The lifetime of micron scale topological chiral magnetic states with atomic resolution

TL;DR

This paper introduces a novel numerical method to compute the lifetimes of micron-scale topological magnetic states with atomic resolution, enabling analysis of large systems previously infeasible with standard techniques.

Contribution

A new recursive algorithm for calculating determinants of the Hessian matrix in harmonic transition state theory for large magnetic systems is proposed.

Findings

Successfully computed lifetimes of 2D and 3D skyrmionic structures.

Demonstrated the method's ability to handle systems with millions of magnetic moments.

Validated the approach with accuracy in topological magnetic state analysis.

Abstract

A new method for the numerical computation of the lifetimes of magnetic states within harmonic transition state theory (HTST) has been developed. In the simplest case, the system is described by a Heisenberg-like Hamiltonian with short-range interaction. Calculations are performed in Cartesian coordinates. Constraints on the values of magnetic moments are taken into account using Lagrange multipliers. The pre-exponential factor in the Arrhenius law in HTST is written in terms of the determinants of the Hessian of energy at the minima and saddle points on the multidimensional energy surface. An algorithm for calculating these determinants without searching for eigenvalues of the Hessian but using recursive relations is proposed. The method allows calculating determinants for systems containing millions of magnetic moments. This makes it possible to calculate the pre-exponential factor and estimate the lifetimes of micron-scale topological structures with atomic resolution, which until now has been impossible using standard approaches. The accuracy of the method is demonstrated by calculating 2D and 3D skyrmionic structures.