What makes magnetic skyrmions different from magnetic bubbles ?

TL;DR

This paper develops a theoretical framework to distinguish magnetic skyrmions from magnetic bubbles, revealing differences rooted in the in-plane phase of magnetization textures and the influence of magnetic anisotropy.

Contribution

The paper introduces a complex calculus-based theory to differentiate magnetic skyrmions from bubbles, emphasizing the role of in-plane phase and anisotropy in their properties.

Findings

Magnetic skyrmions and bubbles can have the same topological charge but differ in in-plane phase.

Magnetic anisotropy influences whether textures exhibit classical-like or quantum-like features.

Theoretical distinctions are established using complex calculus to analyze magnetization textures.

Abstract

A large enough piece of ferromagnet is usually not magnetized uniformly, but develops a magnetization texture. In thin films these textures can be doubly-periodic. Such are the well known magnetic bubble domains and the recently observed "skyrmion" magnetization textures in MnSi. In this paper we develop a theory of periodic magnetization textures, based on complex calculus to answer the question -- is there a difference between those two textures even if they seem to carry the same topological winding number (or topological charge) ? We find that such difference exists, facilitated by a different role played by the magnetization vector's in-plane phase. We separate classical-like and quantum-like features of magnetization textures and highlight the role of magnetic anisotropy in favouring either of these cases.