Shape of a skyrmion

TL;DR

This paper introduces a novel method to determine the shape of two-dimensional magnetic skyrmions using eigenfunction expansion and variational calculations, validated by lattice simulations and applied to complex skyrmion interactions.

Contribution

It presents a new eigenfunction-based approach for analyzing skyrmion shapes and extends it to dissipative dynamics and multi-skyrmion systems.

Findings

Eigenfunction expansion accurately models skyrmion shape.

Variational calculations match lattice simulation results.

Method applicable to skyrmion interactions and dynamics.

Abstract

We propose a method of determining the shape of a two-dimensional magnetic skyrmion, which can be parameterized as the position dependence of the orientation of the local magnetic moment, by using the expansion in terms of the eigenfunctions of the Schr\"{o}dinger equation of a harmonic oscillator. A variational calculation is done, up to the next-to-next-to-leading order. This result is verified by a lattice simulation based on Landau-Lifshitz-Gilbert equation. Our method is also applied to the dissipative matrix in the Thiele equation as well as two interacting skyrmions in a bilayer system.