Intrinsic in-Plane Anomalous Hall Effect

The recent experimental finding of in-plane anomalous Hall effect (IPAHE) opens avenues for exploring the intriguing interplay of in-plane magnetic field and anomalous Hall physics. However, the existing framework relies exclusively on a spin origin, and does not uncover the responsible band geometric properties intrinsic to materials. We reveal that two new intrinsic band geometric quantities-anomalous orbital polarizability (AOP) and anomalous spin polarizability (ASP)-can give rise to an intrinsic bilinear IPAHE. The ASP is allowed in spin-orbit coupled band structures. The AOP originates from the minimal coupling and does not require spin-orbit coupling (SOC). Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the IPAHE in topological semimetals TaSb₂, NbAs₂ and SrAs₃. While the orbital and spin contributions are comparable in TaSb₂, the orbital mechanism is completely dominant in NbAs₂ and SrAs₃ with weaker SOC. In particular, the AOP contribution by the gapped topological nodal-loop across the Fermi surface in SrAs₃ is responsible for the effect, rendering a good platform for exploring the manifestation of momentum space topological structures in exotic transport phenomena.