Effect of Ru substitution on the physical properties of La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ (x = 0.00, 0.05 and 0.15) perovskites

Abstract

Morphology, magnetic, and magnetocaloric properties of La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ (x = 0.00, 0.05 and 0.15) were experimentally investigated. A solid-state reaction method was used for the preparation of the samples. The microstructure of the samples was determined by scanning electron microscopy SEM. Field-cooled (FC) and zero-field-cooled (ZFC) thermomagnetic curves measured at low field and low temperatures exhibit a cluster spin state. A sensitive response to substituting Ru for Mn is observed in the magnetic and magnetocaloric properties. We found that Ru doping is not powerful enough to reduce the Curie temperature T_C, however, it brings about cluster glass behaviors. A magneto-caloric effect has been calculated in terms of isothermal magnetic entropy change. The maximum entropy change |ΔS^max_M| reaches the highest values of 3.32 J kg⁻¹ K⁻¹, 3.11 J kg⁻¹ K⁻¹ and 2.57 J kg⁻¹ K⁻¹ in a magnetic field. However, the relative cooling power decreases with Ru content from 227.44 J kg⁻¹ to 214.14 J kg⁻¹ and then to 188.68 J kg⁻¹ for x = 0.00, 0.05 and 0.15 compositions, respectively.

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1. Introduction

The hole-doped mixed valence perovskite manganites of the type D_1−xA_xMn_1−yB_yO₃ (where D is a trivalent rare earth, A is a divalent alkali earth and B is the transition metals) have attracted considerable attention during the last decade. In these perovskite compounds, the interplay between magnetism, charge ordering and electronic transport has been studied in detail.^1–4 In particular, the metal–insulator transition near the Curie temperature in this type of material has been interpreted in terms of the double exchange (DE) model. Other mechanisms have also provided valuable insights into the colossal magnetoresistance (CMR) phenomenon in manganites, such as the antiferromagnetic super-exchange, Jahn–Teller effects, orbital and charge ordering.^5,6 Other research has focused on perovskite manganites with a general formula D_1−xA_xMnO₃ after observing large magnetocaloric effects (MCE) in these compounds.^7–10 Currently, the magnetocaloric effect (MCE) offers an alternative technology in refrigeration, with an enhanced efficiency but without environmental hazards.^11–14 The key in using magnetic refrigeration at room temperature is to seek appropriate refrigerant materials that can produce a large entropy variation when they go through a magnetization–demagnetization process. In terms of the crucial role of the Mn site, it would be interesting and worthwhile to study the effects of Mn-site element substitution, which may provide clues for exploring novel MCE materials and discerning the mechanism of MCE. Within this framework, the effect of substituting trivalent ions such as Fe, Ni and Sc for Mn³⁺ ions in the B site on the ferromagnetic properties of these manganites has been studied.^15–18 It was experimentally found that any modification on the exchange interaction causes the pair-braking effect associated with a drastic reduction in Curie temperature T_C. However, differently from the common ionic substitution, Ru doping in manganites has a peculiar effect and is attracting more attention. A slight substitution of Ru for Mn ions favors the formation of the ferromagnetic metal (FMM) states.^19–21 Additionally, it was reported that as high as 30 at% of Ru can be added into the Mn sites in La_0.7Sr_0.3 MnO₃, with no change in the crystal structure and a weak effect on the reduction of T_C.²² It is argued that Ru has a more delocalized 4f orbital with itinerant t_2g electrons that facilitate the exchanges coupling interaction. That is to say that, Ru could make a magnetic pair with Mn to form the Mn–O–Mn network, thus favoring the DE-mediated transport mechanism. Enhanced magnetic and metal–insulator transition temperature in Ru-doped layered magnanites La_1.2Ca_1.8Mn_2−xRu_xO₇ have been reported.^23–30 It is known from the literature that mixed valence of Ru³⁺/Ru⁺⁴ appears in the lower-doping region (0 ≤ 0.5) while an additional mixed valence of Ru⁴⁺/Ru⁵⁺ appears in the high-doping region (0 ≥ 0.5).³¹

