Analysis based on scaling relations of critical behaviour at PM–FM phase transition and universal curve of magnetocaloric effect in selected Ag-doped manganites

The critical behaviour of Pr_0.5Sr_0.5−xAg_xMnO₃ (0 ≤ x ≤ 0.2) samples around the paramagnetic–ferromagnetic phase transition is studied based on isothermal magnetization measurements. The assessments based on Banerjee''s criteria reveal the samples undergoing a second-order magnetic phase transition. Various techniques such as modified Arrott plot, Kouvel–Fisher method, and critical isotherm analysis were used to determine the values of the ferromagnetic transition temperature T_C, as well as the critical exponents of β, γ and δ. The values of critical exponents, derived from the magnetization data using the Kouvel–Fisher method, are found to be (β = 0.43 ± 0.002, 0.363 ± 0.068 and 0.328 ± 0.012), (γ = 1.296 ± 0.007, 1.33 ± 0.0054 and 1.236 ± 0.012) for x = 0.0, 0.1 and 0.2, respectively. This implies that the Pr_0.5Sr_0.5−xAg_xMnO₃ with 0 ≤ x ≤ 0.2 systems does not belong to a single universality class and indicates that the presence of magnetic disorder in the system must be taken into account to fully describe the microscopic interaction of these manganites. With these values, magnetic-field dependences of magnetization at temperatures around T_C can be well described following a single equation of state for our samples. From magnetic entropy change (ΔS_M), it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents using a modified Arrott plot (MAP). We used the scaling hypotheses to scale the magnetic entropy change and heat capacity changes to a universal curve respectively for Pr_0.5Sr_0.5−xAg_xMnO₃ samples.

The universal curves of magnetic entropy changes and heat capacity changes for Pr_0.5Sr_0.5−xAg_xMnO₃ (0 ≤ x ≤ 0.2) are obtained by using the critical exponents.