Topological constraints on positions of magnetic solitons in multiply-connected planar magnetic nano-elements

TL;DR

This paper explores how the topology of magnetic textures like Skyrmions interacts with the topology of nano-elements, revealing unique constraints in multiply-connected structures such as magnetic rings.

Contribution

It establishes new topological constraints linking magnetization textures and nano-element connectivity, with specific results for ring-shaped magnetic structures.

Findings

Derived constraints for vortex and antivortex positions in ring magnets

Validated theoretical constraints with experimental data on vortex domain walls

Identified topological effects absent in simply-connected magnetic elements

Abstract

Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of the element itself (its connectivity). We establish the existence of a set of constraints, coupling these topologies, which are specific for multiply connected elements and are absent in simply-connected case. As an example, a specific constraint is derived for a case of planar ring magnet, relating the angular positions of magnetic vortices and antivortices inside. We analyze the recent experimental data on the vortex magnetic domain walls in the ring to validate our findings.