Critical behavior and magnetocaloric effect of Pr_1−xCa_xMnO₃

The critical behavior of Pr_1−xCa_xMnO₃ samples with x = 0.25, 0.27, and 0.29 has been investigated. Detailed analyses of magnetic-field dependences of magnetization at temperatures around the paramagnetic-ferromagnetic transition, M(H, T), reveal that the samples undergo a second-order magnetic phase transition. The Arrott plot method predicts the values of critical parameters to be T_C  ≈ 118 K, β = 0.351 ± 0.003, γ = 1.372 ± 0.002, and δ = 4.90 ± 0.02 for x = 0.25; T_C  ≈ 116 K, β = 0.362 ± 0.002, γ = 1.132 ± 0.004, and δ = 4.09 ± 0.03 for x = 0.27; and T_C  ≈ 110 K, β = 0.521 ± 0.002, γ = 0.912 ± 0.005, and δ = 2.71 ± 0.02 for x = 0.29. The values of β = 0.351 (for x = 0.25) and β = 0.362 (for x = 0.27) are close to the value β = 0.365 expected for the 3D Heisenberg model, proving an existence of short-range ferromagnetic interactions in these samples. A slight increase in Ca-doping content (x = 0.29) leads to the shift of the β value (=0.521) towards that of the mean-field theory (with β = 0.5) characteristic of long-range ferromagnetic interactions. The samples also exhibit a magnetocaloric effect: around T_C of Pr_1−xCa_xMnO₃ compounds, magnetic-entropy change reaches the maximum values of about 5.0, 4.1, and 2.5 J kg⁻¹ K⁻¹ for x = 0.25, 0.27, and 0.29, respectively, under an applied-field change of 50 kOe. Magnetic-field dependences of the maximum magnetic-entropy change (ΔS_max) obey a power law |ΔS_max(H)| ∝ Hⁿ, where exponent values n = 0.68–0.74 are close to those obtained from the theoretical relation n = 1 + (β − 1)/(β + γ).