Scaling of anomalous Hall effect in ferromagnetic thin films

We propose a new scaling law for anomalous Hall effect in ferromagnetic thin films by distinguishing three scattering sources, namely, bulk impurity, phonon, and more importantly a rough surface. This new scaling law fits the recent experimental data excellently with constant coefficients that are independent of temperature and film thickness. This is in stark constrast with previous scaling laws that use temperature/thickness dependent fitting coefficients, and is a strong indicator that this law captures the essential physics. By intepretating the experiments for Fe, Co, and Ni with this new law, we conclude that (i) the phonon-induced skew scattering is unimportant as expected; (ii) contribution from the impurity-induced skew scattering is negative; (iii) the intrinsic (extrinsic) mechanism dominates in Fe (Co), and both the extrinsic and the intrinsic contribution are important in Ni.