Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation

TL;DR

This paper introduces the geodesic nudged elastic band (GNEB) method for accurately finding minimum energy paths and activation energies of magnetic transitions, specifically applied to skyrmion and antivortex annihilation in nano-systems.

Contribution

The paper presents the GNEB method, which accounts for magnetic vector orientations and configuration space curvature, improving transition path calculations in magnetic systems.

Findings

Successfully applied GNEB to complex magnetic transitions

Estimated activation energies for skyrmion and antivortex annihilation

Determined antivortex lifetime using harmonic transition state theory

Abstract

A method for finding minimum energy paths of transitions in magnetic systems is presented and used to determine the mechanism and estimate the activation energy of skyrmion and antivortex annihiliation in nano-systems. The path is optimized with respect to orientation of the magnetic vectors while their magnitudes are fixed or obtained from separate calculations. The curvature of the configuration space is taken into account by: (1) using geodesics to evaluate distances and displacements of the system during the optimization, and (2) projecting the path tangent and the magnetic force on the tangent space of the manifold defined by all possible orientations of the magnetic vectors. The method, named geodesic nudged elastic band (GNEB), and its implementation are illustrated with calculations of complex transitions involving annihilation and creation of skyrmion and antivortex states. The lifetime of the latter was determined within harmonic transition state theory using a noncollinear extension of the Alexander-Anderson model.