Collective transport properties of skyrmions on the depinning phase transition

The pinning phenomena of topological skyrmions in magnetic materials with defects are of vital importance for the precise positioning and the manipulation of skyrmions in experiment. With the Thiele equation of the particle-based model, we investigate the dynamic depinning phase transition of skyrmions, induced by quenched disorder. The phase transition from the pinned glass to the moving liquid is of second order, while the critical driving force and both the static and dynamic exponents are accurately determined for different strengths of the Magnus term and the pinning force based on the dynamic scaling behavior far from stationary. The results show that the skyrmions exhibit very different collective transport properties at the depinning phase transition due to the Magnus force which induces the skyrmion Hall effect compared to the overdamped magnetic systems. Furthermore, the critical behaviors of skyrmions are anisotropic in directions perpendicular and parallel to the driving force, providing an understanding of the force-dependent Hall angle around the phase transition in experiment. Our nonstationary dynamic approach is very efficient in tackling the dynamic phase transitions.