Time Reversible Integration of the Landau-Lifshitz-Gilbert Equation

TL;DR

This paper introduces a second-order Suzuki-Trotter integrator for the Landau-Lifshitz-Gilbert equation that significantly improves time-reversibility over traditional methods with comparable computational effort.

Contribution

The paper presents a novel time-reversible integrator based on Suzuki-Trotter decomposition for the Landau-Lifshitz-Gilbert equation, outperforming existing predictor-corrector methods in reversibility.

Findings

Suzuki-Trotter integrator exhibits superior time-reversibility by several orders of magnitude.

Computational effort is comparable to traditional methods.

Useful for calculating backward trajectories in dynamical systems.

Abstract

A method for time-reversible numerical integration of the deterministic Landau-Lifshitz Gilbert equation by means of a second order Suzuki-Trotter decomposition is presented and tested against commonly used second order predictor-corrector methods. We find the time-reversibility of the Suzuki-Trotter integrator to be superior by several orders of magnitude while the computational effort is similar. Calculations of trajectories backwards in time are useful, for example, when evaluating dynamical corrections to transition state theory.