An efficient composite magnetocaloric material with a tunable temperature transition in K-deficient manganites

Abstract

This paper reports on a magnetic material with high steady relative cooling power (RCP) over a temperature range from 325 to 275 K induced by potassium-deficiency in polycrystalline samples of La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2). The possibility to adjust the temperature transition close to room temperature exists by changing the potassium deficiency rate. All the samples were synthesized using the citrate-gel method. X-ray diffraction and magnetization measurements were conducted to examine the crystallographic structure and magnetocaloric properties. All the samples were found to be a single phase and crystallize in rhombohedral symmetry with R3̄c space group. From the magnetic measurements, a second-order magnetic phase transition from the ferromagnetic to paramagnetic state was noticed at the Curie temperature (T_C), which was found to decrease from 325 to 275 K when the potassium-deficiency rate increased. Besides, the magnetocaloric effect (MCE) as well as the RCP has been estimated. The obtained results have confirmed that our manganite with potassium-deficiency has significant advantages for magnetic refrigeration. Finally, the critical behavior associated with the magnetic phase transition reveals that the estimated critical exponents are consistent with the prediction of the mean field theory (β = 0.5, γ = 1, and δ = 3) for the x = 0.00 and x = 0.10 samples, while the estimated critical exponents for x = 0.2 were consistent with the prediction of the 3D-Heisenberg model (β = 0.365, γ = 1.336 and δ = 4.8).

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1. Introduction

Rare-earth based manganites with the general formula R_1−xB_xMnO₃ (R-rare-earth and B-bivalent ion) has been the focus of many researchers from a fundamental point of view and thanks to their possible potential applications.^1–7 The strong compound interactions with remarkable correlation between transport, magnetic and structural properties of such materials are still the interest of fundamental studies.¹ Furthermore, manganites reveal several fascinating functional properties, such as colossal magnetoresistance (CMR) and large magnetocaloric effect (MCE).^1,7,8 It is recognized that the MCE-based magnetic refrigeration technology (MRT) is a promising substitute for conventional gas compression refrigeration techniques.^8–10 In fact, compared to conventional gas compression, magnetic refrigeration offers a greater cooling efficiency. Besides, the use of hazardous elements related to gas compression-based refrigeration is considered as environmentally precarious.⁹ The selection of a suitable magnetic refrigerant is considered to be the most important factor in governing the performance of a magnetic refrigerator. Examples of the compounds that have been considered as potential magnetic refrigerants (MR) are gadolinium and some other intermetallic alloys.¹⁰ Nevertheless, research studies have recently revealed that manganites also have significant qualities that present them as prospective candidates as magnetic refrigerants.^7–9 These materials show large MCE and their magnetocaloric properties can be tuned by changing the doping concentration, which offers more flexibility to their applications. Compared to metallic compounds, the resistivity of manganites, which can significantly reduce the eddy current losses, is higher and is an additional advantage of these compounds.⁹ Furthermore, the latter show great chemical stability and their production cost is relatively lower compared to other potential refrigerants. Bahl et al. recently reported an effective application of manganites in an active magnetic regenerator, demonstrating their feasibility in practical magnetic refrigeration.¹¹ In addition, our original idea was to change the physical properties by creating a deficiency in the materials. However, only a few studies^5–7 have been proposed to discuss deficiency in the manganite system. As is well known, deficiency in this system leads to a change in the Mn³⁺/Mn⁴⁺ ratio.

This research work aims to study the effect of potassium deficiency on the structural, magnetic and magnetocaloric properties of polycrystalline La_0.8K_0.2−x□_xMnO₃ manganite. We report a compound showing a significant magnetocaloric effect with a tunable temperature transition near room temperature.

2. Experimental

The La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples were prepared using the citrate-gel method. In fact, stoichiometric amounts of the nitrate precursor reagents La(NO₃)₃·6H₂O, Mn(NO₃)₂·4H₂O and KNO₃ were dissolved in water and mixed with ethylene glycol and citric acid, forming a stable solution. The molar ratio of metal : citric acid was 1 : 1. The solution was then heated on a thermal plate under constant sintering at 80 °C to remove the excess water and obtain a viscous gel. The obtained gel was decomposed at 300 °C and the resulting precursor powder was heated in air at 500 °C, 600 °C and 700 °C for 24 h to ameliorate crystallinity. Subsequently, the powder was pelletized and sintered at 700 °C for 12 h. The samples were quenched in air by removing from the furnace. The phase formation and crystal structure of the powders were confirmed by X-ray diffraction (XRD) using a Cu Kα radiation source. The magnetic measurements were performed using a BS1 and BS2 magnetometer developed at the Néel Institute.