La_0.6Pr_0.1Sr_0.3MnO₃ is one of the perovskite compounds which possess rich physical properties but a relatively high Curie temperature (T_C = 360 K).³² Potential applications, particularly magnetic refrigeration (MR) require a transition temperature T_C close to room temperature. This can be achieved by an appropriate amount of oxygen stoichiometry or by the substitution of Mn by a non-magnetic or magnetic cation. So, to decrease the critical temperature of the parent compound La_0.6Pr_0.1Sr_0.3MnO₃, we made a substitution of Ruthenium (Ru) for manganese (Mn) by. Then, we investigated the effect of this substitution on the physical properties of La_0.6Pr_0.1Sr_0.3MnO₃.

2. Experimental details

Polycrystalline samples of La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ series with (x = 0.00, 0.05 and 0.15) were prepared by conventional solid state ceramic processing. High purity (99.99%) starting compounds La₂O₃, Pr₆O₁₁, SrCo₃, MnO₂ and RuO₂ were taken in stoichiometric proportions. Care was taken to remove moisture before weighing by preheating the precursors at 873 K for 12 h. The mixtures were heated in air at 1073 K for 24 h to achieve decarbonization. After grinding, they were heated at 1373 K for 48 h and grind again to ensure homogeneity. Intermediate cooling and mechanical grinding steps were repeated in order to get an accurate homogenization and complete reaction. The powders were pressed into pellets and sintered at 1673 K for 72 h under an Ar/H₂ (5%) atmosphere with several intermediate grinding and repelling. Finally, these pellets were quenched to room temperature.³³ “Magnetizations (M) vs. temperature (T) were measured using BS1 and BS2 magnetometers developed in Louis Néel Laboratory of Grenoble. BS1 (300–900 K) and BS2 (1.5–300 K) magnetometers are used respectively for magnetic measurements at high and low temperatures equipped with a super conducting coil.³⁴ These two instruments are automated by a computer system that allows the registration of digital data for each successive measurement. Magnetization isotherms were measured in the range of 0–5 T and with a temperature interval of 3 K in the vicinity of Curie temperature (T_C). These isothermals were corrected by a demagnetization factor D that was determined by a standard procedure from low-field dc magnetization measurement at low temperatures (H = H_app − DM)”. Finally, the magnetocaloric effect (MCE) was characterized by an isothermal change of the magnetic entropy and the adiabatic change of temperature.

3. Results and discussions

3.1. Morphological characterization

In order to check the existence of all the elements in the LPSMRO (0.00, 0.05 and 0.15) compounds, an energy dispersive X-ray analysis was performed. An example of EDX spectra is represented in Fig. 1 for x = 0.05. This spectrum reveals the presence of all elements (La, Pr, Sr, Mn, Ru and O), which confirms that there is no loss of any integrated element during sintering. The SEM micrographs are given in the inset of this figure for x = 0.05. We can see that the grains exhibit spheroid-like shapes and a good connectivity between each other. This facilitates the intrinsic behaviors, because good current percolation between grains and the opening up of conduction channels do not block the ordering of the Mn spins.

Fig. 1 (a): Plot of EDX analysis of chemical species, the inset represents the scanning electron micrograph of x = 0.05.

