Study of solid-state synthesized Pr_0.55Sr_0.45Mn_1−xCr_xO₃ perovskites with x = 0.0, 0.05, 0.1 and 0.15: Rietveld analysis and magnetic and magnetocaloric properties for magnetic refrigeration applications

Abstract

In the current study, the structural (X-ray diffraction (XRD)), magnetic, critical behavior and magnetocaloric properties of polycrystalline Pr_0.55Sr_0.45Mn_1−xCr_xO₃ manganite samples (with x = 0.0, 0.05, 0.1 and 0.15) were investigated. All our samples were prepared from the stoichiometric powder mixtures of binary oxides via solid-state reactions at high temperatures. The compounds crystallized in an orthorhombic structure with the Pnma space group, according to the Rietveld refinement of the XRD pattern. All the samples exhibited a second-order FM-to-PM phase transition, according to the temperature and field-dependent magnetization measurements; however, the Curie temperature (T_C) value decreased from 300 K to 275 K, as the Cr (% x) content increased from 0.00 to 0.15. Using Maxwell thermodynamic relations, the magnetocaloric effect (MCE) in terms of maximum entropy change (−ΔS^max_M) and relative cooling power (RCP) was calculated with isothermal magnetization data around T_C. In a magnetic field shift of 5 T, the highest values of the magnetic entropy change (−ΔS^max_M) were determined to be 3.8 J kg⁻¹ K⁻¹, 3.63 J kg⁻¹ K⁻¹, 3.87 J kg⁻¹ K⁻¹, and 2.55 J kg⁻¹ K⁻¹ for x = 0.0, x = 0.05, x = 0.1, and x = 0.15, respectively. For x = 0.0, x = 0.05, x = 0.1, and x = 0.15 at 5 T, the highest value of the relative cooling power RCP was found to be 247 J kg⁻¹, 254.1 J kg⁻¹, 205.1 J kg⁻¹, and 201 J kg⁻¹, respectively. The RCP value of 254.1 J kg⁻¹ (5% of chromium) was equivalent to 58% of the RCP value of gadolinium metal. Technically, the developed material is highly promising for magnetic refrigeration because of these significant values.

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1 Introduction

Perovskite manganites with the general formula of RE_1−xAE_xMnO₃ (RE = rare earth ions such as La³⁺, Pr³⁺, Nd³⁺, and Sm³⁺ and AE = alkaline earth ions such as Sr²⁺, Ba²⁺, and Bi²⁺) have drawn a lot of research interest in the recent three decades owing to their unique physical characteristics, including phase separation, charge and orbital ordering, metal-to-insulator transition, and magnetocaloric effects.¹ We focused on a family of perovskite compounds in this work.

Recently, perovskite manganite compounds have been employed in a variety of applications, such as magnetic refrigeration systems,² magnetoresistance devices,^3,4 and high-efficiency photovoltaic solar cells,⁵ which showed that manganite-family perovskites with different doping atoms have extremely high relative cooling power (RCP), making them suitable for clean refrigeration source applications.² Since the discovery of magneto-caloric effects (MCEs) by Warburg in 1881,⁶ they have been extensively studied, becoming the foundation of the so-called “magnetic refrigeration”.

Due to its large magnetic entropy change around room temperature, gadolinium (Gd) is a well-known standard among the magnetocaloric materials. However, the relatively high cost of Gd limits its large-scale technological applications. As a result, substantial effort has been put into developing low-cost alternatives, particularly rare-earth-based perovskite manganites, which exhibit fascinating magnetocaloric properties. The main objective is to identify materials with magnetic entropy change (−ΔS^max_M) and relative cooling power (RCP) values comparable to those of Gd while significantly reducing the material cost. In this case, manganite perovskites constitute a suitable and economically viable class of materials for magnetic refrigeration applications.

