Theory of current-driven skyrmions in disordered magnets

An emergent topological particle in magnets, skyrmion, has several unique features distinct from the other magnetic textures such as domain wall, helical structure, and vortex. It is characterized by a topological integer called skyrmion number N-sk, which counts how many times the directions of the magnetic moments wrap the unit sphere. This N-sk gives the chiral nature of the skyrmion dynamics, and leads to the extremely small critical current density j(c) for the current-driven motion in terms of spin transfer torque effect. The finite j(c) indicates the pinning effect due to the disorder such as impurities and defects, and the behaviors of skyrmions under disorder have not been explored well theoretically although it is always relevant in real systems. Here we reveal by a numerical simulation of LandauLifshitz- Gilbert equation that there are four different skyrmion phases with the strong disorder, i.e., (A) pinned state, (B) depinned state, (C) skyrmion multiplication/annihilation, and (D) segregation of skyrmions, as the current density increases, while only two phases (A) and (B) appear in the weak disorder case. The microscopic mechanisms of the new phases (C) and (D) are analyzed theoretically. These results offer a coherent understanding of the skyrmion dynamics under current with disorder.