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 $Z_2$ 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 non-conserved 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.

通过机器学习框架模拟复杂的交叉磁场和自旋-自旋相互作用来研究三角晶格中手性磁域的增长规律，发现磁域特征尺寸随时间线性增长，这归因于磁域边界的方向各向异性，同时揭示了机器学习模型在研究移动磁体的大规模自旋动力学方面的潜力。

漂移电子磁体中手性结域的粗化：一种机器学习力场方法