3.2. Magnetic behaviors

Fig. 2(a) shows the temperature dependence of the zero field-cooled (ZFC) and field-cooled (FC) magnetization for LPSMRO. As can be seen, all the LPSMRO samples undergo a transition from a ferromagnetic to a paramagnetic phase. It is clear that the ‘FC’ curves do not coincide with the ‘ZFC’ curves below T_C. But the curves ‘FC’ and ‘ZCF’ curves have a common part for the high temperature, wherein the variation of magnetization with temperature is reversible and superposed. At low temperature, the behavior is irreversible with a divergence between ‘ZFC’ and ‘FC’. The magnetic moment decreases gradually. Such irreversibility in the M–T data for the FC and ‘ZFC’ measurements was observed in several manganite systems and it was suggested that this irreversibility is possibly due to the canted nature of the spins or to the random freezing of spins.³⁵ This can be clearly seen at low temperature for x = 0.15, which is generally related to a spin-glass or cluster-glass state. The discrepancy between ‘ZFC’ curve and ‘FC’ curve becomes proportionally larger with the doped content of Ru. It is found that the Curie temperature T_C decreases with increasing x. The variation of T_C versus Ru concentration is tabulated in Table 1. One can note that T_C decreases slowly when Ru content is increased. The abnormal evolution of T_C indicates that the Ru ionic substitution reduces systematically ferromagnetism. The Curie temperature T_C determined by linearly extrapolating the temperature dependence of magnetic susceptibility 1/χ in the paramagnetic state is shown in the inset of Fig. 2(a), which obeys the Curie–Weiss law, 1/χ = (T − T_C)/C above T_C. From the obtained Curie constants (C), we get the effective moment P^exp_eff = 5.76, 5.45 and 4.91 μ_B for x = 0.00, 0.05 and 0.15, respectively.

Fig. 2 (a) Temperature dependences of the zero-field-cooled and field-cooled magnetization for LPSMRO samples under applied magnetic field 0.05 T, the inset show temperature dependent inverse susceptibility χ⁻¹(T) curves. (b) The hysteresis loops of LPSMRO samples (x = 0.00 and 0.15); the inset shows the fields dependence of the magnetization plots taken at 5 K for all the samples in magnetic fields strengths of ±10 T.

Table 1 Maximum entropy change |ΔS^max_M| and relative cooling power (RCP), occurring at the Curie temperature (T_C) and under magnetic field 5 T for La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00, 0.05 and 0.15) compounds, compared to several materials considered for magnetic refrigeration

Composition	TC (K)	μ0ΔH (T)	|ΔS^maxM| (J kg^−1 K^−1)	RCP (J kg^−1)	References
La0.6Pr0.1Sr0.3MnO3	360	5	3.32(1)	227.44(3)	Our work
La0.6Pr0.1Sr0.3Mn0.95Ru0.05O3	350	5	3.11(2)	214.14(1)	Our work
La0.6Pr0.1Sr0.3Mn0.85Ru0.15O3	344	5	2.57(2)	188.68(2)	Our work
La0.52Dy0.15Pb0.33MnO3	290	5	3.51	246	41
Gd5 (Si2Ge2)	275	5	18.5	535	42
La0.8Ba0.2Mn0.1Fe0.1O3	193	5	2.62	211	43
La (Fe0.96Co0.04)11.9Si1.1	243	5	22.5	—	44
La (Fe0.94Co0.06)11.9Si1.1	274	5	20	—	44
Pr0.7Ca0.3Mn0.95Fe0.05O3	89.95	5	2.39	337.4	45
Pr0.7Ca0.3Mn0.95Co0.05O3	104.97	5	2.96	378.2	45
Pr0.7Ca0.3Mn0.95Ni0.05O3	109.97	5	3.1	352.2	45
Pr0.7Ca0.3Mn0.95Cr0.05O3	139.7	5	2.92	405.72	45
Gd	350	5	2	—	46
La0.52Dy0.15Pb0.33MnO3	290	5	3.51	246	47
La0.47Dy0.2Pb0.33MnO3	277	5	2.3	215	47
La0.67Sr0.33MnO3	348	5	1.69	211	48
La0.67Ba0.33MnO3	292	5	1.48	161	49
La0.7Pb0.3MnO3	352	5	0.96	48	50

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The calculated effective paramagnetic moment per formula can be written as:

with μ^th_eff(Mn³⁺) = 4.9 μ_B, μ^th_eff(Mn⁴⁺) = 3.87 μ_B, μ^th_eff(Pr³⁺) = 3.58 μ_B,³⁶ μ^th_eff(Ru³⁺) = 1.73 μ_B,³⁷ μ^th_eff(Ru⁴⁺) = 2.83 μ_B.³⁸ The values of P^th_eff are 4.751, 4.66 and 4.47 for x = 0.00, 0.05 and 0.15, respectively (Table 2). The difference between the effective magnetic moments measured and the theoretical values is possibly due to the possible orbital–charge fluctuations in contrast to charge–orbital ordering in the parent compound La_0.6Pr_0.1Sr_0.3MnO₃.

