Anomalous Hall effect in disordered Fe ferromagnetic films

Recently experiments have shown that disordered Fe thin films on ${\mathrm{C}}_{60}$ substrates exhibit the anomalous Hall effect even in the very high resistance region. To understand this phenomenon, we employ the spin-dependent Boltzmann equations with the inclusion of spin-orbit coupling to investigate the transverse voltage in insulating disordered Fe films. We use the Boltzmann equations to describe each spin channel inside each Fe island, which is about $100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wide. The Hall conductance of the system is shown to be non-vanishing in the high resistance limit and also independent of the longitudinal charge current. Results from our simulations reveal physical mechanisms underlying experimental observations.