Study of the Magnetocaloric Effect and Critical Behavior in Double Perovskite Manganese Oxides Pr 1.5 A 0.5 Mn 2 O 6 (A=Mg, Ba)

doi:10.21203/rs.3.rs-4141743/v1

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Study of the Magnetocaloric Effect and Critical Behavior in Double Perovskite Manganese Oxides Pr 1.5 A 0.5 Mn 2 O 6 (A=Mg, Ba)

https://doi.org/10.21203/rs.3.rs-4141743/v1

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In this study, polycrystalline samples of Pr₂Mn₂O₆ (parent phase) and Pr_1.5A_0.5Mn₂O₆ (A = Mg, Ba) were prepared using the high-temperature solid-phase reaction method. The effects of Mg and Ba doping on magnetocaloric properties and critical behavior of the parent phase were systematically investigated. Under a magnetic field of 7 T, the relative cooling power (RCP) values for this sample series were approximately 483.46 J·kg^− 1, 428.22 J·kg^− 1, and 479.88 J·kg^− 1, respectively. The critical behavior analysis revealed that the parent phase showed short-range exchange interactions, while Pr_1.5A_0.5Mn₂O₆ (A = Mg, Ba) exhibited long-range exchange interactions. The temperature dependence of the order parameter n was studied under different magnetic fields, confirming the phase transition types and validating the accuracy of the critical exponents obtained. The research findings suggest that both the parent phase and Ba-doped ceramics at the A-site hold promise as magnetic refrigeration materials.

Magnetocaloric effects

Magnetic phase transition

Second-order phase transition

Critical behavior

In recent years, magnetocaloric refrigeration (MR) based on the magnetocaloric effect (MCE) has emerged as a promising technology to replace traditional gas compression-expansion techniques[1] [2]. Researchers are actively seeking more suitable magnetocaloric materials, and a considerable focus has been placed on perovskite manganites of the form Ln_1 − xA_xMnO₃(Ln = La, Pr, Nd, ..., A = Sr, Ca, Ba, ...) due to their extensive studies on electrical and magnetic properties with potential applications[3]. Phan and Yu have provided a comprehensive overview of the observed magnetocaloric effects in manganese oxides[4]. The investigation of the LnMnO₃ system is particularly intriguing, characterized by significant MCE values and adjustable phase transition temperatures. These manganese oxides offer convenient synthetic routes, and their Curie temperatures (T_C) are reasonable under various doping conditions. Consequently, the study of the magnetocaloric effect in manganese oxide composites has become a new developmental trend.

Manganese oxides are generally classified into first-order phase transition materials and second-order phase transition materials based on the type of phase transition. It is well-known that first-order phase transition materials often exhibit significant magnetocaloric effect (MCE). However, they are accompanied by challenges such as a narrow cooling temperature range, relatively small refrigeration capacity, and large magnetic hysteresis[5]. On the other hand, second-order phase transition materials, while having a wider cooling temperature range and smaller magnetic hysteresis, face the drawback of a slightly lower maximum magnetic entropy change, making them less practical for applications[5]. Law et al. [6] have pointed out that ideal magnetocaloric materials may lie in a critical state between first and second-order phase transitions. Therefore, the focus of research in the field of magnetocaloric refrigeration should be on the study of MCE and phase transition control to identify suitable magnetocaloric materials.

This study focuses on modulating the properties of Pr₂Mn₂O₆ through the doping of Mg and Ba atoms. The introduction of Mg and Ba may induce lattice distortions and adjust magnetic interactions, thereby influencing the magnetocaloric effect and phase transitions of Pr₂Mn₂O₆. We anticipate that the results of this study will not only contribute to a deeper understanding of the complex magnetic behavior of Pr₂Mn₂O₆ but also provide new insights for the development of functional materials with superior magnetic properties.

