A comparative study of the physical properties of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00–0.30) characterized by “λ” shape dc magnetizations

The magnetoresistance (MR) effect represents the resistances with and without magnetic field in perovskite manganites and was already known in the early 1960s. For example, in 1969, a comprehensive magnetoresistance study and the phenomenological analysis of La_1−xPb_xMnO₃ crystals were reported.¹ Nevertheless, only since the mid-1990s, after the discovery of the so-called colossal magnetoresistance (CMR) in manganites (e.g., up to 127 000% in the La_2/3Ca_1/3MnO₃ thin film at 77 K and 6 T),⁴ much work^2,3 has been invested in manganites. Currently, the underlying origin of the CMR effect is believed to be closely related to the nature of the colossal magnetoresistance manganites, which are strongly correlated electron systems with lattice, spin, charge, and orbital degrees of freedom interactions, such as double exchange interaction, Jahn–Taller effect, electronic phase separation as well as charge ordering, and so on, and has been described in detail in some reviews.^5–8 

Hole-doped mixed valance perovskite manganites of the type D_1−xA_xMnO₃ (where D is a trivalent rare earth and A is a divalent alkali earth) have recently attracted considerable attention. In these perovskite compounds, the interplay between magnetism, charge order, lattice, spin, orbit, and electronic transport has been studied in detail.^9,10 These systems are characterized by complex phase diagrams and different physical properties. Magnetic moments presented by the rare-earth ions in perovskite manganites D_1−xA_xMnO₃ have been polarized by the fact that they couple with the Mn subsystem and influence the magnetic properties of manganites at low temperatures, as mentioned by Sanjay and Sudipta¹¹ and Hemberger et al.¹² in the study of the magnetic properties of PrMnO3. The magnetocaloric effect (MCE), which describes the temperature change of a system when an external magnetic field is applied/removed, is one of the concentrated material properties studied for magnetic cooling applications. Lees et al.¹³ have investigated the magnetic and magnetoresistive properties of Pr_1−xCa_xMnO₃ at low temperatures. The structural and magnetic properties of Pr_1−xBa_xMnO₃¹⁴ and Pr_1-xK_xMnO₃¹⁵ were also investigated and showed interesting magnetic results.

The rich physics of manganites, e.g., phase separation, charge ordering, and semi-metallicity, makes them one of the richest topics in condensed matter physics. The discovery of the colossal magnetoresistance effect in perovskite manganites D_1−xA_xMnO₃ doped with divalent alkaline earth ions has aroused great interest due to the fundamental physics involved and their large potential application in magnetic cooling. This has led to the investigation of the effect of the substitution of La by Sr in Pr_0.63La_0.37MnO₃ systems on the structural, magnetic, and magnetocaloric properties and the effects of the magnetic heating process on the physical properties of the system.

The structure of the D_1−xA_xMnO₃ manganite is cubic perovskite. The trivalent and divalent ions occupy the site with 12-fold oxygen coordination, while the smaller Mn ion is located in the center of an oxygen octahedron with 6-fold coordination. In general, the perovskite-based D_1−xA_xMnO₃ material exhibits lattice distortions as modifications of the cubic structure. In manganites with strong DE interaction (e.g., La_1−xSr_xMnO₃ with x = 1/3) the electrons are delocalized for a certain doping range at low temperature, which leads to a metallic behavior.¹⁶ 

Pr_0.63La_0.37−xSr_xMnO₃ systems (x_Sr = 0.00, 0.05, 0.10, 0.15, 0.20, and 0.30) were prepared by the solid-state reaction by mixing stoichiometric amounts of Pr₆O₁₁, La₂O₃, SrO, and MnO₂. The prepared powder was ground with an agate mortar after this chemical reaction: $0.105Pr6O11+0.37−x2La2O3+xSrO+MnO2→Pr0.63La0.37−xSrxMnO3+gas⃗$⁠.

