Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization

We theoretically investigate the anomalous Hall effect in a system of dense-packed ferromagnetic grains in the metallic regime. Using the formalism recently developed for the conventional Hall effect in granular metals, we calculate the residual anomalous Hall conductivity σ_xy and resistivity ρ_xy and weak localization corrections to them for both skew-scattering and side-jump mechanisms. We find that the scaling relation between ρ_xy and the longitudinal resistivity ρ_xx of the array does not hold, regardless of whether it is satisfied for the specific resistivities of the grain material or not. The weak localization corrections, however, are found to be in agreement with those for homogeneous metals. We discuss recent experimental data on the anomalous Hall effect in polycrystalline iron films in view of the obtained results.