Strong nonlinearity and hysteresis of Hall resistance versus magnetization in nickel thin films

The anomalous Hall effect (AHE) in ferromagnetic materials is perhaps one of the oldest unresolved mysteries in physics. First observed in 1881, its mechanism is still a controversial topic today. The question remains whether AHE is caused by intrinsic (Berry phase and band structure) or extrinsic (defect scattering) effects or a combination of both. Here we present experimental observation in nickel thin films that seems to add to the mystery, but may in fact provide crucial clues for ultimately resolving the controversy. The key observation is that the Hall resistivity of nickel films is a strongly nonlinear function of the magnetization and displays clear hysteresis with respect to M. Specifically, 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 outside our 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.