Numerous studies have examined the crucial character of manganites close to a PM-to-FM phase transition.^7–33 Several methods of changing the physical characteristics of perovskite manganite RE_1−xAE_xMnO₃, for example, replace the trivalent rare earth ions (RE³⁺) in the perovskite structure with a divalent element (AE²⁺). A mixed valence of manganese Mn³⁺ and Mn⁴⁺ appears as a result of the partial substitution of RE³⁺. This valence state is at the base of the changes in the physical properties of these perovskite manganites, in particular the appearance of a ferromagnetic (FM) order of the spins of the Mn ions, following which the electron e_g becomes itinerant and can hop from a Mn cation, via the oxygen anion, to another manganese having an empty e_g band. The strong relationship between structural, electrical, and magnetic properties is one of the essential features of manganites. The double exchange (DE) mechanism, first proposed by Zener in 1951, explains this association.³⁴ The replacement of rare earth elements has an indirect effect on the conduction mechanism, affecting the bandwidth and angle of the connection between the neighbouring manganese ions, according to several recent scientific studies^35–37 on manganites. Another way is to study the impacts of Mn doping by other elements, which is interesting since it is undeniable that Mn ions play a significant role in the double exchange interaction. Over the last few years, many research projects^38–49 have been conducted to comprehend the impact of replacing manganese at the B-site with a transition element. It has been demonstrated that the addition of a transition metal with an electronic configuration distinct from Mn should result in an important change in both Mn and the configurations of the substituent elements. Therefore, the conduction mechanism is directly impacted by the replacement of Mn, making it possible to more effectively modify the physical characteristics of the manganite systems. Additionally, the replacement of trivalent and tetravalent elements for Mn results in an increase in resistivity and a drop in transition temperature (T_C), and magnetism. However, the type of replacement elements mostly determines the precise effect. Chromium is one of these elements that affects the structural and magnetic characteristics of manganites. The doping of Mn by magnetic Cr has been cited in earlier studies,^50–55 and both investigations show that the inclusion of Chromium in both systems has comparable outcomes, specifically a drop in the temperature of the magnetic transition from the FM state to the PM state as the rate of substitution (x) increases. Additionally, the Mn–O–Mn networks are impacted by the substitution of Mn sites by other elements,^56,57 by the strong electron–phonon interaction known as the Jahn–Teller effect,⁵⁸ and the double-exchange (DE) interaction linking Mn³⁺/Mn⁴⁺ ions.⁵⁹ The characteristics of the magnetocaloric effect are explained by these considerations. One of the manganites that has been investigated the most is Pr_1−xSr_xMnO₃, which exhibits a −ΔS^max_M value around 3 J kg⁻¹ K⁻¹under an applied magnetic field of 5 T and passes through a paramagnetic metal-to-ferromagnetic metal transition around T_C ≈ 301 K.⁶⁰ This combination may undergo a ferromagnetic transition at ambient temperature with −ΔS^max_M greater than 4 J kg⁻¹ K⁻¹, by partially substituting Mn ions with other transition metal ions, such as Chromium (M = Cr).

Magnetocaloric manganites have been extensively studied, but enhancing their performance remains challenging. The magnetocaloric response is actually greatly influenced by various parameters, including doping type, concentration, and structural distortions. Therefore, further research is still required to explore alternative replacement procedures and compositional tuning in order to achieve improved characteristics. An alternative and effective method is to study Cr substitution in Pr_0.55Sr_0.45MnO₃ in order to better understand the relationship between structure, magnetism, and magnetocaloric performance, as well as to identify materials that are suitable for magnetic refrigeration near ambient temperature.

The structural, magnetic, and magnetocaloric characteristics of the series of manganite compounds Pr_0.55Sr_0.45Mn_1−xCr_xO₃ with x = 0.0, 0.05, 0.1, and 0.15 were thoroughly examined in this work. The Rietveld method of analysing X-ray diffraction diagrams allowed for the precise determination of the structural characteristics of samples. To do this, we thoroughly examined the magnetocaloric effect and calculated the relative cooling power (RCP), a crucial performance indicator.

2 Experimental details

Pr_0.55Sr_0.45Mn_1−xCr_xO₃ polycrystalline samples (x = 0.0, 0.05, 0.1, and 0.15) were prepared using the traditional solid-state reaction method. As starting materials, high-purity precursor powders (≥99.9% purity) of Pr₆O₁₁, SrCO₃, MnO₂, and Cr₂O₃ were weighed in accordance with the necessary stoichiometric ratios. To guarantee excellent homogeneity and uniform distribution of the contents, the powders were first combined and extensively ground in an agate mortar for several hours.

