A General Energy Barrier Model for Switching of Exchange Spring Media in an External Field

In this paper, a general energy expression is developed for a cluster of multilayer exchange spring media grains. We expand the rotation of the magnetization vectors to second order in elements of an exponential unitary transformation. The first and second derivatives of the energy are determined and a damped optimization procedure is used to efficiently locate minima and transition states on the potential energy surface. In this method, the interaction of neighboring grains is taken into account and thus the effect of inter-granular exchange on the energy barrier is explicitly taken into consideration. Thus, cluster formation is seen as coherent switching of a group of grains and can be studied as a function of anisotropy and exchange distributions in the media. The lowest energy barrier for a grain or cluster is then used to construct a rate constant. We then determine rate constants for an ensemble of interacting grains from which M-H loops and magnetization decay are simulated as a function of an applied field. Both kinetic Monte Carlo and direct integration of the rate equations are used to study the kinetics of these systems. We find that thermal decay rates have better correlation with energy barriers than with nucleation fields.