The prepared powder was then dehydrated at 300 °C for 3 h. The powder was heated at different temperatures, i.e., 500 °C/12 h, 700 °C/12 h, and 800 °C/12 h in an oven Thermo Scientific in the laboratory facilities Electrochemical System, Hamad Bin Khalifa University, Qatar. The powder was divided into three series: x_Sr-500°C, x_Sr-700°C, and x_Sr-800°C series, which were heated to 500, 700, and 800 °C, respectively. The x-ray diffraction diagrams (XRDs) were performed with a D8 Advance Bruker diffractometer.

The scanning electron microscopy (SEM) images were obtained using FEI-Versa3D FESEM. The magnetic measurements were determined using the QD Dynacool Physical Property Measurement System (PPMS)–VSM module. It uses a single two-stage pulse tube cooler to cool both the superconducting magnet and the temperature control system, creating a low-vibration environment for the sample measurements. It also provides continuous cryogenic control and precise field and temperature sweep modes. PPMS allows the magnetic moment of a sample to be measured as a function of temperature or magnetic field. Magnetic phase transitions and hysteretic behavior are quickly resolved with typical acquisition times for a single reference point of about 1 s. All measurements presented were performed at Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University.

Figures 1(a)–1(c) show the XRD patterns of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00, 0.15, and 0.30) heated at 500, 700, and 800 °C. Based on the International Centre for Diffraction Data (ICDD), all these systems have a cubic structure with Fd-3m (225) as a space group. We note here that according to Bragg’s law, the value of the lattice parameter is a = 5.46 Å for the x_Sr-800°C and x_Sr-700°C series (x_Sr = 0.00, 0.15, and 0.3), while for the sample series heated at 500 °C a = 5.47 Å. The xSr-500 °C series illustrates the praseodymium oxide (PrO₂) as an impurity and also shows a cubic structure Fm-3m (225) with a = 5.39 Å. The average percentage of PrO₂ for all samples is about 24%. This additional phase disappears when the temperature is increased from 700 and 800 °C. As the heating temperature increases, the rare earth metal can reach various oxidation states, which facilitates the formation of the desired phase and the suppression of the secondary phase.

The crystalline sizes of the above-mentioned systems were estimated based on the XRD line broadening using the well-known Scherrer formula¹⁷ 

where k = 0.9—a dimensionless shape factor, λ_Cu = 1.5406 Å—the wavelength of Cu-K_α radiation, θ is the Bragg angle of the most intense peak, and β is the full width at half maximum of Bragg’s peak. Equation (1) revealed nanosized crystallites; D_XRD (x_Sr-500°C) = 51 nm for the three samples, D_XRD (x_Sr-700°C = 0.00, 0.15) = 51 nm and D_XRD (x_Sr-700°C = 0.30) = 48 nm, and D_XRD (x_Sr-800°C = 0.00) = 49 nm and D_XRD (x_Sr-800°C = 0.15, 0.30) = 55 nm, as depicted in Table I.

Figures 2(a)–2(c) show the Scanning Electron Microscopy (SEM) micrographs at room temperature of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00, 0.15, and 0.30) heated at 500, 700, and 800 °C, respectively, as well as the statistical distribution with the Gaussian fit of particle number vs particle size. SEM images show that all prepared samples present nanosized particles, as depicted in SEM images, with particle sizes D_SEM−1μm (x_Sr-500°C = 0.00) = 36 nm, D_SEM−1μm (x_Sr-700°C = 0.00) = 41 nm, and D_SEM−1μm (x_Sr-800°C = 0.00) = 68 nm [Fig. 2(a)]. D_SEM−1μm (x_Sr-500°C = 0.15) = 32 nm, D_SEM−1μm (x_Sr-700°C = 0.15) = 37 nm, and D_SEM−1μm (x_Sr-800°C = 0.15) = 65 nm, as presented in Fig. 2(b). Figure 2(c) presents D_SEM−1μm (x_Sr-500°C = 0.30) = 37 nm, D_SEM−1μm (x_Sr-700°C = 0.30) = 48 nm, and D_SEM−1μm (x_Sr-800°C = 0.30) = 62 nm. These values are presented in Table I. The average particle size of the x_Sr-500°C systems is 35 nm, the average particle size of the x_Sr-700°C series is 42 nm, and the average particle size of the x_Sr-800°C samples is 65 nm. Both D_XRD and D_SEM confirm the formation of nanosized manganites.