To eliminate volatile species and initiate solid-state reactions, the combined powders were first calcined in air at 900 °C for 24 hours. To enhance phase formation, the powders were reground after naturally cooling and then calcined again for 24 hours at 1100 °C. Then, the resultant powders were finely milled and compressed under uniaxial pressure into cylindrical pellets with a thickness of about 1 mm. In order to improve the crystallinity, density, and phase purity, the pellets were then sintered in air for 12 hours at high temperatures of 1200 °C and 1300 °C. In between sintering steps, the pellets were reground.^61,62 The samples were furnace-cooled to room temperature after all thermal treatments were carried out in an ambient air environment.

Using a PANalytical X'Pert Pro diffractometer with Cu-Kα radiation (λ = 1.5406 Å), the phase purity, crystal structure, and lattice parameters were examined by powder X-ray diffraction (XRD) at ambient temperature. To guarantee a high signal-to-noise ratio, the diffraction data were gathered in the 2θ range of 10–80° with a step size of 0.02° and a suitable counting duration per step. Structural analysis was performed by the standard Rietveld method^63–65 using the FullProf software.

A vibrating sample magnetometer (VSM) was used to measure magnetic fields up to 5 T. Field-cooled (FC) protocols were used to record the temperature-dependent magnetization (M(T)) in the 20–400 K temperature range. At certain temperatures near the magnetic transition region, isothermal magnetization curves M(H) were recorded with magnetic fields ranging from 0 to 5 T.

Using the Maxwell thermodynamic relation, the magnetic entropy change (ΔS_M) was calculated from the isothermal magnetization data as follows:

In actuality, discrete M(H) curves acquired at various temperatures were used to quantitatively determine ΔS_M. The full width at half maximum (δT_FWHM) of the ΔS_M(T) curve multiplied by the maximum entropy change was used to calculate the relative cooling power (RCP).

3 Results and discussion

3.1 Structural analysis

The X-ray diffraction pattern of Pr_0.55Sr_0.45Mn_1−xCr_xO₃ with x = 0.0, 0.05, 0.1, and 0.15 at room temperature is shown in Fig. 1. The XRD patterns showing sharp, well-defined peaks reveal a completely crystalline phase of Pr_0.55Sr_0.45Mn_1−xCr_xO₃ with a distinct orthorhombic phase with the Pnma space group. The excellent quality and single-phase of the elaborated samples were demonstrated by the absence of secondary-phase-corresponding peaks (no impurity). The structural data are analysed by the Rietveld method using the FullProf program^63,64,66 to gain an improved understanding of the structural characteristics of the orthorhombic phase.

Fig. 1 X-ray powder diffraction patterns and refinement at room temperature for Pr_0.55Sr_0.45Mn_1–xCr_xO₃ ((a) x = 0, (b) x = 0.05, (c) x = 0.1 and (d) x = 0.15) showing the calculated, observed, and difference intensities along the Bragg positions (vertical bars in green).

The goodness-of-fit parameter χ² and the reliability factors R_p and R_wp, which quantify the differences between the calculated and observed diffraction patterns, were used to evaluate the quality of the Rietveld refinement. The lattice parameters a, b, and c, scale factor, zero shift, atomic locations, and isotropic displacement parameters were among the structural and profile characteristics that were adjusted during the refinement process. A pseudo-Voigt function was used to fit the peak profiles, and a polynomial function was used to describe the background. There is good agreement between the calculated and experimental data, as seen by the obtained χ² values being near the predicted range. Lattice parameters, unit cell volume, atomic locations (x, y, z) for all atoms (Pr/Sr, Mn/Cr, O₁, and O₂) with their estimated standard deviations, and computed bond lengths and bond angles with corresponding errors are all included in Table 1, which summarizes all revised structural and reliability metrics. A thorough assessment of the refining quality is also provided by agreement factors, including Bragg R-factor, R_f-factor, R_e, R_p, R_wp, and χ².

