# Path sampling for lifetimes of metastable magnetic skyrmions and direct comparison with Kramers' method

## TL;DR

This paper compares Kramers' theory and path sampling methods for calculating the collapse rates of magnetic skyrmions, highlighting the importance of entropic contributions and rate prefactors in complex systems.

## Contribution

It demonstrates the agreement between Kramers' method and forward flux sampling in skyrmion lifetime estimation and emphasizes the significance of entropic effects.

## Key findings

- Good agreement between the two methods.
- Collapse rate varies by three to four orders of magnitude with magnetic field changes.
- Entropic contributions significantly affect skyrmion lifetimes.

## Abstract

We perform a direct comparison between Kramers' method in many dimensions -- i.e., Langer's theory -- adapted to magnetic spin systems, and a path sampling method in the form of forward flux sampling, as a means to compute collapse rates of metastable magnetic skyrmions. We show that a good agreement is obtained between the two methods. We report variations of the attempt frequency associated with skyrmion collapse by three to four orders of magnitude when varying the applied magnetic field by 5$\%$ of the exchange strength, which confirms the existence of a strong entropic contribution to the lifetime of skyrmions. This demonstrates that in complex systems, the knowledge of the rate prefactor, in addition to the internal energy barrier, is essential in order to properly estimate a lifetime.