The polycrystalline samples of perovskite manganese oxides Pr_1.5A_0.5Mn₂O₆ (A = Mg, Ba) were prepared using the traditional solid-state reaction method. High-purity (> 99.99%) Pr₆O₁₁, MgO, BaCO₃, and MnO₂ dry solid powder raw materials (from Alfa Aesar, America) were accurately weighed according to stoichiometric ratios. The weighed samples were then thoroughly mixed and ground using a ball mill (QM-QX04, full range planetary ball mill, Nanjing Nanda Instruments Co., Ltd., China) for 6 hours. Subsequently, the well-ground samples were first dried and then subjected to decarbonization treatment at 950°C for 12 hours in a box-type sintering furnace (TM KSL-1700X, Hefei Kejing Materials Technology Co., LTD., China). After a second grinding, the samples were calcined again at a high temperature of 1350°C for 24 hours in the box-type sintering furnace, followed by a controlled cooling from 1350°C to 800°C over 5 hours, and then naturally cooled to room temperature. This process yielded well-formed phase samples of Pr₂Mn₂O₆, Pr_1.5Mg_0.5Mn₂O₆, and Pr_1.5Ba_0.5Mn₂O₆ (hereinafter referred to as Sample-A, Sample-B, and Sample-C, respectively). The samples' crystal structure and phase purity were analyzed using a PANalytical X'Pert Powder X-ray diffractometer. Their magnetization as a function of temperature (M(T)) was assessed in a 0.05 T magnetic field, while magnetization versus magnetic field strength (M(H)) was evaluated over a 0–7 T range using a Quantum Design PPMS-9 multifunctional physical property measurement system.

Figure 1 presents the refined X-ray diffraction spectra of polycrystalline samples. No significant impurity peaks were observed in any of the samples, indicating that they possess good single-phase properties and belong to the orthorhombic crystal system with the space group Pbnm. Table 1 lists the cell parameters and refinement parameters for each sample, obtained after refinement using MDI Jade 6. As can be seen from Table 1, the lattice parameters a, b, and c, as well as the cell volume V, decrease with Mg doping and increase with Ba doping. This is due to the smaller ionic radius of Mg (0.65 Å) compared to Pr (1.13 Å), and the larger ionic radius of Ba (1.49 Å) compared to Pr.

samples	a(Å)	b(Å)	c(Å)	V(Å³)	χ²	R_Bragg
Sample-A	5.471	5.590	7.681	234.920	1.5	9.8
Sample-B	5.470	5.470	7.788	233.090	1.2	9.7
Sample-C	5.506	5.531	7.781	236.990	1.6	9.8

The Fig. 2 illustrates the zero-field (ZFC) and field-cooled (FC) magnetization curves for three samples under an applied magnetic field of 0.05 T, with the inset displaying the dM/dT-T curves. It is observable from the graph that all three samples exhibit paramagnetic behavior at relatively higher temperature ranges. As the temperature decreases, the magnetic nature of the samples transitions from paramagnetic (PM) to ferromagnetic (FM) at their respective T_C (T_{C(Sample−A)} ≈ 91 K, T_{C(Sample−B)} ≈ 77 K, and T_{C(Sample−C)} ≈ 152 K). It is evident that doping with Mg and Ba respectively decreases and increases the magnetization strength and T_C of the samples. The doping with Mg leads to a reduction in the Mn-O-Mn bond angle, which in turn increases the lattice distortion in the samples, weakening the double-exchange interaction between Mn³⁺ and Mn⁴⁺, resulting in a lower T_C and reduced magnetization strength[1]. Conversely, doping with Ba has the opposite effect[8]. Additionally, a distinct bifurcation in the magnetization curves of these samples at low temperatures is observed, which may be attributed to the presence of domain-wall pinning effect[9] or spin reorientation[10] .

