Anomalous and spin Hall effects in magnetic granular films

We propose a simple method to confirm the crossover effect; a change in the power-law dependence of the anomalous and spin Hall conductivities with respect to the longitudinal resistivity for magnetic granular films exhibiting giant magnetoresistance (GMR). Adopting a phenomenological theory, which explains the GMR in magnetic granular films, we show that a higher order term of the longitudinal resistivity appears in the Hall resistivity owing to the crossover effect. The result may resolve a controversy in the anomalous Hall effect observed in a magnetic granular film.