Table 2 Magnetic parameters deduced from magnetization such as the effective moment (experimental) μ^exp_eff, effective moment (theoretical) μ^cal_eff, remanence magnetization M_r (emu g⁻¹), saturation magnetization (M_s), the coercive field μ₀H_C (T) and remanence ratio R = (M_r/M_s) of the system La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00, 0.05 and 0.15) compounds

Samples	P^expeff	P^caleff	Mr (emu g^−1)	μ0HC (T)	Ms (emu g^−1)	R = (Mr/Ms) (%)
x = 0.00	5.76(3)	4.75(1)	4.60(1)	2.6(3) × 10^−3	84, 23(1)	0.054
x = 0.05	5.45(4)	4.66(2)	5.75(2)	6.3(2) × 10^−3	80, 11(1)	0.071
x = 0.15	4.91(1)	4.47(1)	18.20(4)	2.3(5) × 10^−2	75, 07(3)	0.240

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The field dependence of magnetization at 5 K is plotted in the inset of Fig. 2(b) in magnetic fields strengths of ±10 T to complement the FC versus T data. The magnetization of all the samples nearly saturates above 1.5 T. On increasing Ru doping, the saturation magnetization (M_s) decreases. The hysteresis loops of x = 0.00 and x = 0.15 samples are plotted at temperature 5 K in Fig. 2(b). The hysteresis in the M–μ₀H curve, along with the saturation, clearly confirms that we have a ferromagnetic state at low temperatures. It can be clearly seen that both the coercive field (μ₀H_c) and the remanence magnetization (M_r) increase systematically with the increases of Ru doping. The coercive field increased by more than an order of magnitude from 2.6 × 10⁻³ T for the undoped (x = 0.00) sample to nearly 2.3 × 10⁻² T for x = 0.15 Ru doped sample. Similarly, the Ru doping resulted in a large change of M_r, by as much as a factor of 4 (Table 2).

Fig. 3 shows the variation of remanence magnetization (M_r) and saturation magnetization (M_s) with Ru³⁺ substitution. The force required for demagnetization of a sample is termed as remanence magnetization and is one of the important parameters to be considered in recording media industry. Remanence is a structure sensitive parameter. For the present system the values of remanence varied in the range of 4.60–18.20 emu g⁻¹. The remanence ratio R = M_r/M_s is a characteristic parameter of the material. It is an indication of the ease with which the direction of magnetization reorients to the nearest easy axis of magnetization direction after the magnetic field is removed. Within this framework, it is desirable to have higher remanence ratio for magnetic recording and memory devices.³⁹ The values of R in the present case varied for one magnitude of order and the values found are 0.054, 0.071 and 0.240 for x = 0.00, 0.05 and 0.15 respectively. The values show an increasing trend with Ru³⁺ substitution.

Fig. 3 Variation of saturation magnetization (M_s) and remanence magnetization (M_r) with Ru content.

Furthermore, to better understand the effect of the substitution of Ru for Mn at low temperature, we calculated the values of saturation magnetic moment at T = 5 K considering the total spins of Mn³⁺, Mn⁴⁺, Pr³⁺, Ru³⁺ and Ru⁴⁺ ions (Mn_{Sat Mn³⁺} = 4μ_B(t³_2ge¹_g), M_{Sat Mn⁴⁺} = 3μ_B(t³_2ge⁰_g), M_{sat Pr³⁺} = 2μ_B, M_{Sat Ru³⁺} = 3μ_B(t⁵_2g state), M_{Sat Ru⁴⁺} = 2μ_B (Low-spin t⁴_2g state)). The spontaneous magnetizations of the La_0.6³⁺Pr_0.1³⁺Sr_0.3²⁺(Mn_1−xRu_x)_0.7³⁺(Mn_1−xRu_x)_0.3⁴⁺O₃ compounds are expressed as follows:

