Decomposition of modified Landau-Lifshitz-Gilbert equation and corresponding analytic solutions

TL;DR

This paper introduces a decomposition method for the modified Landau-Lifshitz-Gilbert equation, enabling exact solutions for parts of the equation and facilitating accurate spin dynamics simulations with minimal numerical errors.

Contribution

It develops a novel decomposition approach for the modified Landau-Lifshitz-Gilbert equation, allowing exact solutions of its components for improved spin system simulations.

Findings

Parts of the decomposed equation can be solved exactly.

The method enables simulations with small numerical errors.

Applicable to various spin dynamics systems.

Abstract

The Suzuki-Trotter decomposition in general allows one to divide the equation of motion of a dynamical system into smaller parts whose integration are easier than the original equation. In this study, we first rewrite by employing feasible approximations the modified Landau-Lifshitz-Gilbert equation for localized spins in a suitable form for simulations using the Suzuki-Trotter decomposition. Next we decompose the equation into parts and demonstrate that the parts are classified into three groups, each of which can be solved exactly. Since the modified Landau-Lifshitz-Gilbert equation from which we start is in rather a general form, simulations of spin dynamics in various systems accompanying only small numerical errors are possible.