Giant nonlinear anomalous Hall effect induced by spin-dependent band structure evolution

The anomalous Hall effect (AHE) is a key transport signature revealing the topological properties of magnetic compounds. In quantum materials, the classical linear dependence of the AHE on magnetization often breaks down, which is typically ascribed to the presence of topological magnetic or electronic textures. However, the complex electronic structure of these compounds may offer alternative, unexplored mechanisms. Here, we show that a giant nonlinear AHE can originate from a series of magnetic-field-induced Lifshitz transitions in the spin-dependent band structure. In our experiments on EuCd2As2 the AHE contributes to 97% of the total Hall response, corresponding to a record anomalous Hall angle of 21%. Our scaling analysis and first-principles calculations demonstrate that the electronic structure is extremely sensitive to spin canting, with the magnetic field causing band crossing and band inversion and introducing a band gap when oriented along specific directions. Our results not only provide an ideal platform for Berry curvature engineering but reveal a general effect that may be applied to other material systems.