Anomalous Hall effect in magnetite: Universal scaling relation between Hall and longitudinal conductivity in low-conductivity ferromagnets

The anomalous Hall effect (AHE) has been studied systematically in the low-conductivity ferromagnetic oxide Fe3-xZnxO4 with x = 0, 0.1, and 0.5. We used (001), (110), and (111) oriented epitaxial Fe3-xZnxO4 films grown on MgO and sapphire substrates in different oxygen partial pressure to analyze the dependence of the AHE on crystallographic orientation, Zn content, strain state, and oxygen deficiency. Despite substantial differences in the magnetic properties and magnitudes of the anomalous Hall conductivity sigma(AHE)(xy) and the longitudinal conductivity sigma(xx) over several orders of magnitude, a universal scaling relation sigma(AHE)(xy) proportional to sigma(alpha)(xx) with alpha = 1.69 +/- 0.08 was found for all investigated samples. Our results are in agreement with recent theoretical and experimental findings for ferromagnetic metals in the dirty limit, where transport is by metallic conduction. We find the same scaling relation for magnetite, where hopping transport prevails. The fact that this relation is independent of crystallographic orientation, Zn content, strain state, and oxygen deficiency suggests that it is universal and particularly does not depend on the nature of the transport mechanism.