Two levels of topology in skyrmion lattice dynamics

Skyrmions are localized, topological spin structures that can be described as quasiparticles. Skyrmions in thin films are an ideal model system to study Brownian motion and lattice formation in two dimensions. They follow an equation of motion, the Thiele equation, which includes a topology-dependent chiral term, linear in velocity, causing a skyrmion Hall effect and a drastic reduction of the diffusion coefficient for individual skyrmions, as compared to normal Brownian particles. Using Brownian dynamics simulations, we show that this topological suppression of the diffusion can be partially lifted in two-dimensional lattices of skyrmions. Counterintuitively, this causes enhanced diffusive properties with increasing particle density, similar to odd-diffusive Brownian particles. We show how the topological charge of the skyrmions influences the dynamics of topological lattice defects, which also affects the dynamics of the phase formation.