3. Results and discussion

3.1. Structural properties

The X-ray diffraction (XRD) patterns recorded at room temperature for all our synthesized samples La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) are shown in Fig. 1. The superposition of all the peaks shows that all the samples crystallized in the same structure and were efficaciously indexed according to a rhombohedral structure with R3̄c space group, in which the La/K atoms are in the 6a (0,0,1/4) position, Mn is in the 6b (0,0,0) position and O is in the 18e (x, 0,1/4) position. The data were analyzed by the Rietveld method using the Fullprof program.¹² Fig. 2 presents the measured and calculated (refined) X-ray diffraction patterns, and the positions of the Bragg reflections for the La_0.8K_0.2−x□_xMnO₃ samples. The refinement results are listed in Table 1. From these results, it is obvious that the unit cell parameters and volume increase almost linearly with an increase in the K vacancy rate (x). The variation of unit cell volume versus x is plotted in Fig. 3. The introduction of the vacancy (x) in our samples implies a partial conversion of Mn³⁺ to Mn⁴⁺ ions according to the formula La_0.8³⁺K_0.2−x⁺□⁰_x(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻. The increase in the vacancy content leads to an increase in the Mn tetravalent ion number, which possesses a smaller ionic radius (r_Mn⁴⁺ = 0.53 Å and r_Mn³⁺ Å (ref. 13)). Because several studies have shown that the vacancy has an average radius 〈r_V〉 that is not equal to zero,^14–17 the decrease in the unit cell volume V with lanthanum vacancies can also be explained by the fact that the average radius of vacancy 〈r_V〉 is larger than that of K⁺.

Fig. 1 XRD patterns of the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds at room temperature.

Fig. 2 Observed (open symbols) and calculated (solid lines) X-ray diffraction patterns for La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2). The positions of the Bragg reflections are marked with vertical bars. The differences between the observed and the calculated intensities are shown at the bottom of the diagram.

Table 1 Results of Rietveld refinements determined from the XRD patterns recorded at room temperature for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples

x	0	0.1	0.2
Space group	R3̄c	R3̄c	R3̄c
Lattice parameter
a = b (Å)	5.50	5.507	5.51
c (Å)	13.36	13.38	13.42
Unit cell volume (Å^3)	87.24	87.87	88.24
dMn–O (Å)	1.958	1.962	1.967
θMn–O–Mn (°)	166.3	165.71	165.45
χ^2 (%)	1.27	1.51	1.51

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Fig. 3 Variation of unit cell volume versus the potassium vacancy for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

In addition, Table 1 proves that while the Mn–O–Mn bond angle decreases, the Mn–O length increases with the doping level x, confirming the increase in the unit cell volume (Fig. 4).

Fig. 4 Bond distances (d_Mn–O) and bond angles 〈Mn–O–Mn〉 as a function of vacancy content for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

3.2. Magnetic properties

Measurements of the temperature dependence of magnetization M(T) were performed under an applied field of 0.05 T for all the samples and the results are shown in Fig. 5. The M(T) curves reveal that when the temperature increases, all the samples display a ferromagnetic–paramagnetic transition. The paramagnetic to ferromagnetic (PM–FM) transition temperatures (T_C) were obtained from the peak of the dM/dT curves (Fig. 6). Thus, it can be clearly noted that the magnetization decreases with an increase in the potassium deficiency rate due to the decrease in the number of Mn³⁺ ions characterized by their high spin S = 2 and the increase in the number of Mn⁴⁺ (S = 3/2) ions according to the La_0.8³⁺K_0.2−x⁺□⁰_x(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻ equation. Besides, the Curie temperature decreases from 325 to 275 K with an increase in x from 0.00 to 0.2, respectively. The decrease in T_C is explained by the reduction of the one-electron bandwidth (W), which is governed by the structural parameters as follows:
where γ is the Mn–O–Mn angle, d_Mn–O is the Mn–O distance and W₀ is a positive constant.¹⁸ The variation of Curie temperature (T_C) as well as the one-electron bandwidth (W) are shown in Fig. 7. Furthermore, the sensitivity of the proposed samples to an applied magnetic field was analyzed. Fig. 8 reveals the variation of the magnetization as a function of the magnetic field at different temperatures on either side of the Curie temperature for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples. First, the ferromagnetic and paramagnetic properties were confirmed below and above the transition temperature, respectively. The nature of the magnetic transitions was tested using the Banerjee criterion,¹⁹ which is based on the Arrott plots (M² versus H/M). The slope of the H/M versus M² curve denotes whether a magnetic transition is of a first or second order. In particular, the magnetic transition is of a second order when all the curves have a positive slope. If the curves above the T_C show a negative slope in the low M² region, the transition is of a first order. Fig. 9 shows the H/M versus M² plots of the isotherms in the vicinity of T_C for the samples. Clearly, these isotherms exhibit positive slopes that are indicators of the second-order character of the phase transition.

