Coarsening of chiral domains in itinerant electron magnets: A machine
  learning force field approach
Yunhao Fan Sheng Zhang Gia-Wei Chern
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.