Symmetry-Guided Machine Learning of Spin-Dependent Nonlinear Hall Response

Abstract

A Berry-curvature dipole can produce a nonlinear Hall current even when the linear Hall response vanishes, but symmetry alone does not determine its magnitude or magnetic tunability. The interplay of structural symmetry, moment orientation, and carrier occupation is examined in a honeycomb model. Curvature maps and the band-summed dipole integrand reveal how velocity and the occupation window near the Fermi level select signed contributions. Removing threefold rotation permits a nonmagnetic dipole perpendicular to the surviving mirror. Generic magnetic reorientation activates the second component and tunes both components through positive and negative values. Global reversal preserves the dipole while reversing the intrinsic linear Hall conductivity, allowing a finite bulk dipole contribution from equally populated reversed domains under uniform-field averaging.A symmetry-constrained polynomial model predicts both dipole components for 256 held-out spin configurations, achieving coefficients of determination $R^2 > 0.9995$ at the reference chemical potential. At fixed carrier density, orientation-dependent shifts of the chemical potential modify the response and yield slightly larger prediction errors for the chosen model. Across the chemical-potential sweep,the prediction accuracy decreases more strongly for $D_y$,revealing an energy dependence of the surrogate's performance. Within semiclassical transport with a constant relaxation time, the calculated dipole determines the angular dependence of the quadratic current and its rectified and second-harmonic components. These results provide a quantitative representation of magnetic-orientation-dependent Berry-curvature dipoles and show how carrier occupation influences both the response and its predictability.