Numerical evidence for spin chirality emerging from bands with Berry curvature in itinerant ferromagnets

The behavior of strongly interacting electrons in bands with Berry curvature is a problem of wide interest. In this paper, we study this problem by numerically studying a fluxed Hubbard-type model on a square lattice. Using this model, we demonstrate that a metallic ferromagnet in electron bands equipped with Berry curvature can develop noncoplanar spin order in which spin-polarization axes at different positions span finite solid angles. We find that spin chirality can emerge in this setting by doping or adding gauge flux on top of a collinear ferromagnet. This result supports the prediction of spin chirality occurring through an emergent spin-orbital interaction. Meanwhile, our result shows that on top a ferromagnetic background, the spin chirality emerges at a finite threshold value of orbital magnetization, resembling the predicted behavior in theory.