Law of Approach to Saturation in Mn–Zn Ferrite Nanoparticles

In this paper, the law of approach to saturation (LAS) was applied to a series of Mn–Zn ferrite nanoparticles with compositional formula Mn1−xZnxFe2O4 where x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5 to study the dependence of magnetization, M, on the applied magnetic field, H. Using the statistical parameters, the field range was chosen. The dependence of magnetization on the applied field was studied based upon the output of the statistical parameters for the curve fitted using different forms of LAS, namely, M=Ms1−aH−bH2+kH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M=M_{s}\left [ 1-\frac {a}{H}-\frac {b}{H^{2}} \right ]+kH$\end{document}, M=Ms1−aH−bH2,M=Ms1−bH2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M=M_{s}\left [ 1-\frac {a}{H}-\frac {b}{H^{2}} \right ], M=M_{s}\left [ 1-\frac {b}{H^{2}} \right ]$\end{document} and M=Ms1−115HA2H12H32+HR32+kH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ M=M_{s}\left (1- \frac {1}{15}\frac {{H_{A}^{2}}}{H^{\frac {1}{2}}\left (H^{\frac {3}{2}}+H_{R}^{\frac {3}{2}} \right )} \right )+k H$\end{document}. A critical examination on the output parameters resulted from fitting into different equations, indicates the dependency of magnetization on the applied field as a characteristic of the composition of Mn–Zn ferrites. The statistical parameters, along with physically meaningful fitted parameters, provide knowledge on dependency of magnetization of different compositions of Mn–Zn ferrites over different regions of applied field.