Table 1 Refined structural parameters of Pr_0.55Sr_0.45Mn_1−xCr_xO₃ at room temperature

X	0	0.05	0.10	0.15
Symmetry	Orthorhombic	Orthorhombic	Orthorhombic	Orthorhombic
Space group	Pnma	Pnma	Pnma	Pnma
Cell parameters
a (Å)	5.4409(3)	5.4372(2)	5.43928(20)	5.4455(5)
b (Å)	7.6558(3)	7.6502(3)	7.6548(3)	7.6514(6)
c (Å)	5.4807(2)	5.48076(19)	5.48331(17)	5.4739(5)
V (Å^3)	228.296(0.018)	227.976(0.015)	228.305(0.013)	228.073(0.035)
Pr/Sr at. positions
X	0.0048(8)	0.00558(2)	0.0060(3)	0.0052(8)
Y	0.2500(0)	0.2500(0)	0.2500(0)	0.2500(0)
Z	0.9876(3)	0.9937(1)	0.9924(2)	0.9935(6)
Mn/Cr at. positions
X	0.0000(0)	0.0000(0)	0.0000(0)	0.0000(0)
Y	0.0000(0)	0.0000(0)	0.0000(0)	0.0000(0)
Z	0.5000(0)	0.5000(0)	0.5000(0)	0.5000(0)
O1at. positions
X	0.4900 (0)	0.5143(1)	0.525(2)	0.4960(4)
Y	0.2500(0)	0.2500(0)	0.2500(0)	0.2500(0)
Z	0.0200(0)	0.0231(6)	0.034(1)	0.0522(9)
O2at. positions
X	0.281(0)	0.2235(6)	0.2457(2)	0.3154(3)
Y	0.0153(3)	0.0186(3)	0.0173(5)	0.0021(4)
Z	0.2950(0)	0.2332(7)	0.232(3)	0.2963(6)
Structural parameters
<dMn1–O2> (Å)	2.0623(2)	1.9129(4)	1.9685(5)	1.9084(4)
<θMn1–O2–Mn1> (°)	173.24(4)	168.21(9)	168.22(4)	154.74(5)
<dMn2–O2> (Å)	1.8057(7)	1.9676(6)	1.9136(8)	2.0477(4)
<θMn2–O2–Mn2> (°)	173.24(4)	168.21(9)	168.22(4)	154.74(5)
<dMn1–O1> (Å)	1.9494(5)	1.9354(5)	1.9366(1)	1.9342(7)
<θMn1–O1–Mn1> (°)	158.09(9)	162.35(5)	162.35(7)	162.93(2)
Agreement factors
Bragg R-factor	3.79	5.55	5.86	4.69
Rf-factor	7.52	10.1	10.3	6.18
Re (%)	16.4	16.5	17.0	17.6
Rp (%)	30.5	31.7	33.6	33.1
Rwp (%)	20.5	20.7	21.8	22.4
χ^2 (%)	1.56	1.57	1.64	1.63
DC−S(nm)	78	50.6	48.6	30.1

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Additionally, the Debye–Scherrer formula was used to obtain the average crystallite size D_C−S from the primary peak of the XRD data:

where k indicates a dimensionless constant (k = 0.9), β defines the peak half-height width, and θ represents the peak Bragg angle.

A thorough comprehension of the structural and functional characteristics intrinsic to our Pr_0.55Sr_0.45Mn_1−xCr_xO₃ compound series (where x = 0.0, 0.05, 0.1, and 0.15) requires a careful examination of the crystallographic parameters, especially the manganese–oxygen <d_Mn−O> distances bond and the inter-octahedral <θ_Mn−O–Mn> angles.

The size and degree of deformation of the MnO₆ octahedra are directly indicated by the <d_Mn−O> interatomic distances. In the Pr_0.55Sr_0.45Mn_1−xCr_xO₃ structure, the substitution of Mn by chromium Cr significantly changes the average oxidation state of the manganese ions, resulting in the introduction of certain structural stresses. The Jahn–Teller effect, which is usually connected to the presence of Mn³⁺ cations, is likewise very sensitive to these ensuing variations in <d_Mn−O> bond lengths. The electrical asymmetry of these ions forces the octahedra to elongate or compress, which is crucial in establishing the local structural environment.

At the same time, the connectivity and coupling effectiveness between neighboring MnO₆ octahedra are determined by the <θ_Mn−O–_Mn> bond angles. The amount of octahedral inclination is directly influenced by the degree of chromium substitution. The double-exchange (DE) process of Mn³⁺/Mn⁴⁺ that drives the observed ferromagnetism in these manganites is crucially mediated by this tilting, making it extremely significant.

In particular, the orbital overlap is maximized when the <θ_Mn−O–Mn> angle gets closer to the optimal 180°, which improves the charge carrier mobility and fortifies the magnetic interactions.

