Stable and fast semi-implicit integration of the stochastic Landau-Lifshitz equation

TL;DR

This paper introduces semi-implicit numerical methods for the stochastic Landau-Lifshitz equation that conserve angular momentum, offering improved stability and efficiency for spin dynamics simulations.

Contribution

The paper presents novel semi-implicit integrators that enhance stability and computational efficiency while conserving angular momentum in stochastic spin dynamics.

Findings

Better stability with larger time steps compared to explicit methods

Comparable accuracy to midpoint implicit methods

Reduced computational cost for simulations

Abstract

We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For this system, our schemes show better stability properties and allow us to use considerably larger time steps than standard explicit methods. At the same time, these semi-implicit schemes are also of comparable accuracy to and computationally much cheaper than the standard midpoint implicit method. The results are of key importance for atomistic spin dynamics simulations and the study of spin dynamics beyond the macro spin approximation.