Critical Behavior at Paramagnetic to Ferromagnetic Phase Transition in GdTbHoErLa Rare Earth Alloy

In this paper, we have studied the critical behavior at the paramagnetic ferromagnetic (PM-FM) phase transition (PT) in GdTbHoErLa (GTHEL) alloy. Near the PM-FM PT, the usefulness of the Landau theory leads to generate isothermal magnetizations M(H,T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{M}(\mathrm{H},\mathrm{T})$$\end{document}. Through an iterative program based on the Kouvel–Fisher method, the critical exponents have been optimized. They were found to be γ=1.04\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =1.04$$\end{document} and β=0.82\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta =0.82$$\end{document}. Thus, the exponent at the Curie temperature δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document} was estimated to be 2.27\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2.27$$\end{document}. Moreover, the critical parameters are unambiguous and reasonable, but they are not matching with the conventional universality classes.