The complicated local structural distortions caused by Cr inclusion at the Mn site are responsible for the non-monotonic evolution of the average <d_Mn−O> bond lengths and <θ_Mn–O–Mn> bond angles with the increasing Cr substitution. As Cr doping has non-uniform effects on the Jahn–Teller distortion, octahedral tilting, and <d_Mn−O> bond covalency in perovskite manganites, it does not always result in a linear structural response. The coexistence of Cr³⁺ and Mn³⁺/Mn⁴⁺ ions causes local strain oscillations and alters the distortion of MnO₆ octahedra, leading to small irregular changes in bond angles and lengths. These minor alterations are in line with the findings from comparable Cr-doped manganite systems and demonstrate the orthorhombic Pnma structure's high sensitivity to compositional disorder and local lattice effects.

In conclusion, examining the simultaneous changes in <d_Mn−O> distances controlled by the Jahn–Teller effect and substitution and the <θ_Mn–O–Mn> angles, which determine the effectiveness of the double-exchange pathway, is crucial to understanding the magnetic properties seen in Pr_0.55Sr_0.45Mn_1−xCr_xO₃.

3.2 Magnetic properties

The temperature dependence of the magnetization (M(T)), under an applied magnetic field µ₀H = 0.05 T, for all our samples, is displayed in Fig. 2(a). We plotted in Fig. 2(b) the magnetization as a function of temperature under a weak applied field of 0.05 T, with the dM/dT curve used to determine the minimum temperature (T_c) of the parent compound curve, clearly demonstrating the paramagnetic–ferromagnetic transition. For the Pr_0.55Sr_0.45Mn_1−xCr_xO₃ series (x = 0.0, 0.05, 0.1, and 0.15), the magnetization versus temperature M(T) curves provide important information on their magnetic behavior. These compounds show a change from a paramagnetic (PM) state to a ferromagnetic (FM) state as the temperature decreases. The key parameter known as the Curie temperature (T_C) indicates the temperature at which a material changes from a paramagnetic state to a ferromagnetic state. The Curie temperatures (T_C) were determined from the minimum value of the dM/dT versus T curves (refer to the inset of Fig. 2), and the T_C values for the Pr_0.55Sr_0.45Mn_1−xCr_xO₃ series are shown to decrease as the Cr concentration increases: for x = 0.0, 0.05, 0.10, and 0.15, T_C (K) = 300 K, 292 K, 286 K and 275 K. This pattern implies that the ferromagnetic interactions are weakened when Mn is replaced with Cr in the lattice, which lowers the Tc, similarly in the literature, that is confirmed in the work of A. K. Saw et al.⁶⁷ and other work.⁶⁸ Furthermore, when Cr is substituted in Cr-doped manganites, the magnetism in the FM region decreases. A qualitative explanation for the decline in T_C and magnetization with the increase in chromium concentration is the decrease in the Mn³⁺/Mn⁴⁺ ratio. This action increases the SE Super exchange antiferromagnetic state by reducing the Mn³⁺/Mn⁴⁺ couples that cause DE Double exchange ferromagnetism and introducing a small amount of Mn³⁺/Mn³⁺, Mn⁴⁺/Mn⁴⁺, Cr³⁺/Cr³⁺, and Mn³⁺/Cr³⁺ couples.⁶⁹

Fig. 2 (a) Temperature dependence of magnetization for the Pr_0.55Sr_0.45Mn_1–xCr_xO₃ (x = 0, x = 0.05, x = 0.1 and x = 0.15) samples. Inset: dM/dT versus temperature curves of the samples. (b) Temperature dependence of magnetization measured at magnetic field (µ₀H) = 0.05 T for the Pr_0.55Sr_0.45MnO₃ sample and the dM/dT versus temperature curves.

The magnetization isotherms (M(H)) recorded for all compounds in magnetic fields equal to 5 T over a broad temperature range of 240–320 K demonstrate that, below the Curie temperature, magnetization increases significantly in weak applied fields until approaching saturation for applied fields (µ₀H = 1 T). Fig. 3(a)–(d) display the usual magnetization isotherm shape for x = 0.0, 0.05, 0.1, and 0.15.

Fig. 3 Isothermal magnetization patterns the for Pr_0.55Sr_0.45Mn_1–xCr_xO₃ ((a) x = 0, (b) x = 0.05, (c) x = 0.1 and (d) x = 0.15) samples at various temperatures.

