curve for multiple magnetic fields (μ₀H). Magnetic entropy change is provided by the following expression:

The entropy is connected to the relative cooling power (RCP) by the relation:²⁰

where δT_FWHM is the full width at half maximum of the magnetic entropy change curve. A good system for applications in the field of magnetic cooling must be characterized by a large heat capacity defined by:

Features of manganites continuously have drawn the attention of multiple researchers specialized in condensed matter physics.^21–26 These compounds are known for their close relations between orbital, charge, spin, and lattice degrees of freedom, which results in a diversity of their phase states and physical properties.^27–30 Among the wide variety of factors specifying the properties of manganites, the most significant ones are the stoichiometry (the types of ions and their ratio) and crystal structure parameters (the mean 〈Mn–O〉 bond length and the mean 〈Mn–O–Mn〉 bond angle).

It is conventionally known that the magnetic and electronic properties of substituted manganites are specified by the e_g electron bandwidth W = cos(1/2[π − 〈Mn–O–Mn〉])/〈Mn–O〉^3.5.³¹ Compounds with a greater bandwidth W display more pronounced ferromagnetic and metallic properties (i.e., higher Curie point (T_C), higher metal insulator transition temperature and lower resistivity (ρ)^32–34).

This study centers around the magnetocaloric effect and Hamed model for the three compounds, x = 0.1, 0.2 and 0.3.

2. Preparation method

The sol–gel technique is the preparation method of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) from the precursors lanthanum nitrate (La(NO₃)₂·6H₂O) and manganese nitrate (Mn(NO₃)₂·4H₂O) up to purity 99%. The method of preparation has been well described in ref. 35.

3. Results and discussion

In the first step, we performed XRD analysis to verify the crystal structure of the studied samples. Powder XRD patterns of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) compounds collected at room temperature are plotted in Fig. 1. We note that our samples are of a single phase with a very small amount of Mn₃O₄ for x = 0.3, as found in recent studies.³⁵ XRD data were analyzed using Rietveld refinement.³⁶ Fig. 2 illustrates the Rietveld refinement of the XRD profiles for La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) samples, with a good agreement between the observed and the calculated profiles, this is due to the excellent goodness of χ². The analyzed data showed that our samples crystallize in the rhombohedral system with R3̄c. The SEM micrographs of Fig. 3 show a non-homogenous microstructure and non-uniform grain size distribution. In order to check the existence of all elements in the compound, EDX was performed. Fig. 3 shows that the energy dispersive analysis of X-ray (EDX) spectra reveals the presence of La, Mn and O elements in La_1−x□_xMnO₃ compounds, confirming that there is no loss of any integrated element. In order to examine the distribution of detected elements, the EDX mapping of La (slate blue), Mn (green) and O (red) is checked and presents non uniform dispersion. All samples reveal the presence of the characteristic peaks of La and Mn and O elements The inset curves in Fig. 4 display the magnetic isotherms of x = 0.1, 0.2 and 0.3 samples measured with a magnetic field change from 0 to 2 T in the temperature interval of 4 K. Here, the maximum magnetization is recorded for x = 0.2 and 0.3 samples, suggesting that adiabatic magnetization and demagnetization result in the maximum order and disorder in these samples. The Arrott plots (Fig. 4) exhibit the variation of M² vs. μ₀H/M for the three compounds (x = 0.1, 0.2 and 0.3) to determine the nature of transition (first order: negative slope and second order: positive slope). We notice that these curves have a positive slope, which indicates that the transition from the FM to the PM state at the Curie temperature (T_C) is a second order magnetic phase transition, according to the criteria reported by Banerjee.³⁷

Fig. 1 XRD patterns of the La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) compounds at room temperature.

Fig. 2 Rietveld refinement of the X-ray patterns of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3). Experimental data presented in black, calculated data presented in red, difference between them presented in blue, Bragg position presented in green.

Fig. 3 SEM micrographs and corresponding EDS spectra of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) samples.

Fig. 4 Isothermal magnetization plots M versus H of the La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) series, and the inset is the Standard Arrot.

In order to apply the phenomenological model,^38,39 Fig. 3 depicts the variation in the magnetization M as a function of temperature at various magnetic applied fields for x = 0.2. Experimental data (symbols) were modified by the eqn (1)⁴⁰ (solid line). We find that this equation well portrays the pace of magnetization, which proves the validity of this model in our case. Model parameters are presented in table in the inset Fig. 5. Furthermore, the curves M(H, T) at μ₀H unveil the presence of a second order paramagnetic–ferromagnetic transition, where the magnetization varies from continuous way deduced from the increase in T_C with the magnetic field.

Fig. 5 Magnetization versus temperature for La_0.8□_0.2MnO₃. The symbols are the experimental data and the solid lines are the modeled results.