M^(cal)_Sat = (M_{Sat Pr³⁺})(n_Pr³⁺) + (M_{Sat Mn³⁺})(n_Mn³⁺) + (M_{Sat Mn⁴⁺})(n_Mn⁴⁺) + (M_{Sat Ru³⁺})(n_Ru³⁺)

where n_Mn³⁺, n_Mn⁴⁺, n_Pr³⁺ and n_Ru³⁺ are the contents of Mn³⁺, Mn⁴⁺, Pr³⁺ and Ru³⁺ ions respectively and μ_B is Bohr magneton. The measured spontaneous magnetizations at T = 5 K for x = 0.00, 0.05 and 0.15 compounds are found to be about 3.61 μ_B, 3.22 μ_B and 2.45 μ_B respectively, while the calculated values for full spin alignment are 3.9 μ_B, 3.64 μ_B and 3.191 μ_B, respectively. The spontaneous magnetization decreases with increasing Ru content. The difference between measured and calculated values especially for x = 0.15 should be explained by spin canted state at low temperature.⁴⁰

In Fig. 4, we show magnetization isotherms, M(μ₀H), for x = 0.00 and x = 0.15 samples taken over a certain temperature range around their respective Curie temperatures. The data were taken at 5 K intervals close to T_C and away from T_C. We found a soft ferromagnetic behavior at all temperatures in Ru-doped compounds. The same result is shown during Fe doping at Mn site in the same parent compound.⁴⁰ Banerjee⁴¹ suggested an experimental criterion which allows the determination of the nature of the magnetic transition (first or second order). It consists in observing the slope of the isotherms plots M² versus μ₀H/M. Applying a regular approach, the straight line was constructed simply by extrapolating the high magnetization parts of the curves for each studied temperature. A positive or negative slope indicates a second or a first order transition, respectively. Fig. 5(a) and (b) shows the isotherm plots M² versus μ₀H/M above and below T_C for x = 0.00 and x = 0.15 samples, respectively. These samples show positive slopes in the complete M² range, indicating that the system exhibits a second-order ferromagnetic to paramagnetic phase transition.

Fig. 4 Isothermal magnetization as a function of applied field for La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00 and 0.15) measured in the temperature ranges 299 to 384 K.

Fig. 5 The Arrott plots of M² vs. μ₀H/M at various temperatures for La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00 and 0.15) samples.

3.3. Magnetocaloric behaviors

The magnetocaloric effect is an intrinsic property of magnetic materials. It is the response of the material to the application or removal of magnetic field, which is maximized when the material is near its magnetic ordering temperature (Curie temperature T_C).

From Maxwell's thermodynamic equation, the magnetic entropy change as the field is varied from μ₀H = 0 to μ₀H = μ₀H_max. Can be written as:

The numerical evaluation of this integral can be approximated to give

ΔS_M = ∑[(M_i(T_i, μ₀H) − M_i+1(T_i+1, μ₀H))/(T_i − T_i+1)]Δμ₀H (2)

where M_i and M_i+1 are the magnetization values measured at temperatures T_i and T_i+1, respectively and Δμ₀H represents the field variation from μ₀H = 0 until μ₀H_max.

The −ΔS_M values for different Δμ₀H as a function of temperature are presented in Fig. 6 determined under an applied magnetic field up to 5 T. The −ΔS_M is positive in the entire temperature range for all the samples. The magnetic entropy for Δμ₀H = 5 T increases with lowering temperature for T ≪ T_C, others goes through a maximum around T_C and then decreases for T ≫ T_C. The magnitude of the peak increases with increasing the value of Δμ₀H for each composition but the peak position is nearly unaffected because of the second order nature of the ferromagnetic transition in these compounds. Furthermore, the value of the peak decreases with increasing Ru content around T_C from −ΔS_M = 3.32 J kg⁻¹ K⁻¹ for =0.00 to 2.57 J kg⁻¹ K⁻¹ for x = 0.15. It should be noted that |ΔS^max_M| values found in this study are relatively the same as that observed by R. Cherif et al. for x = 0.00.⁴⁰ For comparison, we listed in Table 2 the data of various magnetic materials that could be used as magnetic refrigerants. Although the values of |ΔS^max_M| are smaller than the most conspicuous MC material La (Fe_1−xCo_x)_11.9Si_1.1,⁴⁴ these perovskite manganites are easy to manufacture and exhibit higher A-or B-site doping. Consequently, a large magnetic entropy change can be tuned from low temperature to near or above room temperature which is beneficial for operating magnetic refrigeration at various temperature ranges.

