Critical behavior and magnetocaloric simulation of La${}_{0.7}$Ba${}_{0.2}$Ca${}_{0.1}$Mn${}_{1-x}$Sn${}_x$O${}_3$ near room temperature

In this article, we focus on the critical behavior of La${}_{0.7}$Ba${}_{0.2}$Ca${}_{0.1}$Mn${}_{1-x}$Sn${}_x$O${}_3$ samples (x = 0.00 and 0.01) around the PM-FM phase transition by measuring the magnetization M (µ${}_0$H) versus magnetic field. The study is based on an iterative process using modified Arrott plots. We then use other techniques to confirm the critical parameters obtained for our manganites, such as the Kouvel-Fisher (KF) method and the critical isotherm (CI) around Tc. Our samples are characterized by a second-order phase transition. The critical parameters determined (β, γ and δ) have no known universal classes. Moreover, Widom's scaling formula δ = 1 + γ/β, demonstrates the accuracy of the critical exponent parameters. In addition, we employ the scaling equation (H, ε) = ε${}^{\beta }$$f_{\pm }$ ($\frac{H}{{\epsilon }^{\beta +\gamma }}$) with ε = (T-T${}_C$)/T${}_C$ to further verify the reasonableness of the critical exponent in which the curves (M-µ0H-T) split into two distinct branches under and over the T${}_C$. Furthermore, the simulated M (H, T) plots were generated to determine the -∆S${}_M$ (T) plots; according to the Gibbs free energy within the obtained critical exponent.