Crystallization dynamics of magnetic skyrmions in a frustrated itinerant magnet

Itinerant frustrated magnets with electron-mediated spin-spin interactions often exhibit a ground state characterized by complex non-coplanar spin textures. Thesespin structures of metallic magnets are not only of great fundamental interest but also have important implications in the emerging field of spintronics. Interestingly, these complex magnetic patterns can often be viewed as a periodic array of skyrmions; an example of the skyrmion lattice (SkL). While the structural properties, stability, and elementary excitations of the SkL have been extensively studied, their nonequilibrium behaviors, such as the phase-ordering or crystallization dynamics, have yet to be investigated. The lack of progress is partly due to the difficulty of efficiently modeling the long-range electron-induced exchange fields in dynamical simulations.

In this work, we present a numerical framework for large-scale simulations of the crystallization dynamics of skyrmions in a metallic magnet. We consider a s-d type itinerant spin model with an exchange interaction between electrons and local classical spins[1]. The SkL in such systems is characterized by multiple ordering wave vectors. This observation allows one to construct an effective classical spin Hamiltonian in momentum space, which translates to complex long-range spin-spin interactions in real space. Importantly, efficient large-scale dynamical simulations can be achieved based on this effective classical spin Hamiltonian. We study the phase ordering of the SkL after a thermal quench by numerically solving the Landau-Lifshitz-Gilbert equation for a system of up to 10⁶ spins. We show that the late-stage coarsening dynamics is dominated by the annihilation dynamics of dislocations, which are topological defects of the skyrmion lattice. Other unique features that are distinct from atomic crystallization dynamics are also discussed.

[1] K. Shmizu and G.-W. Chern, arXiv:2305.16182 (2023).