Fig. 6 Temperature dependence of the magnetic entropy change (−ΔS_M) at different applied magnetic field change interval for La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00, 0.05 and 0.15) samples.

On the other hand, the specific heat can be calculated from the field dependence of the external magnetic entropy from zero to μ₀H_max by the following equation:^51,52

From this formula, ΔC_P(T, μ₀H) of La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.05) sample versus temperature at different magnetic fields is shown in Fig. 7. The value of ΔC_P suddenly changes from positive to negative around Curie temperature (T_C) and rapidly decreases with decreasing temperature.

Fig. 7 Change of specific heat of the sample as a function of temperature at different magnetic fields for x = 0.05.

For practical applications, not only the high value of ΔS_M. but also the temperature range over which it remains large is important. The relative cooling power (RCP), defined as the product of peak value of ΔS_M and full width at half maximum (FWHM) of ΔS_M in the corresponding temperature scale (RCP = ΔS_M × ∂T_FWHM), is a measure of the quantity of heat transferred by the magnetic refrigerant between hot and cold sinks. We found that RCP = 227.445 J kg⁻¹, 214.148 J kg⁻¹ and 188.684 J kg⁻¹. for x = 0.00, 0.05 and 0.15 respectively. These values are higher than those of La_0.67Ba_0.33MnO₃ (RCP = 161 J kg⁻¹ at T = T_C).⁵³ Since the RCP factor represents a good way for comparing magnetocaloric materials, our compounds can be considered as potential candidates thanks to their high RCP values compared with available refrigerant materials.^41,43

We can use ΔS^max_M and μ₀H to confirm that our materials exhibit a second order transition.^54,55 The magnetic materials with a second order transition generally obey ΔS^max_M = −kM_s(0)h^2/3 − S(0, 0), where h is the reduced field just around T_C [h = (μ₀μ_BH)/(k_BT_C)], k is a constant, M_s(0) is the saturation magnetization at low temperatures and S(0, 0) is the reference parameter, which may not be equal to zero.⁵⁵ Fig. 8 shows the linear dependence of ΔS^max_M versus h^2/3 which implies the second order transition in La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00, 0.05 and 0.15). The fact that ΔS^max_M is estimated at T_C and in fields larger than the critical field required for the metamagnetic transition justifies the conclusion about the second order transition.

Fig. 8 Temperature dependence of magnetic entropy change −Δ^ma_M versus h^2/3 for La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00 and 0.15) samples.

A phenomenological universal curve for the field dependence of ΔS_M has recently been proposed,⁵⁶ being the theoretical justification for its existence based on scaling relations.⁵⁷ Its phenomenological construction is based on the assumption that if such a universal curve exists, the equivalent points belonging to several ΔS_M(T) curves measured up to different maximum applied fields should collapse onto the same point of the universal curve. Therefore, the main aspect of constructing the universal scaling curve has been the selection of the equivalent points of the experimental curves. For this purpose, the peak entropy change |ΔS^max_M| is taken as a reference. It was assumed that all points that are at the same level with respect to |ΔS^max_M| should be in an equivalent state.

This phenomenological universal curve can be constructed by normalizing all ΔS_M(T) curves by using their respective maximum value ΔS^max_M, namely, ΔS′ = ΔS_M(T)/ΔS^max_M and by rescaling the temperature axis below and above T_C, as defined in (eqn (4)) with an imposed constraint that the position of two additional reference points in the curve corresponds to θ = ±1:

where T_r1 and T_r2 are the temperatures of the two reference points that were selected as those corresponding to 0.5ΔS^pk_M. This procedure has been successfully applied to different families of soft magnetic amorphous alloys and lanthanide based crystalline materials.^58–60 The phenomenological construction of the universal curve for the studied La_0.6Pr_0.1Sr_0.3Mn_0.95Ru_0.05O₃ manganite is reported in Fig. 9.

