  The anomalous Hall effect (AHE) has been extended into the nonlinear regime,
where the Hall voltage shows higher-order response to the applied current.
Nevertheless, the microscopic mechanism of the nonlinear AHE remains unclear.
Here we report the orbital polarization and its induced third-order AHE in
few-layer WTe2 flakes. Through angle-dependent electric measurements, it is
found that the third-order AHE is quite consistent with the electric field
induced polarization of orbital magnetic moment caused by the Berry connection
polarizability tensor, which is further directly detected by polar reflective
magnetic circular dichroism spectroscopy. The microscopic mechanisms of
third-order AHE are analyzed through the scaling law, that is, the opposite
orbital magnetic moments (up or down) deflect to opposite directions driven by
electric field induced Berry curvature, forming the intrinsic contribution;
driven by the Magnus effect of the self-rotating Bloch electrons, the opposite
orbital magnetic moments are scattered towards opposite transverse directions,
resulting in the skew scattering.
