In-plane Anomalous Hall Effect: A Novel Off-diagonal Response

The Hall effect is conventionally understood as a transverse voltage generated by an electric current on the deflection plane, through diagonal coupling between the out-of-plane Hall vector component and the out-of-plane magnetic field or spin magnetization. However, in recent years, theoretical studies based on various models have suggested that even an in-plane magnetic field can induce an anomalous Hall effect, through off-diagonal coupling between the out-of-plane Hall vector component and the in-plane magnetic field or spin magnetization. Here we present the observation of in-plane anomalous Hall effect in thin films of several quantum materials, including Dirac and Weyl semimetals [1-4]. We also introduce recent finding on the unique multipolar nature of the off-diagonal coupling underlying the in-plane anomalous Hall effect [5].