Critical behavior study near the paramagnetic to ferromagnetic phase transition temperature in Pr0.6−xErxCa0.1Sr0.3MnO3 (x = 0, 0.02 and 0.06) manganites

Abstract

The aim of the present work is to study the critical behavior of Pr_0.6−xEr_xCa_0.1Sr_0.3MnO₃ (x = 0, 0.02 and 0.06) manganites, synthetized by the conventional solid-state reaction method, around the paramagnetic (PM)–ferromagnetic (FM) phase transition. The critical behavior is investigated through various techniques such as the modified Arrott plots, Kouvel–Fisher method, and critical isotherm analysis. The experimental results have revealed that our samples exhibit a second-order magnetic phase transition and the critical exponents β and γ are consistent with the prediction of the 3D-Ising model for x = 0 and x = 0.02, while, the estimated critical exponents of x = 0.06 are close to those found by the 3D-Heisenberg model. This proves the existence of a short-range ferromagnetic order in all our samples. The third exponent δ was determined independently from the critical magnetization isotherm satisfying the Widom scaling relationship for all our compounds. The validity of the calculated critical exponents using the various methods has been confirmed by the scaling equation of state. The obtained critical exponents are found to follow the scaling equation with the magnetization data scaled into two different curves below and above T_C.