Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets

Abstract

The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral magnets, can each be considered as forms of density waves but with distinct topologies. The SkX exhibits gyrodynamics analogous to electrons under a magnetic field, while the HL state resembles topological trivial spin density waves. However, unlike the charge density waves, the theoretical analysis of the sliding motion of SkX and HL remains unclear, especially regarding the similarities and differences in sliding dynamics between these two spin density waves. In this work, we systematically explore the sliding dynamics of SkX and HL in chiral magnets in the limit of large current density. We demonstrate that the sliding dynamics of both SkX and HL can be unified within the same theoretical framework as density waves, despite their distinct microscopic orders. Furthermore, we highlight the significant role of gyrotropic sliding induced by impurity effects in the SkX state, underscoring the impact of nontrivial topology on the sliding motion of density waves. Our theoretical analysis shows that the effect of impurity pinning is much stronger in HL compared with SkX, i.e., $\chi^{SkX}/\chi^{HL}\sim \alpha^2$ ($\chi^{SkX}$, $\chi^{HL}$: susceptibility to the impurity potential, $\alpha$ ($\ll 1$) is the Gilbert damping). Moreover, the velocity correction is mostly in the transverse direction to the current in SkX. These results are further substantiated by realistic Landau-Lifshitz-Gilbert simulations.