Critical behavior and the universal curve for magnetocaloric effect in Pr0.6Ca0.1Sr0.3Mn1−xFexO3 (x = 0, 0.05 and 0.075) manganites

• The PM to FM phase transition of our samples is found to be of second-order.
• Critical exponents for our samples are close to the 3D Heisenberg model.
• Widom scaling relation confirms the critical exponent value.

We have investigated the critical behavior of the ferromagnetic Pr0.6Ca0.1Sr0.3Mn1−xFexO3 (x = 0, 0.05 and 0.075) compounds by the data of magnetization measurements. To investigate the nature of the magnetic phase transition, a detailed critical exponent study has been performed. The critical exponents β, γ, and δ determined using the modified Arrott plot (MAP), the Kouvel–Fisher method (KF), as well as the critical isotherm (CI) analysis. With these critical exponents, the experimental M (T, H) relations below and above Curie temperature collapse into two universal branches, fulfilling the single scaling equation m = f±(h), where m and h are renormalized magnetization and field respectively. The estimated critical exponents β (0.361 ⩽ β ⩽ 0.380), γ (1.254 ⩽ γ ⩽ 1.342) and δ (4.30 ⩽ δ ⩽ 4.71) are close to those expected for three-dimensional Heisenberg. Interestingly, for the doped samples the values of γ decreased and approached the 3D-Ising (γ = 1.24). This reflects an existence of ferromagnetic short-range order in our samples. The substitution of Mn by Fe greatly weakens the influence of double exchange (DE) interactions and promotes the antiferromagnetic interactions (AFM). Moreover, the temperature dependence of the exponent n for a different magnetic field is also studied. The values of n obey to the Curie Weiss law above the transition temperature. In particular, n can be related to the critical exponents β, γ and δ   at the magnetic transition from the relation n(TC)=β-1β+γ+1=1+1δ1-1β, where n = 0.624, 0.617 and 0.620. These results confirmed the invalidity of mean field theory. Moreover, rescaled entropy data for all compositions collapses into the same universal curve, revealing universal behavior for the magnetocaloric effect in this series of compounds.