Size dependence study of the ordering temperature in the Fast Monte Carlo method

Based on the framework of the Fast Monte Carlo approach, we study the diameter dependence of the ordering temperature in magnetic nanostructures of cylindrical shape. For the purposes of this study, Fe cylindrical-shaped samples of different sizes (20 nm height, 30–100 nm in diameter) have been chosen, and their magnetic properties have been computed as functions of the scaled temperature. Two main set of results are concluded: (a) the ordering temperature of nanostructures follows a linear scaling relationship as a function of the scaling factor x, for all the studied sizes. This finding rules out a scaling relation T′c = x3ηTc (where η is a scaling exponent, and T′c and Tc are the scaled and true ordering temperatures) that has been proposed in the literature, and suggests that temperature should scale linearly with the scaling factor x. (b) For the nanostructures, there are three different order–disorder magnetic transition modes depending on the system’s size, in very good agreement with previous experimental reports.