As the temperature decreases, the saturation magnetization increases. The purely ferromagnetic behavior of the samples at low temperatures is confirmed by this result. Important information on the magnetic characteristics and phase transitions of manganites is provided by the magnetization versus magnetic field M(H) measurements. The nature of the magnetic ordering and the transitions between various magnetic phases are revealed by these observations. For example, the M(H) curves in Pr_0.55Sr_0.45Mn_1−xCr_xO₃ (x = 0.00, 0.05, 0.1, and 0.15) show a second-order ferromagnetic (FM)-to-paramagnetic (PM) phase transition, where the Curie temperature (T_C) decreases with the increase in Cr-doped concentration. Similarly, the M(H) measurements reveal a second-order PM-to-FM transition in Pr_0.67Sr_0.33Mn_1−xM_xO₃ (0.0 < x ≤ 0.09) in the study by A. Dhahri et al.⁷⁰ These findings are also essential for comprehending the magnetic interactions and the possible uses of the materials in magnetic refrigeration and other technologies.

3.3 Critical behavior

The analysis of the Arrott curve makes it possible to understand the critical behavior at the critical point. The magnetic equation of state for a system that adheres to the theory of the average field (MFT) is as follows:

The order of the magnetic phase transition is revealed by a thorough analysis of M(H) isotherms. From the M(H) isotherms near T_C, we inferred the Arrott plots (M^1/β vs. (µ₀H/M)^1/γ), which are shown in Fig. 4(a)–(d). Banerjee criterion⁷¹ states that a first-order or second-order magnetic phase transition is indicated by a negative or positive slope of Arrott curves. The results of M² against µ₀H/M graphs for Pr_0.55Sr_0.45Mn_1−xCr_xO₃ reveal the second-order FM-to-PM phase transition, with a positive slope in all cases throughout the entire M² range, and the values of exponents β and γ are 0.5 and 1, respectively, as expected from the mean field theory. The Curie temperatures (T_C) determined from the Arrott plots coincide with those obtained from the low-field magnetization curves (M(T)) for all compounds.

Fig. 4 Arrott plots ((M^1/β vs. µ₀H/M)^1/γ) with β = 0.5 and γ = 1, of the Pr_0.55Sr_0.45Mn_1–xCr_xO₃ ((a) x = 0, (b) x = 0.05, (c) x = 0.1 and (d) x = 0.15) compounds.

Fig. 5 shows the temperature dependence of the spontaneous magnetization (M_sp) deduced from the M(H) curves and the inverse of the susceptibility (1/χ) as a function of temperature for the Pr_0.55Sr_0.45MnO₃ sample. In the paramagnetic phase (T > T_C), this sample exhibits linear inverse susceptibility behavior. Χ = C/(T − θ_P), where θ_P is the Curie constant and C is the Curie–Weiss temperature. For x = 0.0, the θ_P value is determined to be 303 K. The presence of a ferromagnetic exchange interaction between the closest neighbors is indicated by the positive value of θ_P. The resultant value is marginally above the Curie temperatures. Short-range magnetic correlations above the Curie temperature are linked to this material-dependent differential, which is suggestive of magnetic inhomogeneity.⁷² For x = 0.0, the critical exponent β is determined to be 0.362, indicating that all of our samples exhibit ferromagnetic activity at low temperatures. The ferromagnetic condition described for manganites^63,72,73 is in good agreement with this value.

Fig. 5 Spontaneous magnetization (M_sp) and the inverse of susceptibility 1/χ as a function of temperature for the Pr_0.55Sr_0.45MnO₃ compound.

3.4 Magnetocaloric measurements

The thermodynamic theory states that the magnetic entropy change caused by the magnetic field variation from 0 to H_max is as follows:⁷⁴

Using Maxwell's relation:

The following expression can be obtained:

Eqn (4) states that the magnetic entropy change reaches its highest during the magnetic transition phase. The magnetic entropy change was calculated approximately using the numerical formula employing isothermal magnetization data in small discrete field and temperature intervals:⁷⁵

where M_i and M_i+1 are the experimental magnetization values obtained at the temperatures T_i and T_i+1, respectively, in an applied magnetic field (H_i). The magnetic entropy changes |ΔS_M| of Pr_0.55Sr_0.45Mn_1−xCr_xO₃ samples as a function of temperature under various magnetic applied field variations are plotted in Fig. 6(a)–(d). The magnetic entropy change increases with temperature and reaches a maximum near the Curie temperature.

