A robust theory of thermal activation in magnetic systems with Gilbert damping

TL;DR

This paper derives a general formula for thermally activated transition rates in multi-dimensional magnetic systems with Gilbert damping, extending the harmonic theory of Langer and providing insights into the Arrhenius law prefactor.

Contribution

It introduces a new activation rate expression for multi-dimensional spin systems that accounts for Gilbert damping and applies to coherent spin reorientation, expanding theoretical understanding.

Findings

The activation rate depends on the Gilbert damping parameter, α.

The derived expression is valid for small α (α ≪ 1).

For finite antiferromagnetic chains, the activation barrier scales exponentially with system size.

Abstract

Magnetic systems can exhibit thermally activated transitions whose timescales are often described by an Arrhenius law. However, robust predictions of such timescales are only available for certain cases. Inspired by the harmonic theory of Langer, we derive a general activation rate for multi-dimensional spin systems. Assuming local thermal equilibrium in the initial minimum and deriving an expression for the flow of probability density along the real unstable dynamical mode at the saddle point, we obtain the expression for the activation rate that is a function of the Gilbert damping parameter, $\alpha$. We find that this expression remains valid for the physically relevant regime of $\alpha\ll1$. When the activation is characterized by a coherent reorientation of all spins, we gain insight into the prefactor of the Arrhenius law by writing it in terms of spin wave frequencies and, for the case of a finite antiferromagnetic spin chain, obtain an expression that depends exponentially on the square of the system size indicating a break-down of the Meyer-Neldel rule.