The effect of the heating temperature on the magnetic measurements was investigated. Figures 3(a)–3(c) depict the thermal variation of zero-field cooling and field cooling (ZFC/FC) dc magnetizations of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00, 0.15, and 0.30) heated at 500, 700, and 800 °C, respectively, and carried out at 500 Oe in the temperature range of 5–300 K. The x_Sr-700°C series shows, roughly, the same aspects comparing to the x_Sr-800°C samples but with weaker magnitudes. For example, for x_Sr = 0.00, M_FC (x_Sr-800°C) ∼ 6 emu/g vs M_FC (x_Sr-700°C) ∼ 0.48 emu/g. The same scenario occurred for x_Sr = 0.15 and 0.30.

While the temperature was increased for all samples of the two series x_Sr-800°C and x_Sr-700°C, the magnetization of FC decreased. This points to the establishment of ferromagnetic (FM) orders at low temperatures¹⁸ for all systems, as announced by Ning et al.⁹ in the investigation of the magnetic properties of Pr_1−xCa_xMnO₃. The ZFC magnetization for both x_Sr-800°C and x_Sr-700°C series increases initially as the temperature is increased to reach the maximum of the value at the junction temperature, TB. TB is the transition temperature from the superparamagnetic (SPM) state to the blocked order of the ferromagnet (FM), as found in PrMnO₃ by Anustup et al. The FM clusters are frozen for T TB, which represent the spin-glass order.^9,20–23 This TB rises from 43 K for x_Sr-800°C = 0.00 to 186 K for x_Sr-800°C = 0.30, as shown in Fig. 3, and is tabulated in Table II.

In the same case for x_Sr-700°C, TB increases from about 38 K to 83 K for x_Sr-700°C = 0.00 and 0.30. Hence, if you lower the temperature from 800 °C to 700 °C, TB can also decrease. As soon as the temperature is increased, the temperature and spin-glass state start to disappear, which illustrates an upward trend. The presence of TB is due to a magnetic interaction between the FM clusters and the externally applied magnetic field.^9,23–25 With respect to the x_Sr-500°C series, it shows a different aspect of ZFC/FC magnetizations compared to the other two series of manganites. Nevertheless, the x_Sr-500°C samples did not show TB. This excludes the possibility of an existing superparamagnetic (SPM) state. An important irreversibility behavior between ZFC and FC measurements was shown by all prepared compounds, and this is particularly evident in the x_Sr-800°C and x_Sr-700°C series.

When the samples are cooled in the presence of a magnetic field, irreversibility is observed in the ZFC/FC curves, which bifurcate at a temperature (about 300 K) at which the thermomagnetic irreversibility temperature, T_irr, should be reached.^17,26–29

It varies from one sample to the other, as depicted in Figs. 3(a)–3(c) and summarized in Table II, as well. T_irr increased for the x_Sr-800°C series from 134 K to 244 K for x_Sr-800°C = 0.00 and 0.30, respectively. It rises also for the x_Sr-700°C series from 120 K to 150 K for x_Sr-700°C = 0.00 and 0.30, respectively. However, the x_Sr-500°C samples presented a little different behavior; the x_Sr-500°C = 0.00 sample showed an important irreversibility that until 300 K, T_irr was not noticed, as depicted in Fig. 3(a). Augmenting the quantity of Sr (x_Sr) led to the appearance of T_irr, which was around 104 K for x_Sr-500°C = 0.15. Then, for x_Sr-500°C = 0.30, T_irr could not be defined due to the fact that irreversibility was not shown by this sample. It diminished with augmenting x_Sr for the x_Sr-500°C series. For x_Sr-500°C = 0.00 and 0.30, T_C was defined as the temperature transition to the paramagnetic (PM) state, as illustrated in Figs. 3(a) and 3(c).

