The Kibble-Zurek Scenario and Coarsening Across Nonequilibrium Phase Transitions in Driven Vortices and Skyrmions

TL;DR

This study explores how topological defects in driven vortices and skyrmions evolve during nonequilibrium phase transitions, revealing different scaling behaviors and coarsening dynamics influenced by the Magnus force and defect mobility.

Contribution

It demonstrates distinct Kibble-Zurek scaling exponents for vortices and skyrmions and links defect mobility to coarsening behavior in nonequilibrium transitions.

Findings

Vortices exhibit directed percolation scaling during ordering.

Skyrmions show coarsening with different scaling exponents.

Defect populations decrease as a power law during coarsening.

Abstract

We investigate the topological defect populations for superconducting vortices and magnetic skyrmions on random pinning substrates under driving amplitudes that are swept at different rates or suddenly quenched. When the substrate pinning is sufficiently strong, the system exhibits a nonequilibrium phase transition at a critical drive into a more topologically ordered state. We examine the number of topological defects that remain as we cross the ordering transition at different rates. In the vortex case, the system dynamically orders into a moving smectic, and the Kibble-Zurek scaling hypothesis gives exponents consistent with directed percolation. Due to their strong Magnus force, the skyrmions dynamically order into an isotropic crystal, producing different Kibble-Zurek scaling exponents that are more consistent with coarsening. We argue that in the skyrmion crystal, the topological defects can both climb and glide, facilitating coarsening, whereas in the vortex smectic state, the defects cannot climb and coarsening is suppressed. We also examine pulsed driving across the ordering transition and find that the defect population on the ordered side of the transition decreases with time as a power law, indicating that coarsening can occur across nonequilibrium phase transitions. Our results should be general to a wide class of nonequilibrium systems driven over random disorder where there are well-defined topological defects.