Fig. 6 portrays the schematic representation of the magnetic refrigeration cycle whose value of the change in entropy of a ferromagnetic material depends on both μ₀H and T. Fig. 7 illustrates the variation in the magnetic entropy change (−ΔS_M) as a function of T for different μ₀H using eqn (3) for the three samples x = 0.1, 0.2 and 0.3. It increases by augmenting the value of μ₀H and reaches a maximum around T_C. For x = 0.2 and using eqn (5),⁴⁰ we plot the theoretical entropy as a function of magnetic field for x = 0.2. We can assert that the maximum magnetic entropy is obtained around T_C. Zener model was appropriate to justify the change to perovskite large magnetic entropy. This model discloses an indirect interaction between Mn³⁺ and Mn⁴⁺ related to the change in their ratio.⁴¹ Guo et al.⁴² assumed that the large magnetic entropy change in perovskite manganites could refer to the spin-lattice coupling in the magnetic ordering process, which plays an intrinsic role in additional magnetic changes.^43,44

Fig. 6 Schematic representation for the magnetic refrigeration cycle.

Fig. 7 Thermal variation of the magnetic entropy (−ΔS_M) of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) systems under different magnetic fields between 0.5 T and 2 T and modeled for x = 0.2.

The experimental values of (−ΔS_M), RCP and T_C for our compound are compared to other references at 2 T, which are listed in the inset table in Fig. 8. We observe that −ΔS_M increases and RCP decreases. This is explained by the effect of spin coupling, which became less important when the applied magnetic field increased. We can detect that the proposed compounds exhibit important values. The maximum values of ΔS_M and RCP obtained at 2 T were compared to gadolinium Gd⁴⁵ as well as several other materials reported in literature.^46–48 The results are in favor of promising magnetic refrigerants in terms of application. The good value of RCP equal to 131.4 J kg⁻¹ for x = 0.1 is due to the strong magneto-structural coupling.

Fig. 8 Comparative histogram representation of the values of (−ΔS_M), RCP and Curie temperature (T_c) at 2 T for La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) with the family of La-manganite materials and the standard gadolinium (Gd) sample. The dotted orange line shows the room temperature. The inset shows the table with corresponding materials with their respective references.

Using eqn (5), we plot the experimental (−ΔC_P) as a function of temperature for x = 0.1 and 0.2 in Fig. 9. Using eqn (6),⁴⁰ we plot the theoretical variation of (−ΔC_P) for x = 0.2 as an example. This figure demonstrates that the intersection of these curves is around T_C. It is clear that (−ΔC_P) is positive when T_C > T and negative when T_C < T.

Fig. 9 Variation in the specific heat as a function of temperature at different magnetic fields of La_1−x□_xMnO₃ (x = 0.1 and 0.2) and modeled for x = 0.2.

A universal behavior of ΔS_M and its dependence on the field in materials with a second order transition have recently been proposed by Franco et al.,^49,50 who set forward a universal behavior of −ΔS_M. The phenomenological universal curve consists of the collapse of the entropy variation curves after a scaling process, regardless of the applied magnetic field. Therefore, the main hypothesis is based on the fact that if a universal curve exists, then the equivalent points of ΔS_M (T) curves measured for different applied magnetic fields should collapse on the same universal curve. It is also demonstrated that these curves are unique for each class of universality.⁵⁰ MCE data from different materials of the same universality class should overlap on the same curve regardless of the applied magnetic field.

This phenomenological universal curve can be established by normalizing all ΔS_M(T) curves by their respective maximum value. ΔS^max_M, as a function of and the temperature axis are rescaled by a new parameter θ = ±1, identified by the expression:

T_r1 and T_r2 are the temperature values of the two reference points on each curve.

Fig. 10 illustrates the universal curve for x = 0.2 (as an example). We can clearly infer that all the curves collapse on a single universal curve regardless of the magnetic field, which proves the validity of the technique and suggests that the transition is of a second order.

Fig. 10 The universal curve for x = 0.2.

4. Conclusion

In this study, we investigated the magnetocaloric effects of La_1−x□_xMnO₃ (x = 0.1, 0.2 and 0.3) prepared via a sol–gel technique. We demonstrated that our samples displayed a second order transition, as implied from the Arrot plot. In order to verify the second order, we traced the variation of M vs. T at different magnetic fields for x = 0.2. This exhibited an FM–PM transition when the temperature increased. Based upon the Maxwell formula, we determined the variation in the entropy (−ΔS_M) as a function of temperature for different magnetic fields for the three samples. It is noteworthy to mention that all studied systems stand as good candidates for magnetic refrigeration at about 131.4, 83.38 and 57.26 J kg⁻¹ with magnetic fields under to 2 T, respectively. The study also proved that this La_0.8□_0.2MnO₃ system presents a universal behaviour. After exploring the magnetocaloric effect by a phenomenological model for x = 0.2, the extracted data confirm that this phenomenological model is convenient for the prediction of magnetocaloric properties.

Being a promising compound, in future studies, we aspire to further explore its additional interesting features so as to be invested in technological as well as industrial fields.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge the financial support of the research project by the Tunisian Ministry of Higher Education and Scientific Research and the FCT-Portugal within the framework of Tunisian-Portuguese cooperation in the field of scientific research and technology.

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