Orbital magnetization as the origin of the nonlinear Hall effect

The nonlinear Hall effect is a type of Hall effect that has recently attracted significant attention. For the physical origin of the nonlinear Hall effect, while orbital magnetization has long been hypothesized to underpin the nonlinear Hall effect, a general relation between the two quantities remains elusive. Here, we resolve the problem by deriving the first explicit formula connecting the electric field-induced orbital magnetization to the second-order Hall conductivity. Our theory reveals that the applied electric field plays dual roles in generating the nonlinear Hall effect: It first generates nonequilibrium orbital magnetization associated with an edge current, and subsequently perturbs the circulating edge states to produce transverse Hall voltage. For the experimental verification, we propose to apply a combination of direct and alternative currents to identify the circulating edge current in the nonlinear Hall effect. Based on the orbital magnetization origin, we point out that in isotropic chiral metals of T and O point groups, the crystalline symmetry suppresses the nonlinear Hall response for a monochromatic linear polarized electric field, but a noncollinear bichromatic electric field can generate a finite nonlinear Hall current that manifests the chiral correlation of the field. This discovery finally enables us to incorporate both the nonlinear Hall effect and circular photogalvanic effect into the framework of orbital magnetization.