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Abstract

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].

[1] A. Nakamura et al., Physical Review Letters 133, 236602 (2024)
[2] H. Lee et al., Physical Review B 111, L241106 (2025)
[3] S. Nishihaya et al., Physical Review Letters 135, 106603 (2025)
[4] S. Nishihaya et al., Advanced Materials 37, e02624 (2025)
[5] A. Nakamura et al., arXiv:2507.21458 (2025)