Geometry and Symmetry in Skyrmion Dynamics

TL;DR

This paper investigates how the motion of chiral magnetic skyrmions depends on their topological charge and shape, revealing geometric patterns and symmetry effects through simulations and analysis.

Contribution

It introduces a geometric analysis of skyrmion dynamics, showing how symmetry influences velocity distribution and challenging previous assumptions about trivial skyrmion speeds.

Findings

Velocity depends on skyrmion symmetry, forming circles in velocity space.

Low-symmetry skyrmions exhibit a family of velocity circles.

Antiskyrmions can surpass the speed of topologically trivial skyrmions.

Abstract

The uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's equation. In particular, we show that the velocity distribution of topologically non-trivial skyrmions depends on their symmetry: it is a single circle for skyrmions of high symmetry and a family of circles for low-symmetry configurations. We also show that the velocity of the topologically trivial skyrmions, previously believed to be the fastest objects, can be surpassed, for instance, by antiskyrmions. The generality of our approach suggests the validity of our results for exchange frustrated magnets, bubble materials, and others.