It is worth mentioning that T_B and T_irr were not the same for any rate of Sr. For T < T_irr, the increase of FC branches showed that the spins in the FM region are parallel and polarized up to the lowest temperature value while cooling the samples, as it is generally known that the appearance of spin-glass order causes the bifurcation between ZFC/FC measurements.³⁰ As illustrated by all samples of both series x_Sr-800°C and x_Sr-700°C, ZFC/FC magnetizations present the “λ” shape confirming the transition from the FM to PM state at T_irr in the perovskite structure²⁰ based on manganese oxide, as found in PrMnO₃ by Christopher et al.²³ x_Sr-800°C = 0.30 presents at T_co = 10 K a state of charge ordering (CO) illustrated by the minimum reached via ZFC measurements. This state was found also in both x_Sr-500°C = 0.15 and 0.30 samples. Thus, for higher doping concentration x_Sr, the CO state has a chance to appear, as presented in Pr_1−xCa_xMnO₃ by Elovaara et al.²⁰ Note here that the charge ordering is a fascinating phenomenon consisting in a spatial ordering of the Mn³⁺ and Mn⁴⁺ ions in real space so as to have an alternation of these ions in the three directions of space.

The magnetocaloric effect (MCE) of these systems extracted from magnetic results was discussed. The MCE was investigated to test the possibility of cooling by changing the applied magnetic field.^9,31–33 Two different methods can be used to determine the MCE: the direct method, where the system is exposed to a change in the magnetic field and the temperature change obtained can be directly determined in various ways,²² and an indirect method (the one we have chosen): the MCE is determined on the basis of the magnetic data. The ability of the prepared systems to be suitable magnetic refrigerants was evaluated by determining two factors:

• The magnetic entropy change (−ΔS) is connected to magnetization M, temperature T, and magnetic field through Maxwell’s relation^35–36 

  $∂S(T,H)∂HT=∂M(T,H)∂TH.$

  (2)
  Upon integrating Eq. (2), the following equation is obtained:

  $ΔST,ΔH=∫0HdS(T,H)T=∫0H∂MT,H∂THdH.$

  (3)
• The refrigerant capacity (RC) is defined as the energy that can be transferred between the hot and cold reservoirs^37,38 to estimate the power of the MCE,

  $RC=−∫T1T2ΔS(T)dT$

  (4)

  with T₁ and T₂ representing the cold and hot ends of temperatures, respectively.

Figures 4(a)–4(c) depict the thermal evolution of the magnetic entropy change (−ΔS) of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00, 0.15, and 0.30) heated at 800 °C, 700 °C, and 500 °C for various applied magnetic fields varying from 1 to 7 T. For all samples, the −ΔS plots increased with the applied magnetic field. A clear difference appears between the 1 and the 7 T entropies. For the x_Sr-800°C = 0.00 sample [Fig. 4(a)], the −ΔS plots decreased with augmenting temperature to present a slight convex in the temperature range of 31–87 K, followed by a small peak at ∼87 K where −ΔS resume the lowering of the values. For the x_Sr-700°C = 0.00 sample, the −ΔS values increased while increasing the temperature to reach a maximum at around 26 K with −ΔS^peak1−0.00 = 0.29 J kg⁻¹ K⁻¹ at 7 T and then decreased to present a convex from 47 to 99 K, followed by a second maximum at about 100 K with −ΔS^peak2−0.00 = 0.10 J kg⁻¹ K⁻¹ at the same applied magnetic field.

While for the x_Sr-500°C = 0.00 system, the −ΔS entropies decreased monotonically with increasing temperature. Both convexities are related to the existence of an irreversibility in the thermal evolution of the magnetization in these systems. The absence of convexity in the −ΔS diagrams of the x_Sr-500°C = 0.00 system is explained by the absence of irreversibility in the ZFC/FC magnet measurements. Regarding the x_Sr = 0.15 samples heated at 800 and 700 °C [Fig. 4(b)], the behavior of their magnetic entropy change was almost the same as for the x_Sr = 0.00 systems with the convexities in both x_Sr = 0.00 samples sintered at 800 and 700 °C becoming deeper due to the irreversibility shown by ZFC/FC measurements.

