Harmonic transition-state theory of thermal spin transitions

Abstract

A rate theory for thermally activated transitions in spin systems is presented. It is based on a transition-state approximation derived from Landau-Lifshitz equations of motion and quadratic expansion of the energy surface at minima and first order saddle points. While the flux out of the initial state vanishes at first order saddle points, the integrated flux over the hyperplanar transition state is nonzero and gives a rate estimate in good agreement with direct dynamical simulations of test systems over a range in damping constant. The preexponential factor obtained for transitions in model systems representing nanoclusters with 3 to 139 transition metal adatoms is on the order of ${10}^{11}$ to ${10}^{13}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, similar to that of atomic rearrangements.