We performed measurements to evaluate the effect of magnetic field variability near the T_C on the magnetization of the samples. The M–µ₀H curves were plotted as illustrated in Fig. 3. The data show that above T_C, M increases in a linear fashion with µ₀H, which indicates the presence of an unsaturated paramagnetic state. Below T_C, the plots show a sharp increase in M with µ₀H, tending toward saturation and exhibiting ferromagnetic behavior. The partial saturation that has been observed at low temperatures can be attributed to the competition between antiferromagnetic and ferromagnetic clusters within the sample[11]. In all samples, no significant hysteresis was observed in the M–µ₀H curves below and around T_C, suggesting the possible presence of a magnetic field driven second-order phase transition in the system[12] .

To investigate the magnetocaloric effect of this series of samples, we calculated the isothermal magnetic entropy change (|-ΔS_M|) of the samples using the Maxwell thermodynamic equations, as shown in the following relationship[13] :

$$\begin{array}{c}\left|-{\Delta }{S}_{\text{M}}\right|={\int }_{0}^{{H}_{\text{m}\text{a}\text{x}}}{\left(\frac{\partial M}{\partial T}\right)}_{\text{H}}dH\#（1）\end{array}$$

Figure 4 shows the temperature dependence of the |-ΔS_M| in the sample. The |-ΔS_M| increases with the applied magnetic field. This can be explained by the strengthening of magnetic order with the increase in the external magnetic field. As the magnetic field enhances, the magnetization near the T_C increases, leading to a higher |-ΔS_M| value. Under a 7 T magnetic field, the maximum magnetic entropy changes are approximately |-∆S_M^max|_(Sample−A) ≈ 4.40 J·kg^− 1·K^− 1, |-∆S_M^max|_(Sample−B) ≈ 3.66 J·kg^− 1·K^− 1, and |-∆S_M^max|_(Sample−C) ≈ 3.72 J·kg^− 1·K^− 1. Notably, although the |-∆S_M^max| decreases with Mg and Ba doping, the refrigeration temperature range (FWHM) broadens (FWHM_(Sample−A) ≈ 110 K, FWHM_(Sample−B) ≈ 117 K, FWHM_(Sample−C) ≈ 128 K), suggesting a more continuous phase transition in doped samples. The reduction in |-∆S_M^max| is consistent with the broadening of the FM-PM transition[14] .

From a refrigeration perspective, the Relative Cooling Power (RCP) is a crucial parameter for evaluating the cooling capacity of materials. The equation is as follows[15] :

$$\begin{array}{c}RCP=\left|-\varDelta {S}_{\text{M}}^{\text{m}\text{a}\text{x}}\right|\bullet \left(\varDelta {T}_{\text{F}\text{W}\text{H}\text{M}}\right)\#\left(2\right)\end{array}$$

Herein, ∆T_FWHM denotes the full-width at half-maximum of the |-∆S_M|(T) profile. It is observed that at a magnetic field strength of 7 T, the RCP values are approximately RCP_(Sample−A) ≈ 483.46 J·kg^− 1, RCP_(Sample−B) ≈ 428.22 J·kg^− 1, and RCP_(Sample−C) ≈ 478.88 J·kg^− 1. This demonstrates that the reduction in |-∆S_M^max| due to doping with Mg and Ba surpasses the broadening of the cooling temperature range. Additionally, Table 2 presents the magnetocaloric parameters for PrMnO system refrigeration materials. The findings indicate that Sample-A in this study is more apt as a magnetocaloric refrigerant.