Furthermore, the −ΔS plots of the x_Sr-500°C = 0.15 sample reveal an important change compared to the x_Sr-500°C = 0.00 sample. It increased from the very low temperatures starting from negative values to present a concave in the temperature range of 28–70 K accompanied by a decrease in the −ΔS values for all the applied magnetic fields. Augmenting the quantity of the Sr doping La, x_Sr-500°C = 0.30 [Fig. 4(c)] resumes the initial behavior of −ΔS as that of x_Sr-500°C = 0.00. For x_Sr-700°C = 0.30, −ΔS illustrates nearly the same behavior as x_Sr-700°C = 0.00 and 0.15 with −ΔS^peak1−0.30 = 0.25 J kg⁻¹ K⁻¹ at 25 K and −ΔS^peak2−0.30 = 0.05 J kg⁻¹ K⁻¹ at 102 K under 7 T. However, x_Sr-800°C = 0.30 showed a different form of −ΔS; it presented a negative peak centered at about 90 K with −ΔS^peak1−0.30 = −0.91 J kg⁻¹ K⁻¹ at 7 T followed by a positive one at around 110 K with −ΔS^peak2−0.30 = 1.341 J kg⁻¹ K⁻¹ at the same applied magnetic field. This could be attributed to the successive structural and magnetic transitions, as announced by Ibarra-Gaytán et al.³⁹ A similar result was also found in La_0.5 Ca_0.5MnO₃ studied by Smari et al.⁴⁰ 

In order to further analyze the suitability of these samples as suitable magnetic refrigerants, the isotherm RC for Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr = 0.00, 0.15, and 0.30), heated at 800 °C, 700 °C, and 500 °C under 1 and 7 T, was examined and shown in Figs. 5(a) and 5(b). All samples showed that RC increased with the applied magnetic field. A large difference between the values of RC was observed at 1 T [Fig. 5(a)] 7 T [Fig. 5(b)].

For example, for x_Sr-800°C = 0.00, RC (1T) = 13.111 J/kg [Fig. 5(a)] vs RC (7T) = 171.159 J/kg [Fig. 5(b)]. For x_Sr-800°C = 0.30, RC (1T) = 4.535 J/kg [Fig. 5(a)] vs RC (7T) = 92.693 J/kg [Fig. 5(b)]. Similarly, when RC values were compared at 7 T of the three systems that were heated at different temperatures, it was obvious that augmenting temperature favored the increase in the RC values, e.g., for x_Sr-800°C = 0.00, RC (7T) = 171.159 J/kg vs RC (7T) = 23.065 J/kg and RC (7T) = 21.386 J/kg for x_Sr = 0.00 sintered at 700 and 500 °C, respectively.

Therefore, the rising temperature favored an increase in the values of RC. From Fig. 5, we can also deduce that the substitution of La by Sr in Pr_0.63La_0.37−xSr_xMnO₃ does not serve to optimize the MCE. This can be explained by the fact that an increase in Sr leads to a weakening of the magnetism because Sr dilutes the magnetism of systems, as mentioned in an earlier study.¹⁷ Consequently, the x_Sr-800°C series, sintered at 800 °C, was chosen because it can be used more efficiently in magnetic refrigeration. Three further samples were prepared, e.g., x_Sr-800°C = 0.05, 0.10, and 0.20, to study the physical properties in more detail and also to draw a phase diagram of this system Pr_0.63La_0.37−xSr_xMnO₃.

Figure 6 shows the XRD patterns of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr-800°C = 0.00, 0.05, 0.10, 0.15, 0.2, and 0.30) heated at 800 °C. The mean ionic radius of the A-site of the perovskite structure ABO₃ (A = Pr_0.63La_0.37−xSr_x and B = Mn) was determined, and the data were tabulated in Table I. In the case of our prepared system Pr_0.63La_0.37−xSr_xMnO₃, the A-site (A = Pr_0.63La_0.37−xSr_x and B = Mn in the perovskite structure ABO3) is occupied by (0.63) Pr, (0.37-x) La, and (x) Sr. Based on the table from the work of Shanon,⁴¹ the following equation is given:

where y_i represents the fractional occupancy and 〈r_i〉 is the average ionic radius of the ith cation of the A-site.

