# The profile of chiral skyrmions of small radius

## TL;DR

This paper derives exact formulas for the profile and radius of small-radius chiral skyrmions in ferromagnets with Dzyaloshinskii-Moriya interaction, revealing their length scales and core structure.

## Contribution

It provides analytical solutions for skyrmion profiles in the small DM parameter limit, linking core structure to the Belavin-Polyakov solution.

## Key findings

- Exact formulas for skyrmion profiles and radius
- Identification of multiple length scales in skyrmions
- Skyrmions evolve from Belavin-Polyakov solutions as DM parameter increases

## Abstract

Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulas for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively large anisotropy). The matching of these two fields leads to a formula for the skyrmion radius as a function of the DM parameter. The derived solutions show the different length scales which are present in the skyrmion profiles. The picture is thus created of a chiral skyrmion that is born out of a Belavin-Polyakov solution with an infinitesimally small radius, as the DM parameter is increased from zero. The skyrmion retains the Belavin-Polyakov profile over and well-beyond the core before it assumes an exponential decay; the profile of an axially-symmetric Belavin-Polyakov solution of unit degree plays the role of the universal core profile of chiral skyrmions.