Quadrupole anomalous Hall effect in magnetically induced electron nematic state

Abstract Berry phases in both momentum and real space cause transverse motion in itinerant electrons, manifesting various off-diagonal transport effect such anomalous and topological Hall effects. Although these Hall effects are isotropic within the plane perpendicular to the fictitious magnetic field, here, we report the manifestation of the anisotropic linear anomalous Hall effect (AHE) in the spinel oxide NiCo2O4 epitaxial film. The unconventional Hall effect indicates a quadrupole dependence on the in-plane current direction being added to the uniform AHE. Moreover, its sign can be manipulated just by magnetic-field cooling. The anisotropic effect is attributed to an electron nematic state originating from a deformed electronic state owing to an extended magnetic toroidal quadrupole and ferrimagnetic order.