Due to a larger ionic radius of Sr (1.18 Å) than that of La (1.032 Å), substituting La by Sr increased the average ionic radius of the A-site cations 〈r_A〉.⁴⁰ It also increased the mismatch factor $σA2$⁠,¹⁷ as shown in Table I. It is given by

where y_i represents the fractional occupancy and r_i is the ionic radius of the ith cation.

The crystal structure of these samples (x_Sr-800°C = 0.05, 0.15, and 0.2) is indexed to the cubic Fm-3m (225) space group following the International Centre for Diffraction Data (ICDD) software. They are classified also as nanosized manganites, as shown in Table I.

Figures 7(a)–7(c) depict the SEM micrographs of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr-800°C = 0.05, 0.10, and 0.20) heated at 800 °C and their statistical distributions fitted via a Gaussian function. Based on the ImageJ software, the particle sizes of the prepared materials are nanosized with D_SEM−1μm around 55, 40, and 40 nm for x_Sr-800°C = 0.05 [Fig. 7(a)], 0.10 [Fig. 7(b)], and 0.20 [Fig. 7(c)], respectively. These values are summarized in Table I. All the grains are randomly oriented and have irregular shapes, which are highly interconnected and form a network of grains. This may be due to the milling process used in the manufacture of these systems.

All pictures from SEM illustrate a large agglomeration of these nanoparticles, which leads to an uneven distribution of the grain size.⁴² Note that despite the high heating temperature of 800 °C, the average particle size of these systems (x_Sr-800°C = 0.00, 0.05, 0.10, 0.15, 0.20, and 0.30) was only about 55 nm; this indicates the advantage of the non-aqueous solid-state reaction.

Figure 8(a) presents the thermal variation of the ZFC/FC magnetizations of x_Sr-800°C = 0.05, 0.10, and 0.20 at 500 Oe. Experiments were performed to investigate the effect of Sr substitution (x_Sr) on the magnetic properties of Pr_0.63La_0.37−xSr_xMnO₃ heated at 800 °C. The T_B values were at 80, 94, and 170 K for x_Sr-800°C = 0.05, 0.10, and 0.20, respectively (Table I). The presented bifurcation between ZFC and FC is marked by T_irr in Fig. 8(a).

The x_Sr-800°C = 0.20 sample presents the appearance of a charge ordering sate at around 10 K as the x_Sr-800°C = 0.30 system, Fig. 3(c). The irreversibility in the x_Sr-800°C series (x_Sr-800°C = 0.00, 0.05, 0.10, 0.15, 0.20, and 0.30) is presented vs the rate of Sr in Fig. 8(b) showing that this behavior is non-uniform. Initially, it increases from x_Sr-800°C = 0.00 to x_Sr-800°C = 0.05, and then it decreases when reaching x = 0.10 to restart and present the highest value for x_Sr-800°C = 0.15 with 6.95 emu/g. Still below T_irr, the largest difference between ZFC and FC measurements is a signature of the highest FM state.¹⁹ Thus, the x_Sr-800°C = 0.15 sample was considered as the FM sample compared to other samples presenting short-range FM interactions.¹⁸ Based on the extracted results from the thermal variation of ZFC/FC for all the samples, the magnetic phase diagram of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr-800°C = 0.00–0.30) heated at 800 °C, Fig. 8(c), was plotted.

Figures 9(a) and 9(b) show a set of isothermal magnetization plots at different temperatures, from 5 to 300 K, and the thermal evolution of magnetic entropy change curves up to 7 T of Pr_0.63La_0.37−xSr_xMnO₃ (x_Sr-800°C = 0.05, 0.10, and 0.20) heated at 800 °C. For all systems, the isothermal magnetization plots depict the presence of different magnetic phases vs temperature.³¹ For each temperature, the magnetization is rising with increasing applied magnetic field, and concerning the corresponding applied field magnitude, it diminishes with decreasing temperature. This corresponds to the SPM behavior,³⁷ in conformity with the results extracted from ZFC/FC measurements.

