The phase purity and crystal structure of the samples are characterized by using the Rietveld refinement of room temperature X-ray diffraction data. Figure 1(a, b) show the Rietveld refined XRD pattern and the polyhedral crystal structure of the ENMO, GNMO, and TNMO sample, respectively. These diffraction patterns shows that all the studied compositions were crystallized in the monoclinic crystal system with space group P21/n. The structural parameters are refined by Rietveld’s profile fitting method by using the TOPAS program24. The refinement parameters such as lattice parameters, bond length, the goodness of fit (χ2), and bond angle of the studied compounds given in Table 1. It is seen that cell volume and crystal density increases with an increase in an atomic number of rare earth elements but the volume decreases. The crystal structure of GNMO is heavily tilted (β = 124°), as compared to ENMO and TNMO (β = ~ 90°).
Table 1
Structural parameters for ENMO, GNMO, and TNMO from the Rietveld refinement.
|
|
Eu2NiMnO6
|
Gd2NiMnO6
|
Tb2NiMnO6
|
Space Group
|
|
P21/n
|
P21/n
|
P21/n
|
Cell Mass (g/mol)
|
|
1027.11
|
1048.26
|
1054.96
|
Cell Volume (Å3)
|
|
222.86
|
221.56
|
219.58
|
Crystal Density (g/cm3)
|
7.653
|
7.857
|
7.978
|
Lattice Parameters:
|
a (Å)
|
5.3206
|
5.2915
|
5.2706
|
|
b (Å)
|
5.5251
|
5.4103
|
5.5358
|
|
c (Å)
|
7.5811
|
9.2220
|
7.5261
|
|
β (°)
|
90.003
|
124.976
|
90.158
|
Rexp
|
|
4.97
|
4.43
|
4.30
|
Rwp
|
|
9.40
|
6.25
|
8.05
|
GoF
|
|
1.89
|
1.41
|
1.87
|
Bond length (Å):
|
Ni – O
|
1.9961
|
2.0781
|
1.8256
|
|
Mn – O
|
1.9481
|
1.9120
|
2.0444
|
Bond angle (°)
|
Ni – O – Mn
|
161.84
|
153.07
|
147.30
|
The X-ray photoemission spectroscopy (XPS) technique is used to understand the chemical oxidation states and the ligand coordination of a system. The oxidation state analysis of manganese (Mn) in ENMO, GNMO, and TNMO samples have been performed and Fig. 2 (a, b, c) represents the XPS spectra for Mn2p. The spectra have been fitted with Shirley background subtraction. The deconvoluted XPS peak of Mn 2p3/2 splits into two peaks at the binding energy 641.2 eV and 643.2 eV which correspond to Mn4+ and Mn3+, respectively25. The ratio of Mn4+/Mn3+ for ENMO, GNMO, and TNMO is found to be 1.02, 0.76, and 1.64 respectively, indicating the presence of Mn4+ is more in the case of ENMO and TNMO while in the case of GNMO, Mn3+ is higher. The ratio of Mn4+/Mn3+ shows the change in surface oxidation state caused by different A-site rare earth elements having different ionic radii. This clearly indicate the superexchange mechanisms of Ni2+-O-Mn3+ and Ni2+ – O – Mn4+ in the studied compounds are different.
Figure 3 (a) shows field-cooled (FC) temperature-dependent magnetization curves of ENMO, GNMO, and TNMO samples measured with an applied magnetic field of 100 Oe between 2-300 K. It is clearly seen that, with increasing the temperature, the magnetization in the samples decreased because of the magnetic phase transition temperature from ferromagnetic state to paramagnetic state. The studied samples show the same behavior which confirms the ferromagnetic to paramagnetic phase transition due to well-known superexchange exchange phenomena. The temperature dependences of dM/dT for all samples are shown in the inset to determine the Curie temperature (Tc). It is defined that the minima in the dM/dT curve, and curie temperatures for ENMO, GNMO and TNMO samples are found to be 142, 130, and 112 K, respectively. It is seen that with a decrease in rare earth size Eu3+ (0.947 Å) > Gd3+(0.938 Å) > Tb3+(0.923 Å), the TC shifts to lower temperature gradually which is probably due to the decreases of the Ni – O – Mn bond angle [161.84 (Eu), 153.07 (Gd), and 147.30 (Tb)]26. The temperature dependent inverse susceptibility χ−1(T) has been demonstrated in Fig. 3 (b, c, d). The linear fitting of the experimental χ−1(T) curve with the Curie-Weiss (C-W) law \(\chi =\frac{C}{T-\theta }\) in the paramagnetic region, where C is the Curie constant, and θ corresponds to paramagnetic Curie-Weiss temperature. The calculated values of effective magnetic are 8.6, 12.4, 15.1 µB/f.u. for ENMO, GNMO, and TNMO, respectively, which are comparable with the corresponding theoretical values 7.0, 12.2, 14.6 µB/f.u. The difference in the theoretical and calculated effective magnetic moment is associated with the amount of Mn3+ and Mn4+ present in the compound. The positive values of Curie-Weiss temperature for studied DPs confirms the second-order magnetic phase transition. The Curie- Weiss fitting also shows that how evolution of Griffith phase with smaller ionic size of Eu, Gd, and Tb in double perovskite.