Fig. 6 Magnetic entropy change (−ΔS_M) vs. T around the Curie temperature (T_C) for the Pr_0.55Sr_0.45Mn_1–xCr_xO₃ ((a) x = 0, (b) x = 0.05, (c) x = 0.1 and (d) x = 0.15) compounds.

The −ΔS_M value exhibits a broad positive peak around T_C (normal MCE) for all samples. The maximum values of the magnetic entropy change (|ΔS^max_M|) are 3.8 J kg⁻¹ K⁻¹, 3.63 J kg⁻¹ K⁻¹, 3.87 J kg⁻¹ K⁻¹ and 2.55 J kg⁻¹ K⁻¹ in a magnetic field change of 5 T for x = 0.0, x = 0.05, x = 0.1 and x = 0.15, respectively. The relative cooling power (RCP)^76–78 is evaluated as follows:

RCP = −ΔS_M(T,H) × δT_FWHM, (6)

where δT_FWHM is the full width at half maximum of −ΔS_M versus temperature.^79–81 For our samples, the RCP values are, respectively, 247 J kg⁻¹, 254.1 J kg⁻¹, 205.1 J kg⁻¹ and 201 J kg⁻¹ at 5 T for x = 0.0, x = 0.05, x = 0.1 and x = 0.15. Despite having the lowest |ΔS^max_M|, the composition of 5% of chromium-doped manganese seems to be the most promising for magnetic refrigeration applications because of its high RCP value. For cooling cycles to be effective, entropy change and temperature range must be balanced. As seen in Fig. 7, the delta |ΔS^max_M| values obtained and the RCP values computed using eqn (6) are plotted versus µ₀H.

Fig. 7 Relation of the maximum entropy changes (−ΔS^max_M) and relative cooling power (RCP) with µ₀H for the Pr_0.55Sr_0.45MO₃ compound.

It was evident that at T_C, the relative cooling power (RCP) and maximum entropy change (|ΔS^max_M|) are both proportional to µ₀H (Table 2). RCP is a field-dependent variable, as evidenced by its trend with µ₀H. Our sample RCP (5% of chromium) value of 254.1 J kg⁻¹ is 58% of Gd, which is the industry standard for refrigeration⁷⁵ materials with high δT_FWHM, and RCP values can operate over a wide temperature range and have a large cooling capacity. Magnetic refrigeration works well with these materials.^82,83

Table 2 Summary of −ΔS^max_M, the Curie temperature T_C and relative cooling power (RCP) a values of Pr_0.55Sr_0.45Mn_1–xCr_xO₃ with x = 0.0, 0.05, 0.1, and 0.15

X	0	0.05	0.10	0.15
TC (K)	300	292	286	275
−ΔS^maxM(J kg^−1 K^−1)	3.80	3.63	3.87	2.55
δTFWHM	65	70	53	79
RCP (J kg^−1)	247	254.1	205.1	201

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A comparison of the magnetocaloric performance of the benchmark material Gd under an applied magnetic field of 5 T is shown in Table 3. The Curie temperatures (T_C) of all the samples remain near room temperature, which is advantageous for magnetic refrigeration applications. As would be predicted for perovskite manganites, the maximum magnetic entropy change (−ΔS^max_M) values of the examined compounds, which range from 2.55 to 3.87 J kg⁻¹ K⁻¹, are lower than those of Gd (10.2 J kg⁻¹ K⁻¹). However, the RCP values, especially for x = 0 and x = 0.05, approach considerable values (247 and 254.1 J kg⁻¹, respectively), but they are still quite similar to Gd (410 J kg⁻¹). This suggests that the wider operating temperature range of manganites helps to maintain competitive RCP values even though the entropy change is less. These findings verify that the investigated compounds are viable low-cost substitutes for Gd in magnetic refrigeration close to room temperature.

Table 3 Collected data for the Curie temperature (T_C), −ΔS^max_M, and RCP of our studied compounds and the reference material Gd

x	TC (K)	ΔH (T)	−ΔS^maxM(J kg^−1 K^−1)	RCP (J kg^−1)	Ref.
x = 0	300	5	3.8	247	This work
x = 0.05	292	5	3.63	254.1	This work
x = 0.1	286	5	3.87	205.1	This work
x = 0.15	275	5	2.55	201	This work
Gd	294	5	10.2	410	75

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The temperature interval is primarily responsible for the higher RCP values despite the lower ΔS^max_M values. Because of the gradual nature of the magnetic transition and Cr-related magnetic disorder, this rise in δT_FWHM makes up for the decreased peak entropy change and improves the overall refrigeration efficiency.