Table 2

Comparison of the magnetocaloric parameters of Sample-A, Sample-B, and Sample-C with some other magnetic refrigerants in magnetic fields of 5 T.
Samples	T_C /K	\|-ΔS_M \|/ J·kg^− 1·K^− 1	RCP/J·kg^− 1	µ₀ΔH/T	Ref
Sample-A	91	4.40	483.46	7	This work
Sample-A	91	3.35	301.85	5	This work
Sample-B	77	3.66	428.22	7	This work
Sample-B	77	2.84	269.35	5	This work
Sample-C	152	3.72	479.88	7	This work
Sample-C	152	3.00	311.53	5	This work
Pr_0.87Ca_0.13MnO₃	-	4.608	460.77	7	[16]
Pr₂CoMnO6	-	1.862	126.62	7	[17]
Pr_0.55Sr_0.45MnO₃	291	1.70	143.60	3	[18]

In addition, the Normalized Refrigeration Capacity (NRC) serves as an alternative metric for the selection of magnetic refrigeration materials. The formula for NRC is[19] :

$$\begin{array}{c}NRC=\frac{1}{{\Delta }{\mu }_{0}H}{\int }_{{T}_{C\text{o}\text{l}\text{d}}}^{{T}_{\text{H}\text{o}\text{t}}}\left|\varDelta {S}_{\text{M}}\left(T\right)\right|dT\#\left(3\right)\end{array}$$

where T_Hot and T_Cold represent the high and low-temperature ends, respectively. As depicted in Fig. 5(a), the plots of the maximum NRC (NRC_max) for temperature intervals of 4 K under external magnetic fields of 2 T and 5 T are shown. It is evident that NRC_max escalates with the increase in ΔT_H−C, the temperature differential between the hot and cold ends. Notably, at 2 T, both Sample-A and Sample-C exhibit enhanced magnetic refrigeration efficiency.

The Temperature-Averaged Entropy Change (TEC) is another indicator used to quantify the MCE of magnetic refrigeration materials within a specific temperature range. It is calculated using the following formula[20] :

$$\begin{array}{c}TEC\left(\varDelta {T}_{\text{H}-\text{C}}\right)=\frac{1}{\varDelta {T}_{\text{H}-\text{C}}}max\left\{{\int }_{{T}_{\text{m}\text{i}\text{d}}-\frac{\varDelta {T}_{\text{H}-\text{C}}}{2}}^{{T}_{\text{m}\text{i}\text{d}}+\frac{\varDelta {T}_{\text{H}-\text{C}}}{2}}\left|\varDelta {S}_{\text{M}}\right|\text{d}T\right\}\#\left(4\right)\end{array}$$

where T_mid represents the average temperature at the midpoint of the entropy change curve, and ΔT_H−C corresponds to the temperature difference between the hot and cold ends. A ΔT_H−C value of 4 K is used in this context. Figure 5(b) illustrates the |-∆S_M^max|(µ₀H) curves and TEC(µ₀H) curves for the series of samples at different magnetic fields. The overlapping nature of the curves for the three samples indicates a good alignment. This suggests that the series of samples can effectively serve as magnetic refrigerants within a working range of 4 K, for instance, in applications like Active Magnetic Regeneration (AMR) cycles[21]. This enables the achievement of performance close to their maximum potential. Similar research results provide favorable references for future exploration of novel magnetic heat materials.

The type of phase transition in a material is generally divided into first- and second-order phase transitions. Therefore, we use Arrott's plot to further identify the type of phase transition in the sample. By the criterion of Banerjee [22], a negative slope or "S" shaped curve in the Arrott plot indicates a first-order phase transition, while a positive slope indicates a second-order phase transition. Figure 6 illustrates that all Arrott curves display positive slopes, indicating that the series of samples experience field-driven second-order phase transitions.

Through the analysis of the relationship between magnetic entropy change and magnetic field, the magnetic ordering of the sample is further examined, with the formula given as follows[23] :

$$\begin{array}{c}n=\frac{\text{d}(\text{l}\text{n}\varDelta {S}_{\text{M}})}{\text{d}\left[\text{ln}\left({\mu }_{0}H\right)\right]}\#\left(5\right)\end{array}$$