Fig. 5 Variation of magnetization (M) vs. temperature (T) for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds measured under an applied magnetic field of 0.05 T.

Fig. 6 Variation of dM/dT as a function of temperature (T) for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

Fig. 7 The vacancy content (x) dependence on the Curie temperature (T_C) and electron-one bandwidth (W/W₀).

Fig. 8 Isothermal magnetization of the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples measured at different temperatures around the T_C.

Fig. 9 Arrott plots (M² vs. H/M) for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples around the T_C.

3.3. Magnetocaloric effect

The magnetocaloric effect is an inherent property of a magnetic material and its response to the application or removal of a magnetic field. Such a response is maximized when the temperature of the material is near its magnetic ordering temperature (Curie temperature, T_C). The total entropy can be defined as the sum of the entropy due to the lattice (S_L), the electrons (S_E) and the magnetic order (S_M). Under a constant pressure, this would be a function of both the temperature (T) and applied magnetic field (H). For an adiabatic process, the application of a magnetic field leads to a decrease in S_M, then to an increase in S_L, and therefore leads to the heating of the material. By analogy, the suppression of the magnetic field causes the cooling of the material. The magnetocaloric effect is indirectly predicted with Maxwell's relationship^20,21 from the magnetization data under different applied magnetic fields from 0 to μ₀H_max.

Hence, the entropy change ΔS_M, which determines the MCE behavior can be numerically calculated from the area enclosed between the two isothermal magnetizations of the M(H,T) curves shown in Fig. 8 and by the use of the following equation:

Fig. 10 shows the magnetic entropy changes as a function of temperature for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples under an applied magnetic field up to 5 T. The ΔS_max increases with an increase in the μ₀H value for each composition, following the increase in the magnetization and the spin alignment with this magnetic field.

Fig. 10 Magnetic entropy change (−ΔS_M) as a function of temperature under various magnetic fields between 0.5 and 5 T for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

As anticipated, the magnetic entropy change (ΔS_M) depends on both the applied magnetic field and sample temperature, i.e., ΔS_M increases and reaches a maximum value (ΔS_Mmax) when the temperature approaches the Curie temperature. Interestingly, these curves were found to reveal that all the samples present a large magnetocaloric effect. This ΔS_Mmax is found to be sensitive to the potassium deficiency. Indeed, under H = 5 T, ΔS_Mmax is equal to 3.33 J kg⁻¹ K⁻¹ at 325 K, 3.42 J kg⁻¹ K⁻¹ at 300 K and 4.54 J kg⁻¹ K⁻¹ at 275 K for x = 0.00, 0.10 and 0.2, respectively (Fig. 11).

Fig. 11 Temperature dependence of the magnetic entropy change corresponding to an applied field of μ₀H = 5 T for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

Moreover, the critical behavior near the paramagnetic to ferromagnetic phase transition temperature has been analyzed based on the field dependence of entropy change. According to Oesterreicher et al.,²² the field dependence of the magnetic entropy change of materials with a second order phase transition can be expressed as ΔS_Mα(μ₀H)ⁿ, where n depends on the magnetic state of the sample. The n exponent is found from the fit of the ΔS_Mmax vs. μ₀H curve (Fig. 12(a)), in which n is found to be 0.778; 0.778 and 0.676 in the samples for x = 0.00, 0.10 and 0.2, respectively. It is clear that the value of n is larger than the predicted value of 2/3 (ref. 23 and 24) in the mean field approach for the x = 0.2 sample. This difference can be attributed to the local inhomogeneities or superparamagnetic clusters in the vicinity of a transition temperature.^25,26 Then, the other exponents β, γ, and δ, which are associated with the spontaneous magnetization (M_S), inverse of initial susceptibility (χ₀⁻¹), and magnetization isotherm (M–H at T_C), respectively,²⁷ are calculated with the help of eqn (3) and (4) using the value of n. The δ exponent is estimated by fitting the M(H) curve at the Curie temperature with the M = DH^1/δ equation (D is a critical amplitude),²⁷ this fit is presented in Fig. 12(b), in which the δ exponent is found to be 3.53, 3.11 and 4.44 for x = 0.00, 0.10 and 0.2, respectively.

Fig. 12 (a) Variation of −ΔS_Mmax as a function of the applied magnetic field for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples. The red line indicates the linear fit for n. (b) Magnetization as a function of the magnetic field M(H) at T_C (symbols), the solid line shows the fitting with the M = DH^1/δ equation.

