Commensurability between element symmetry and the number of skyrmions governing skyrmion diffusion in confined geometries

TL;DR

This paper investigates how the diffusion of magnetic skyrmions in confined geometries depends on the relationship between skyrmion number and the shape of the confinement, revealing a key role of commensurability.

Contribution

It demonstrates that skyrmion diffusion in confined geometries is governed by the interplay between skyrmion number and geometry, highlighting the importance of commensurability effects.

Findings

Diffusion behavior differs significantly between circular and triangular confinements.

In triangular geometries, commensurate skyrmion numbers lead to distinct diffusion dynamics.

Simulations support the experimental findings, emphasizing the role of element symmetry and skyrmion count.

Abstract

Magnetic skyrmions are topological magnetic structures, which exhibit quasi-particle properties and can show enhanced stability against perturbation from thermal noise. Recently, thermal Brownian diffusion of these quasi-particles has been found in continuous films and applications in unconventional computing have received significant attention, which however require structured elements. Thus, as the next necessary step, we here study skyrmion diffusion in confined geometries and find it to be qualitatively different: The diffusion is governed by the interplay between the total number of skyrmions and the structure geometry. In particular, we ascertain the effect of circular and triangular geometrical confinement and find that for triangular geometries the behavior is drastically different for the cases when the number of skyrmions in the element is either commensurate or incommensurate with a symmetric filling of the element. This influence of commensurability is corroborated by simulations of a quasi-particle model.