Figure 7(a) illustrates the relationship n (T, µ₀H) for this series of samples. It is noteworthy that the spin-ordered states of the sample system increase with the increase in magnetic field, leading to significant variations in the n values under different magnetic fields[24]. Figure 7(b) clearly shows whether the sample exhibits portions exceeding the numerical value "2," as indicated by the black region. This finding serves as a criterion for identifying first-order phase transitions[25]. These results also corroborate the phase transition phenomena observed in the Arrott plot. Additionally, the mean field theory and 3D-Heisenberg theory explain that the minimum value of n at the critical temperature (T = T_C) is projected to be around 0.67 and 0.637[26]. From Fig. 7(a), it can be observed that the minimum values of n for the samples are approximately 0.619, 0.656, and 0.649, respectively. This suggests that Sample-A is close to the 3D-Heisenberg Model, while Sample-B and Sample-C are close to the Mean Field Model.

The critical exponents β, γ, and δ characterizing the second-order phase transition of the samples were determined using the Kouvel-Fisher (K-F) method. The equations are expressed as follows[27] :

$$\begin{array}{c}{M}_{\text{S}}\left(T\right){\left[\text{d}{M}_{\text{S}}\left(T\right)/\text{d}T\right]}^{-1}=\left(T-{T}_{\text{C}}\right)/\beta \#\left(6\right)\end{array}$$

$$\begin{array}{c}{\chi }_{0}^{-1}\left(T\right){\left[\text{d}{\chi }_{0}^{-1}\left(T\right)/\text{d}T\right]}^{-1}=\left(T-{T}_{\text{C}}\right)/\gamma \#\left(7\right)\end{array}$$

$$\begin{array}{c}\delta =1+\left(\gamma /\beta \right)\#\left(8\right)\end{array}$$

where M_S and χ₀ represent spontaneous magnetization and initial susceptibility, respectively. The critical exponents β and γ for this series of samples were determined through M_S(dM_S/dT)⁻¹-T and χ₀⁻¹(dχ₀⁻¹/dT)⁻¹-T as shown in Fig. 8. The slopes of the fitted lines correspond to 1/β and 1/γ. The results indicate that β_(Sample−A) ≈ 0.388 ± 0.005, γ_(Sample−A) ≈ 1.056 ± 0.005, β_(Sample−B) ≈ 0.460 ± 0.005, and γ_(Sample−B) ≈ 1.025 ± 0.005, β_(Sample−C) ≈ 0.435 ± 0.005, and γ_(Sample−C) ≈ 0.940 ± 0.005. Comparing with the critical exponents of different models in Table 3, it can be observed that the critical exponents of Sample-A are close to the theoretical values of the 3D-Heisenberg Model, while Sample-B and Sample-C are closer to the Mean Field Model. This suggests that near the T_C, Sample-A exhibits short-range exchange interactions in the system, while Sample-B and Sample-C demonstrate long-range exchange interactions[28] .

For the doped samples, the β value has increased significantly from 0.39 to 0.46. This implies that Mg and Ba doping contribute to the formation of long-range ferromagnetic order in sample-A. As can be seen in Table 3, we can notice a slight discrepancy in the critical exponents of this series of samples from those of the Mean Field Model and the 3D Heisenberg Model. In the Mean Field Model, spin transitions of Mg and Ba ions at T_C or in hole-poor regions can lead to changes in the β value[29]. Doping and then high temperature annealing in manganese oxides significantly affects the host lattice, changing the magnetic order and the strength of magnetic interactions. Therefore, the inherent inhomogeneity and coexistence of multiple phases in these materials make them non-universal.

