Abstract
We report experimental observation that the Hall resistivity of nickel films is a strongly nonlinear function of the magnetization $M$ and displays clear hysteresis with respect to $M$. At low temperatures, the anomalous Hall coefficient switches between two saturated values under the magnetic field with a narrow transition region, but with a strong hysteresis, in contrast to the slow saturation of the magnetization. The nonlinearity and the hysteresis become more apparent with decreasing temperature or film thickness. Despite the simplicity of the lattice and magnetic structure of nickel films, these results are outsideour current understanding of AHE, whether using intrinsic or extrinsic mechanisms of AHE. It presents a challenge for these models, and may be used as a test of validity for both types of theories.