Anomalous Hall effect in ZnxFe3-xO4: Universal scaling law and electron localization below the Verwey transition

We show that the well-established universal scaling σxyAHE ∼ σxx1.6 between anomalous Hall and longitudinal conductivities in the low conductivity regime (σxx < 104 Ω−1 cm−1) transforms into the scaling σxyAHE ∼ σxx2 at the onset of strong electron localization. The crossover between the two relations is observed in magnetite-derived ZnxFe3-xO4 thin films where an insulating/hopping regime follows a bad metal/hopping regime below the Verwey transition temperature Tv. Our results demonstrate that electron localization effects come into play in the anomalous Hall effect (AHE) modifying significantly the scaling exponent. In addition, the thermal evolution of the anomalous Hall resistivity suggests the existence of spin polarons whose size would decrease below Tv