Peak effect, melting, and transport in skyrmion crystals

We numerically examine the transport of skyrmions driven over weak random quenched disorder using a modified Thiele approach that includes the thermal softening of skyrmion pairwise interactions introduced by Wang et al. [Phys. Rev. Appl. 18, 044024 (2022)]. The depinning transition is elastic at low temperatures but becomes plastic with a reduced threshold at higher temperatures due to the competition between thermal creep and thermal softening, indicating a temperature-induced order to disorder transition into a glass state. The resulting nonmonotonic critical depinning forces and crossing of the velocity-force curves are similar to what is observed in the peak effect for type-II superconducting vortex lattices, where the softening of vortex-vortex interactions with temperature leads to an order-disorder transition. For low skyrmion densities the peak effect is absent since the system is always in a disordered state. We map the dynamical phase transition as a function of temperature, density, drive, and materials parameters, and show that the signatures are similar to those of the superconducting peak effect. Our results are consistent with recent experiments.