Symmetry Analysis and Dynamic Equilibrium in Travelling Skyrmions

Magnetic skyrmions provide a promising avenue for novel spintronic computing applications, due to the possibility of efficient motion in ferromagnetic materials driven by electrical current via spin-orbit torque (SOT). However, structural expansions and eventual breakdown of their structure have been observed in traveling skyrmions. This gives rise to a separation between a regime of stable steady-state motion, and an unstable regime. However, existing explanations of these mechanisms are mostly based on modeling studies with a limited range of material and operating parameters, as well as experimental techniques, which do not provide the same level of microscopic transparency of the spin structure. Through a detailed micromagnetic modeling study of SOT motion of ferromagnetic skyrmions we examine their dynamic distortions in the context of steady-state dynamic equilibrium, both in the global - center-of-mass directed motion, and local scale - structural deformations to compensate for the local Thiele-based forces. We show that the local dynamic equilibrium necessitates a shift of the skyrmion locus (center) point. This is demonstrated with a combined analytical-numerical approach based on an elastic expansion model from skyrmion energy expressions. These results not only expand the understanding of the fundamental properties of magnetic skyrmions, but also pave the way for their potential use in spintronic applications.