Table 3

The values of critical exponents for the samples and the predicted critical exponents of the various theoretical models.
Sample	Method	β	γ	δ	Ref
Mean field Model	-	0.5	1	3	[5]
3D-Heisenberg Model	-	0.365	1.386	4.8	[5]
Tricritical Model	-	0.25	1	5	[5]
Sample-A	K-F	0.388 ± 0.005	1.056 ± 0.005	3.722 ± 0.002	This Work
Sample-B	K-F	0.460 ± 0.005	1.025 ± 0.005	3.228 ± 0.002	This Work
Sample-C	K-F	0.435 ± 0.005	0.940 ± 0.005	3.161 ± 0.003	This Work

The scaling hypothesis states that the magnetic equation of state can be defined through the correlation between M(H,ε), H, and T, expressed as[30] :

$$\begin{array}{c}M\left(H, \epsilon \right)={\epsilon }^{\beta }f\pm \left(H/{\epsilon }^{\beta +\gamma }\right)\#\left(9\right)\end{array}$$

Here, f represents a conventional analytic function, with f₊ and f₋ applicable respectively for T > T_C and T < T_C. ε is the reduced temperature (ε=(T − T_C)/T_C). The rescaled graph of M/|ε|^β is a function of H/|ε|^β+γ, showing two independent branches near T_C[31]. Figure 9 shows the two branches corresponding to T > T_C and T < T_C. The results provide confirmation that the critical parameters are consistent with the scaling hypothesis. In addition, the separate lnM/|ɛ|^β-lnH/|ɛ|^β+γ plot in the inset of Fig. 9 further demonstrates the accuracy of T_C and the critical exponents.

This study successfully prepared polycrystalline samples of Pr₂Mn₂O₆ and Pr_1.5A_0.5Mn₂O₆ (A = Mg, Ba) through high-temperature solid-phase reaction. The influence of Mg and Ba doping on the magnetocaloric effects and critical behavior of these materials was investigated. The results show that the samples exhibit excellent single-phase characteristics in the orthorhombic crystal system (space group Pbnm). Under a 7 T magnetic field, the maximum magnetic entropy change values for the samples are |-∆S_M^max|_(Sample−A) ≈ 4.40 J·kg^− 1·K^− 1, |-∆S_M^max|_{( Sample−B)} ≈ 3.66 J·kg^− 1·K^− 1, and |-∆S_M^max|_{( Sample−C)} ≈ 3.72 J·kg^− 1·K^− 1. The relative cooling powers are RCP_(Sample−A) ≈ 483.46 J·kg^− 1, RCP_(Sample−B) ≈ 428.22 J·kg^− 1, and RCP_(Sample−C) ≈ 479.88 J·kg^− 1, indicating significant magnetic refrigeration potential. The series of samples undergo a second-order phase transition with a small magnetic hysteresis, crucial for magnetic refrigeration applications. Using the Kouvel-Fisher method, a detailed analysis of critical behavior was conducted to determine critical exponents (β, γ, and δ). The results suggest that Sample-B and Sample-C are ferromagnets with a small amount of weakly itinerant electrons, exhibiting long-range exchange interactions near T_C, while Sample-A exhibits short-range exchange interactions near T_C. In summary, the Pr₂Mn₂O₆ ceramics investigated in this study exhibit significant potential as materials for magnetic refrigeration, offering valuable insights for research in magnetic refrigeration technology.

Acknowledgements

This project was supported by the National Natural Science Foundation of China (NSFC) under grant nos.52061035, 51871124, 51561026 and 51401111, Young Leading Talent of “Grassland Talents” Project of Inner Mongolia Autonomous Region, Inner Mongolia Natural Science Cultivating Fund for Distinguished Young Scholars (no. 2020JQ05), Science and Technology Planning Project of Inner Mongolia Autonomous Region (no. 2020GG0267), Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (no. NMGIRT2211), Inner Mongolia University of Technology Key Discipline Team Project of Materials Science (no. ZD202012).

The authors declare no conflict of interest.

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21 Mar, 2024

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Study of the Magnetocaloric Effect and Critical Behavior in Double Perovskite Manganese Oxides Pr 1.5 A 0.5 Mn 2 O 6 (A=Mg, Ba)

Status:

Version 1

Abstract

Figures

1 Introduction

2 Experimental methods

3 Results and analysis

4 Conclusion

Declarations

References

Additional Declarations

Status:

Version 1