Crystallization dynamics of the skyrmion lattice in frustrated metallic magnets

Magnetic skyrmions are topological spin textures in a two-dimensional magnet, and have been attracted much attention as a candidate for next-generation magnetic memory devices. Although there have been intensive studies on the skyrmion lattice (SkL), the crystallization dynamics have not been fully understood thus far. In this work, we theoretically investigated the crystallization dynamics of the SkL in a frustrated metallic magnet [1] by performing large-scale Landau-Lifshitz-Gilbert dynamics simulations based on the effective spin model for metallic magnets [2]. We found that in the formation of the square SkL viewed as a superposition of two magnetic stripes, the initial fast crystallization of skyrmions is followed by a slow relaxation dominated by the annihilation dynamics of dislocations, which are topological defects of the constituent magnetic stripe orders. We also showed that the annihilation of dislocations follows a power-law time dependence with a logarithmic correction that depends on magnetic fields. Furthermore, we clarified that the effective spin Hamiltonian can be mapped to the XY model exhibitting the similar phase ordering dynamics accompanied by pair annihilation of vortices. Our work sheds new light on the fundamental subject of 2D crystallization dynsmics and provides a new perspective on the non-equilibrium phenomena of topological spin crystals.