Fig. 9 The master curve behavior of the curves as a function of the rescaled temperature for different magnetic field (μ₀H = 5, 4, 3, 2 T) for x = 0.05.

It can be clearly seen that the experimental points of the samples distribute on one master curve of the magnetic entropy change (ranging from 1 T up to 5 T), demonstrating the predictions of master curve behavior for different magnetic fields of the same sample. This universal curve can be particularly helpful for studying the order of phase transition and the refrigeration capacity of similar materials, such as manganite series with the same universality class.⁶¹

3.4. Correlation between critical exponents and magnetocaloric effect

Numerous works have focused on the dependence of the magnetic entropy change (ΔS_M) of manganites at the FM–PM transition on T_C. According to Oesterreicher et al.,⁶² the magnetic field dependence on the magnetic entropy change ΔS_M at a temperature T for materials obeying a second-order phase transition follows an exponent power law of the type ΔS_M = b(μ₀H)ⁿ:⁶³where b is a constant and the exponent n depends on the values of field and temperature. By fitting the data of ΔS_M versus μ₀H to eqn (4), we obtained the value of n as a function of temperature at different magnetic fields for example x = 0.05, as depicted in Fig. 10. From this figure, the exponent n is close to 1 in the FM regime and increases to 2 in the PM regime. The exponent n exhibits a moderate increase with decreasing temperature and takes extreme values around Curie temperature of the existing phase, then sharply increases with increasing temperature. In a mean field approach, the value of n at Curie temperature is predicted to be 2/3.⁵⁵ It is well known in manganites that the exponent is roughly field independent and approaches approximate values of 1 and 2, far below and above the transition temperature respectively.⁶⁴ Then the values of n around T_C are 0.561, 0.584 and 0.613 for x = 0.00, 0.05 and 0.15 respectively, which confirms not only the invalidity of the mean field model in the description of our materials at near the transition temperature for our samples but also the possibility of 3D Ising model and 3D Heisenberg model to describe our material. These values are similar to those obtained for soft magnetic materials containing rare earth metals.^65–67

Fig. 10 Temperature dependence of the local exponent n for x = 0.05 at different magnetic field.

The field dependence of RCP, for our samples is also analyzed. It can be expressed as a power law by taking account of the field dependence of entropy change ΔS_M and reference temperature into consideration.⁵⁷

where δ is the critical exponent of the magnetic transition. Field dependence of RCP is displayed in Fig. 11 for x = 0.05. The obtained values of δ are 3.2(3), 3.34(2), and 2.82(4) for x = 0.00, 0.05 and 0.15, respectively. In the particular case of T = T_C or at the temperature when the entropy is maximal, the exponent (n) becomes an independent field.⁶⁸ In this case,where β and γ are the critical exponents.⁶⁹ With βδ = (β + γ),⁶⁹ the relation (eqn (7)) can be written as:

Fig. 11 Variation of Ln (RCP) as function of applied magnetic field for x = 0.05 sample. Red line indicates the linear fit for d calculation.

From the values of n and δ, the critical parameters β and γ are deduced for each compound using (eqn (7)) and (eqn (8)) (Table 3).

Table 3 Critical β and γ parameters calculated from n and δ

Samples	n	δ	β	γ	TC (K)	References
x = 0.00	0.561	4.98	0.313	1.251	360	This work
x = 0.05	0.584	5.02	0.323	1.304	350	This work
x = 0.15	0.613	4.85	0.347	1.340	344	This work

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4. Conclusion

In conclusion, we have reported detailed investigations of Morphological, magnetic and magnetocaloric properties of La_0.6Pr_0.1Sr_0.3Mn_1−xRu_xO₃ for (x = 0.00, 0.05 and 0.15). The samples were prepared by the standard ceramic process. T_C decreases slowly by substituting Ru for Mn. Moreover, there is cluster spin state in all investigated samples at low temperatures. We also found that the entropy change and the relative cooling power during the transition phase are reduced with the increase in Ru. These observations indicate that the existence of Ru has the effect of weakening ferromagnetism in LPSMRO perovskite.

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