Coarsening of chiral domains in itinerant electron magnets: A machine learning force-field approach

Frustrated itinerant magnets often exhibit complex noncollinear or noncoplanar magnetic orders which support topological electronic structures. A canonical example is the anomalous quantum Hall state with a chiral spin order stabilized by electron-spin interactions on a triangular lattice. While a long-range magnetic order cannot survive thermal fluctuations in two dimensions, the chiral order which results from the breaking of a discrete Ising symmetry persists even at finite temperatures. We present a scalable machine learning (ML) framework to model the complex electron-mediated spin-spin interactions that stabilize the chiral magnetic domains in a triangular lattice. Large-scale dynamical simulations, enabled by the ML force-field models, are performed to investigate the coarsening of chiral domains after a thermal quench. While the chiral phase is described by a broken Z2 Ising-type symmetry, we find that the characteristic size of chiral domains increases linearly with time, in stark contrast to the expected Allen-Cahn domain growth law for a nonconserved Ising order-parameter field. The linear growth of the chiral domains is attributed to the orientational anisotropy of domain boundaries. Our work also demonstrates the promising potential of ML models for large-scale spin dynamics of itinerant magnets.