Disorder and temperature dependence of the anomalous Hall effect in thin ferromagnetic films:: Microscopic model

We consider the anomalous Hall (AH) effect in thin disordered ferromagnetic films. Using a microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling, we develop a general formulation for strong, finite range impurity scattering. Explicit calculations are done within a short range but strong impurity scattering to obtain AH conductivities for both the skew scattering and side-jump mechanisms. We also evaluate quantum corrections due to interactions and weak localization effects. We show that for arbitrary strength of the impurity scattering, the electron-electron interaction correction to the AH conductivity vanishes exactly due to general symmetry reasons. On the other hand, we find that our explicit evaluation of the weak localization corrections within the strong, short-range impurity scattering model can explain the experimentally observed logarithmic temperature dependences in disordered ferromagnetic Fe films.