To investigate the magnetocaloric properties, the isothermal magnetization (MH) curves at different temperatures were measured before and after the TC. The temperature interval ΔT = 3 K near to TC, and ΔT = 5 K, rest of the region were kept constant. Figure 4 (a, b, c) shows isothermal magnetization of ENMO, GNMO, and TNMO samples in a magnetic field range from 0–5 T. The MH curves depicts that at lower magnetic field region, the MH curves rise rapidly and afterward with increasing magnetic field MH curves try to saturate, and this phenomenon is associated with ferromagnetic behavior of magnetic materials. The MH curves at higher temperatures region show linear behavior which confirms the paramagnetic nature of samples, and this is due to thermal agitation which disorients the magnetic moments at higher temperature. To know the order of magnetic phase transition, well-known Arrott plots (M2 vs H/M) were analyzed, and which are deduced from the magnetic isotherms given in Fig. 4 (d, e, f). Banerjee’s criterion, suggest that the slope of Arrott plots is important to know the type of magnetic phase transition. The negative slope corresponds to the first-order phase transition undergoes into the sample while positive slope confirms second-order phase transition27. It is seen that positive slope observed in the Arrott plot at all temperatures for studied samples. Therefore, we can confirm that ferromagnetic–paramagnetic transition is consistent of second-order type. The order of degree of the magnetic domains, variation of lattice volume and latent heat of phase transformation are extremely small in case of second order phase transition. It might be one of the reasons that the magnetic entropy changes of second-order phase transition materials smaller than that of first-order phase transition materials.
The magnetic entropy change determined by using the isothermal magnetization data, shown in Fig. 4, and which is initiated by the changing the applied magnetic field from 0 to H is determined by using the well-known Maxwell thermodynamic correlation, which is given by the equation,
Where, ΔS is the entropy change, dH is the change in the applied magnetic field, M is the magnetization and T is the temperature.
Figure 5 (a, b, c) shows the temperature dependence of magnetic entropy curves (– ΔSM) under different applied field changes ranging between 0 and 5 T for ENMO, GNMO, and TNMO. The maximum value of – ΔSM is found to be around the magnetic phase transition temperature. All these samples show similar behavior, – ΔSM value reaches a maximum near the Curie temperature (TC) at low applied fields and it increases with increasing H which may be due to the improvement of FM interactions. The calculated – ΔSM are 3.2, 3.8, and 3.5 J/kgK at ΔH = 5 T for ENMO, GNMO, and TNMO samples, respectively. Rawat et al. The MCE properties of nanocrystalline Pr2CoMnO6 DPs prepared by sol-gel with an average particle size of 192 nm, found to be – ΔSM = 1.98 J/kgK at the field change of 5 T and relative cooling power (RCP) was calculated to be 110 J/kg28. The MCE properties in Eu2NiMnO6 and Dy2NiMnO6 was reported by Su et al. The maximum value of magnetic entropy change – ΔSM reaches 4.0 J/kg K for Eu2NiMnO6 and 5.2 J/kg K for Dy2NiMnO6 for a field change of 0–7 T, respectively23. Chakraborty et al.22 reported MCE value for Ho2NiMnO6 is 6.2 J/kg K and for Tb2NiMnO6 is 4.1 J/kg K with ΔH = 5 T. From this study and literature, one interesting observation to be noted that as ionic radii of rare earth elements decrease in double perovskite there is the evolution of Griffith phase. From Fig. 3 (b, c, d) we can observe that inverse susceptibility does not obey the Curie–Weiss law for all samples, this is due to Griffith phase present in the GNMO and TNMO samples.
To know the effectiveness of MCE material, another an important parameter is measuring the cooling efficiency of the materials called relative cooling power (RCP). It is defined as, an amount of heat transferred between temperatures corresponding to the full width at half maximum of magnetic entropy curve, and it can be evaluated by following equation.
The RCP values are 150, 182, 176 J/kg for ENMO, GNMO, and TNMO samples, respectively. The comparison of transition temperature, maximum entropy change, and RCP values have been summarized in Table 2 for the studied double perovskite and other reported double perovskite compounds. The – ΔSM and RCP values for ENMO, GNMO, and TNMO does not show considerable change with different rare earth elements in double perovskite, change in Curie temperature (TC) observed. From Table 2, we can notice that the MCE parameters for studied DPs compounds are comparable with other DPs as well as other MCE materials, indicating ENMO, GNMO, and TNMO compounds are also considerable for magnetic cooling applications. The comparative study shows the Curie temperature and RCP behavior with decreasing ionic radii of the rare earth element in Ln2NiMnO6 double perovskite. Expecting a change in MCE properties with different rare earth element having different ionic radii in A2BB’O6 double perovskite is not much feasible, because of phase transition in double perovskite is associated with M2+ – O – Mn4+ superexchange interaction but playing with working temperature this could be one of tool to tune the Curie temperature.
Table 2
Comparison of – ΔSM and RCP values for the R2NiMnO6 (R = Eu, Gd, Tb, Dy, Ho, Er) sample.
Compound
|
Tc
(K)
|
ΔH
(T)
|
– ΔSM
(J/kgK)
|
RCP
(J/kg)
|
Ref.
|
Eu2NiMnO6
|
143
|
5
|
3.2
|
150
|
Present
|
Gd2NiMnO6
|
130
|
5
|
3.7
|
182
|
Present
|
Tb2NiMnO6
|
112
|
5
|
3.5
|
176
|
Present
|
Dy2NiMnO6
|
101
|
5
|
3.4
|
175
|
19
|
Ho2NiMnO6
|
93
|
5
|
3.7
|
194
|
19
|
Er2NiMnO6
|
84
|
5
|
3.4
|
169
|
19
|