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

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.

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