Nondegenerate and almost hexagonal skyrmion lattices

TL;DR

This paper finds low-energy solutions for skyrmion field equations, revealing nondegenerate vortex structures with an almost hexagonal lattice tendency, and discusses their properties and potential improvements.

Contribution

It introduces new nondegenerate solutions with opposite vortex swirls and predicts a mixed skyrmion lattice structure, advancing understanding of skyrmion arrangements.

Findings

Identified two nondegenerate solutions with opposite vortex directions.

Predicted that a hexagonal skyrmion lattice involves both vortex types.

Discussed methods to improve magnetization norm consistency.

Abstract

We obtain the lowest energy solutions for the skymion field equations and their corresponding vortex structures. Two nondegenerate solutions emerge with their vortex swirls in opposite directions. The solutions are associated with an extremum property, which favors an array of almost hexagonal shape. We predict that a regular hexagonal lattice must have a mix of skyrmions of both swirls. Although our solutions could not keep the norm of the magnetization constant at unity, their greatest deviation from unity occurred in regions where the spins are far from planar; we show how to improve this situation.