Numerous methods for figuring out the order of magnetic phase transitions have been proposed in the literature.^71,84 One of these is to use the relation ΔS_M(H,T) ≈ aHⁿ, where a is a constant and n is an exponent related to magnetic order, to examine the field dependence of the samples' MCE.^85–87 Important details regarding the type of magnetic phase transition in the investigated materials can be found by calculating the exponent values at specific temperatures. The logarithmic derivative of experimental data can be used to determine the exponent n at a specific temperature and magnetic field ΔS_M(H,T)⁸⁵ as follows:

The Curie–Weiss rule causes the n values to approach n = 2 at high temperatures in the paramagnetic phase (over the T_C).⁸⁶ In the ferromagnetic phase, n typically has a value that tends to be n = 1 at temperatures well below the transition point. The value of n changes according to the kind of phase transition (first- or second-order) of the material within a crucial temperature range surrounding the Curie temperature.

Previous investigation has demonstrated that a quantitative criterion of n > 2 close to the transition temperature T = T_C could be interpreted as a first-order magnetic phase transition of the material. It has also been demonstrated that this criterion could be successfully applied to a variety of magnetocaloric materials in order to identify the type of magnetic phase transition.⁸⁷

Fig. 8 illustrates the Pr_0.55Sr_0.45MnO₃ compound temperature dependency of exponent n under various magnetic fields (n(T)). The sample exponent n tends to approach 1 at temperatures significantly below the Curie temperature (ferromagnetic region). The exponent n tends to 2 for temperatures greater than T_C (paramagnetic zone). This behavior for exponent n is typically explained by a second-order phase transition. As the temperature drops near the transition temperature, a fall in n is seen, with a minimum value at the Curie temperature. Other magnetic materials with first- and second-order transitions have been reported to exhibit similar behaviors.^{41,71,84–86,88}

Fig. 8 Temperature dependence of the exponent (n(T)) of the magnetic entropy change (−ΔS_M) for several applied magnetic field values of Pr_0.55Sr_0.45MO₃.

4 Conclusions

In summary, this study focused on the structural, magnetic, and magnetocaloric characterisation of Pr_0.55Sr_0.45Mn_1−xCr_xO₃ manganite compounds with x = 0.0, 0.05, 0.1, and 0.15, which were successfully elaborated using a solid–state reaction method. The crystalline structure was found to be orthorhombic, corresponding to the Pnma space group, and X-ray diffraction investigations verified the production of a single phase over the compositional range without any impurity phase.

For all the prepared compounds, magnetization measurements as a function of temperature and applied field consistently showed a magnetic phase transition from the ferromagnetic (FM) state to the paramagnetic (PM) state. It is remarkable that this transition was found to be of second order. It was discovered that the Curie temperature (T_C), which decreased from 300 K to 275 K over the examined substitution period, could be efficiently modulated by gradually adding chromium in place of manganese. The crucial impact of the Cr³⁺ ion on the magnetic exchange processes inside the crystal lattice is shown by this dependence.

Using isothermal magnetization data and the Maxwell thermodynamic laws, the magnetocaloric effect (MCE) was thoroughly examined. The outcomes for a 5 T change in the magnetic field are very encouraging. For the x = 0.1 composition, the highest magnetic entropy change (−ΔS^max_M) was found to peak at 3.87 J kg⁻¹ K⁻¹. More significantly, the Pr_0.55Sr_0.45Mn_0.95Cr_0.05O₃ sample had the highest relative cooling power (RCP) value, measuring 254.1 J kg⁻¹.

Considering that its RCP value is roughly 58% of that of pure gadolinium, an accepted industrial measurement, this performance places the material with x = 0.05 in a very promising category for magnetic refrigeration applications. In conclusion, the Pr_0.55Sr_0.45Mn_1−xCr_xO₃ family of manganites are an attractive class of magnetocaloric materials for the fabrication of effective and eco-friendly magnetic cooling devices, especially because the chromium concentration can be used to adjust the operating temperature.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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