A theory on skyrmion size and profile

TL;DR

This paper derives analytical formulas for skyrmion size and wall width based on energy considerations, which match simulations and experiments across various materials, enhancing understanding of skyrmion properties.

Contribution

It provides the first general quantitative expressions for skyrmion size and profile, validated by simulations and experiments, linking theory with practical observations.

Findings

Formulas agree with experimental data across materials

Skyrmion profiles match Walker-like domain wall models

Analytical expressions accurately predict skyrmion characteristics

Abstract

A magnetic skyrmion is a topological object consisting of an inner domain, an outer domain, and a wall that separates the two domains. The skyrmion size and wall width are two fundamental quantities of a skyrmion that depend sensitively on material parameters such as exchange energy, magnetic anisotropy, Dzyaloshinskii-Moriya interaction, and magnetic field. However, there is no quantitative understanding of the two quantities so far. Here, we present general expressions for the skyrmion size and wall width obtained from energy considerations. The two formulas agree almost perfectly with simulations and experiments for a wide range of parameters, including all existing materials that support skyrmions. Furthermore, it is found that skyrmion profiles agree very well with the Walker-like 360\textdegree{} domain wall formula.