A theory on skyrmion size

TLDR

A magnetic skyrmion is a topological object whose size and wall width depend on material parameters such as exchange energy, anisotropy, Dzyaloshinskii‑Moriya interaction, and magnetic field, yet no quantitative description of these quantities has been established. The study aims to derive general expressions for skyrmion size and wall width from energy considerations. These expressions are obtained by analytically minimizing the skyrmion energy with respect to its radius and wall width, yielding closed‑form formulas. The resulting formulas agree almost perfectly with simulations and experiments across a wide range of materials and parameters, and the skyrmion profiles closely follow the Walker‑like 360° domain wall solution.

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.