Nonlinear Transport, Dynamic Ordering, and Clustering for Driven Skyrmions on Random Pinning

TL;DR

This study uses numerical simulations to explore the complex nonlinear dynamics, ordering, and clustering behaviors of driven skyrmions over random pinning, revealing transitions from elastic to plastic depinning and the influence of Magnus force.

Contribution

It provides new insights into how skyrmion dynamics change with pinning strength and Magnus force, including the discovery of phase separation and nonlinear velocity responses.

Findings

Elastic depinning retains sixfold order at weak pinning.

Transition to plastic depinning involves topological defects.

Magnus force induces clustering and negative differential conductivity.

Abstract

Using numerical simulations, we examine the nonlinear dynamics of skyrmions driven over random pinning. For weak pinning, the skyrmions depin elastically, retaining sixfold ordering; however, at the onset of motion there is a dip in the magnitude of the structure factor peaks due to a decrease in positional ordering, indicating that the depinning transition can be detected using the structure factor even within the elastic depinning regime. At higher drives the moving skyrmion lattice regains full ordering. For increasing pinning strength, we find a transition from elastic to plastic depinning that is accompanied by a sharp increase in the depinning threshold due to the proliferation of topological defects, similar to the peak effect found at the elastic to plastic depinning transition in superconducting vortex systems. For strong pinning and strong Magnus force, the skyrmions in the moving phase can form a strongly clustered or phase separated state with highly modulated skyrmion density, similar to that recently observed in continuum-based simulations for strong disorder. As the Magnus force is decreased, the density phase separated state crosses over to a dynamically phase separated state with uniform density but with flow localized in bands of motion, while in the strongly damped limit, both types of phase separated states are lost. In the strong pinning limit, we find highly nonlinear velocity-force curves in the transverse and longitudinal directions, along with distinct regions of negative differential conductivity in the plastic flow regime. The negative differential conductivity is absent in the overdamped limit. The Magnus force is responsible for both the negative differential conductivity and the clustering effects, since it causes faster moving skyrmions to partially rotate around slower moving or pinned skyrmions.