The isothermal magnetizations were used as a means to determine the variation of magnetic entropy (−ΔS) as a function of temperature for different applied magnetic fields (from 1 to 7 T) in order to conclude whether or not these existing systems can be considered as suitable magnetic refrigerants. For these three samples, −ΔS increases with the applied magnetic field, as shown in Fig. 9(b). There is a clear difference between the 1 and the 7 T entropies. All curves start to rise strongly, while the temperature decreases where they become more pronounced. All compounds forming the x_Sr-800°C series show almost the same behavior of −ΔS, and only x_Sr-800°C = 0.30 shows a different shape, as shown in Fig. 4(c).

The RC values for the samples constituting the x_Sr-800°C series were determined taking into account that temperature has an important impact on the RC values. For example, for x_Sr-800°C = 0.00, RC (1T/30 K) = 0.931 J/kg and RC (1T/285 K) = 13.111 J/kg vs RC (7T/30 K) = 35.264 J/kg and RC (1T/285 K) = 171.159 J/kg. Similarly, x_Sr-800°C = 0.30 with RC (1T/30 K) = 1.125 J/kg and RC (1T/285 K) = 4.535 J/kg vs RC (7T/30 K) = 34.281 J/kg and RC (1T/285 K) = 92.693 J/kg.

As shown in the insets of Figs. 10(a) and 10(f), the RC values obey the power law RC ∼ H^a43,44 of the applied magnetic field with the parameter of the “a” design related to this law, the cyan curves. These values were as follows: for x_Sr-800°C = 0.00, at 30 K, a = 1.720; and at 285 K, a = 1.434. For x_Sr-800°C = 0.30, at 30 K, a = 1.476; and at 285 K, b = 1.456. These results are slightly different from those found by Franco et al.,⁴⁵ who found a = 1.47 from RC vs H, which was a fixed value that did not change when the core or shell material was changed. Franco confirmed that the nature of the spin-glass state is not changed by changing the material properties. This is not true in the present case, as the parameter “a” changes from one material to another, even from temperature to temperature for the same system. We concluded that the spin-glass state is changed from sample to sample by changing xSr. This is also confirmed by the fact that the TB temperature of these current systems varies. Figure 10(g) shows the isomagnetic development of the RC values compared to the amount of Sr (x_Sr). It is clear that RC, as mentioned above, increases with the magnetic field, and the x_Sr-800°C = 0.05 sample shows the highest values of RC compared to other systems with 17.278 J/kg at 1 T and 208.264 J/kg at 7 T, making it the most suitable candidate for the magnetic cooling method.

Comparing both materials of the same family, the Relative Cooling Power (RCP) value of Pr_0.55Bi_0.05Sr_0.4MnO₃ was 56 J/kg and that of the Pr_0.6Sr_0.4MnO₃ compound was 93.5 J/kg.⁴⁶ 

It is true that the magnetic entropy change and refrigerant capacity are the most important parameters of MCE, but they are complementary. As we can see here, the values of magnetic entropy change are not high either; the RC represent important values.

Pr_0.63La_0.37−xSr_xMnO₃ nanoparticles (x_Sr = 0.00, 0.05, 0.10, 0.15, 0.20, and 0.30) were prepared at three different temperatures, i.e., 500, 700, and 800 °C. The structural, magnetic, and magnetocaloric properties through the evolution of x_Sr and through the effect of heat treatment were studied. The systems crystallized in a cubic structure. They showed different magnetic states. The change in magnetic entropy showed a different behavior based on x_Sr and the heat treatment process. These systems can be good magnetic refrigerants, especially the promising x_Sr-800°C = 0.05 sample with RC by 17.278 J/kg at 1 T and 208.264 J/kg at 7 T.

The authors would like to acknowledge the contribution of Core Labs group supervised by Dr. Said A. Mansour in Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Qatar Foundation, especially Dr. Akshath Raghu Shetty for carrying out the XRD measurements, and Dr. Mujaheed Pasha and Mr. Mohamed I. Helal for conducting the SEM images.

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