Lifetime of skyrmions in discrete systems with infinitesimal lattice constant

TL;DR

This study examines the stability and lifetime of magnetic skyrmions in discrete lattice systems as the lattice constant approaches zero, revealing conditions for thermally stable skyrmions at room temperature.

Contribution

It provides a detailed analysis of skyrmion lifetime in discrete systems with infinitesimal lattice constant, connecting lattice models to continuous micromagnetic descriptions.

Findings

Energy barrier approaches the Belavin-Polyakov bound as lattice constant decreases.

Entropy contribution stabilizes, leading to thermally stable skyrmions at room temperature.

Skyrmion lifetime can be significant even without dipole-dipole interactions.

Abstract

Topological protection of chiral magnetic structures is investigated by taking a two-dimensional magnetic skyrmion as an example. The skyrmion lifetime is calculated based on harmonic transition state theory for a discrete lattice model using various values of the ratio of the lattice constant and the skyrmion size. Parameters of the system corresponding to exchange, anisotropy and Dzyaloshinsky-Moriya interaction are chosen in such a way as to keep the energy and size of the skyrmion unchanged for small values of the lattice constant, using scaling relations derived from continuous micromagnetic description. The number of magnetic moments included in the calculations reaches more than a million. The results indicate that in the limit of infinitesimal lattice constant, the energy barrier for skyrmion collapse approaches the Belavin-Polyakov lower bound of the energy of a topological soliton in the $\sigma$-model, the entropy contribution to the pre-exponential factor in the Arrhenius rate expression for collapse approaches a constant and the skyrmion lifetime can, for large enough number of spins, correspond to thermally stable skyrmion at room temperature even without magnetic dipole-dipole interaction.