On quantifying the topological charge in micromagnetics using a lattice-based approach

TL;DR

This paper presents a lattice-based method for calculating topological skyrmion charge in micromagnetics, demonstrating improved robustness over finite difference methods, especially at finite temperatures and during nucleation and annihilation events.

Contribution

It introduces a lattice-based approach integrated into MuMax3, offering enhanced robustness for topological charge computation in dynamic micromagnetic simulations.

Findings

Lattice-based approach is more accurate at finite temperatures.

It is more robust during nucleation and annihilation processes.

Compared to finite difference methods, it provides better reliability in complex scenarios.

Abstract

An implementation of a lattice-based approach for computing the topological skyrmion charge is provided for the open source micromagnetics code MuMax3. Its accuracy with respect to an existing method based on finite difference derivatives is compared for three different test cases. The lattice-based approach is found to be more robust for finite-temperature dynamics and for nucleation and annihilation processes in extended systems.