Hybrid Skyrmions in Magnetic Multilayer Thin Films are Half-Integer Hopfions

TL;DR

This paper reveals that hybrid skyrmions in magnetic multilayer thin films are topologically equivalent to half-integer Hopfions, with knotted field lines, explaining their stability and linking their topological charge to surface helicity.

Contribution

It introduces the concept that hybrid skyrmions are half-integer Hopfions with knotted field lines, connecting their topology to experimental surface measurements.

Findings

Hybrid skyrmions are described as half-integer Hopfions.

Their knotted field lines resemble Hopf fibration structures.

Topological charge relates to domain wall helicity at surfaces.

Abstract

Magnetic skyrmions are chiral spin textures which have attracted intense research for their fundamentally novel physics and potential applications as spintronic information carriers. The stability which makes them so potentially useful is a result of their underlying non-trivial topology. While skyrmions were originally predicted and observed in crystalline materials lacking inversion symmetry, some of the most promising host systems for skyrmions are multilayer thin films, where skyrmions have been stabilized at ambient conditions, which is critical for their use in real world devices. The skyrmions found in multilayer thin films have additional three-dimensional structure, with their domain wall helicities twisting through the thickness of the film to create a hybrid skyrmion composed of a Bloch-type core with N\'eel-type caps of opposite chiralities at the surfaces. In this work, we show that this three-dimensional variation creates additional knotted topological structure, providing an explanation for their exceptional stability in ambient conditions. We show that hybrid skyrmions can be described as half-integer Hopfions, and that their field lines have the knotted structure of the Hopf fibration. Furthermore, we show that the topological charge of partially twisted hybrid skyrmions can be related to the domain wall helicity at the surfaces, providing a straightforward way to connect experimental measurements to underlying topology.