After a simple calculation using eqn (3) and (4), we find that β = 0.56, γ = 1.42 and δ = 3.53 for the x = 0.00 sample; β = 0.51, γ = 1.69 and δ = 3.11 for the x = 0.1 sample, and β = 0.41, γ = 1.41 and δ = 4.44 for the x = 0.2 sample. These values are consistent with the prediction of the mean field theory (β = 0.5, γ = 1 and δ = 3) for x = 0.00 and x = 0.10, and with the prediction of the 3D-Heisenberg model (β = 0.365, γ = 1.336 and δ = 4.8) for the x = 0.2 sample.

On the other hand, the cooling efficiency of a magnetic refrigerant is evaluated through the so-called relative cooling power (RCP). The latter corresponds to the amount of heat transferred between the cold and hot sinks in the ideal refrigeration cycle, which is defined as follows:²⁸

RCP = −ΔS_max × δT_FWHM (5)

where ΔS_max is the maximum of magnetic entropy change and δT_FWHM is a full width at half maximum. Fig. 13 presents the RCP dependence on the vacancy content x, under different applied magnetic fields.

Fig. 13 Variation of the RCP factor as a function of vacancy content (x) under different magnetic fields.

It is clearly seen that for the different x values, the RCP factor remains almost constant under the same magnetic field. Besides, a refrigerator capable of working in a wide temperature range can be achieved with a series of magnetocaloric materials with significant and similar RCP factors. These materials are combined to form a composite refrigerant working in the temperature range limited by their T_C. Lastly, from our materials, a magnetocaloric composite that operates with a considerable efficacy in the temperature range between 275 and 325 K can be synthesized.

For an applied magnetic field of 5 T, the RCP values were found to be 238 J kg⁻¹ for x = 0.1. Table 2 exhibits the comparison between our obtained results and those of other magnetocaloric materials. From the comparison with Gd data and from a technological point of view, our data confirms that the proposed material can be considered as a prospective candidate to be used in a cooling system based on magnetic refrigeration. From an industrial point of view, this material presents beneficial parameters such as low cost, lacking rare-earths, low weight, no corrosion, ease of synthesis, and chemical stability. For all these reasons, the suggested material can be considered as a considerable candidate for magnetic refrigeration.

Table 2 Summary of the magnetocaloric properties of the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds compared to those of other magnetic materials

Materials	TC (K)	−ΔSMmax (J kg^−1 K^−1)	RCP (J kg^−1)	ΔC^maxP/ΔC^minP (J kg^−1 K^−1)	Reference
Gd	299	4.20	196	—	29
La0.8Ca0.2MnO3	183	2.23	112.36	—	6
La0.8Na0.2MnO3	335	2.83	76.91	—	6
La0.8K0.2MnO3	325	1.64	77.16	10.76/−22.19	This work
La0.8K0.1□0.1MnO3	300	1.65	95.81	10.03/−21.04	This work
La0.8□0.2MnO3	275	2.53	80.43	30.45/−37.98	This work

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The change in specific heat (ΔC_P) linked to a magnetic field variation from 0 to μ₀H can be calculated as follows:³⁰

Fig. 14 shows the temperature dependence of the change in specific heat (ΔC_P) for different field variations for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) samples. ΔC_P is calculated from the ΔS_M data using eqn (6). Indeed, the value of ΔC_P changes abruptly from negative to positive around the Curie temperature and increases quickly with an increase in temperature. The maximum/minimum values of ΔC_P (ΔC^max_P/ΔC^min_P) increase with the applied magnetic field. They occur at the temperatures of 318.5/339.5, 292.5/313.5 and 273.5/288.5 for the x = 0.0, 0.1 and 0.2 samples, respectively. Moreover, the values of ΔC_P (ΔC^max_P/ΔC^min_P) under an applied magnetic field of 2 T are listed in Table 2.

Fig. 14 Variation of the specific heat (ΔC_P) as a function of temperature under different applied magnetic fields for the La_0.8K_0.2−x□_xMnO₃ (x = 0, 0.1 and 0.2) compounds.

4. Conclusions

Systematic investigations on the magnetic and the magnetocaloric properties of La_0.8K_0.2−x□_xMnO₃ (x = 0; 0.1 and 0.2) samples were conducted. A second-order transition for magnetic transition from ferromagnetic to paramagnetic phase is observed. The Curie temperature was found to decrease with an increase in the potassium vacancy content. As a main result from an application point of view, for x = 0.1, the T_C is equal to 300 K and the RCP values were found to be equal to 238 J kg⁻¹ under an applied magnetic field of 5 T, which is suitable for potential application in magnetic refrigeration at room temperature.

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