  Anomalous Hall effect (AHE) is the key transport signature unlocking
topological properties of magnetic materials. While AHE is usually proportional
to the magnetization, the nonlinearity suggests the existence of complex
magnetic and electron orders. Nonlinear AHE includes the topological Hall
effect (THE) that has been widely used to identify the presence of spin
chirality in real space. But it can in principle be induced by band structure
evolution via Berry curvatures in the reciprocal space. This effect has been
largely overlooked due to the intertwined mechanisms in both real and
reciprocal spaces. Here, we observed a giant nonlinear AHE with the resistivity
up to 383.5 uohm cm, contributing unprecedentedly 97% of the total Hall
response in EuCd2As2. Moreover, it can be further enhanced by tilting the
magnetic field 30{\deg} away from [001] direction, reaching a large anomalous
Hall angle up to 21%. Although it shows exactly the same double-peak feature as
THE, our scaling analysis and first-principles calculations reveal that the
Berry phase is extremely sensitive to the spin canting, and nonlinear AHE is a
consequence of band structure evolution under the external magnetic fields.
When the spins gradually tilt from the in-plane antiferromagnetic ground state
to out-of-plane direction, band crossing and band inversion occur, introducing
a bandgap at {\Gamma} point at a canting angle of 45{\deg}. That contributes to
the enhancement of Berry curvature and consequently a large intrinsic Hall
conductivity. Our results unequivocally reveal the sensitive dependence of band
structures on spin tilting process under external magnetic fields and its
pronounced influence on the transport properties, which also need to be taken
into consideration in other magnetic materials.
