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Anomalous Hall effect (AHE) is the key transport signature unlockingtopological properties of magnetic materials. While AHE is usually proportionalto the magnetization, the nonlinearity suggests the existence of complexmagnetic and electron orders. Nonlinear AHE includes the topological Halleffect (THE) that has been widely used to identify the presence of spinchirality in real space. But it can in principle be induced by band structureevolution via Berry curvatures in the reciprocal space. This effect has beenlargely overlooked due to the intertwined mechanisms in both real andreciprocal spaces. Here, we observed a giant nonlinear AHE with the resistivityup to 383.5 uohm cm, contributing unprecedentedly 97% of the total Hallresponse in EuCd2As2. Moreover, it can be further enhanced by tilting themagnetic field 30{\deg} away from [001] direction, reaching a large anomalousHall angle up to 21%. Although it shows exactly the same double-peak feature asTHE, our scaling analysis and first-principles calculations reveal that theBerry phase is extremely sensitive to the spin canting, and nonlinear AHE is aconsequence of band structure evolution under the external magnetic fields.When the spins gradually tilt from the in-plane antiferromagnetic ground stateto out-of-plane direction, band crossing and band inversion occur, introducinga bandgap at {\Gamma} point at a canting angle of 45{\deg}. That contributes tothe enhancement of Berry curvature and consequently a large intrinsic Hallconductivity. Our results unequivocally reveal the sensitive dependence of bandstructures on spin tilting process under external magnetic fields and itspronounced influence on the transport properties, which also need to be takeninto consideration in other magnetic materials.

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