Topological dynamics and current-induced motion in a skyrmion lattice

TL;DR

This paper analyzes the dynamics of skyrmion lattices under current using the Thiele equation, revealing unique topological effects and pinning behaviors crucial for data storage applications.

Contribution

It introduces soluble models of pinning potential in the Thiele equation, highlighting the topological effects on skyrmion motion and identifying pinning thresholds and trajectories.

Findings

Pinning threshold velocity identified for 1D potential

Skyrmion trajectories in 2D potential are spirals towards a pinning point

Frequency and amplitude decay depend on Gilbert constant and potential

Abstract

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele's equation resembles Newton's law but in virtue of the topological character of the first two, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skykrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional potential and for a two-dimensional potential we find a pinning point and the skyrmion trajectories toward the point are spirals whose frequency (compare Kepler's second law) and amplitude decay depends only on the Gilbert constant and potential at the pinning point.