Machine learning for crystallization dynamics of skyrmions in itinerant chiral magnets*

Itinerant magnets exhibit complex magnetization textures due to the long-range electron-mediated spin-spin interactions, which depend intimately on the underlying electron Fermi surface. The resultant effective spin Hamiltonian is often highly frustrated, giving rise to non-coplanar spin structures that endow the electrons with a nontrivial Berry phase. Of particular interest is magnetic skyrmions that play a crucial role in the emerging field of spintronics. However, accurate large-scale Landau-Lifshitz-Gilbert (LLG) dynamics simulation of itinerant magnets is computationally highly demanding due to the electron degrees of freedom, which have to be integrated out on-the-fly at every time-step. Here we present a general and scalable machine learning (ML) model for efficient and accurate prediction of local electron-induced effective fields. To demonstrate our approach, we incorporate the ML model, which is trained from small-size exact solutions, into large-scale LLG simulations to systematically study the phase-ordering dynamics of skyrmion crystals in the well-known s-d model of itinerant magnets. Our work opens a new avenue for multi-scale dynamical modeling of metallic spin systems.