Universal two-stage dynamics and phase control in skyrmion formation

Abstract

We uncover a universal two-stage dynamics during skyrmion formation and establish its connection to equilibrium phases through the introduction of a chiral correlation $\ddot{I}‡$. Stage I involves stripe coarsening governed by the exchange-to-DMI ratio $J^{\prime }$, while stage II entails stripe contraction driven by the synergy between $J^{\prime }$ and the anisotropy-to-DMI ratio $K^{\prime }$. The magnetic field-to-DMI ratio $B^{\prime }$ influences both stages. By combining symbolic regression with neural networks, we model the competition and cooperation among these parameters and derive a skyrmion formation criterion, $0.58K^{\prime }{J}^{\prime }+\hat{I}¼B^{\prime }{J}^{\prime }>1$. Our model disentangles their distinct roles: $J^{\prime }$ sets the stripe width, $K^{\prime }$ primarily controls the skyrmion size, and $B^{\prime }$ strongly affects the topological charge. This approach provides a general framework for predicting and controlling magnetic phases in chiral magnets.