Anomalous Hall Effect in Magnetite: Universal Scaling Relation Between Hall and Longitudinal Conductivity in Low-Conductivity Ferromagnets

TL;DR

This study reveals a universal scaling relation between anomalous Hall conductivity and longitudinal conductivity in low-conductivity ferromagnetic oxides, independent of structural and compositional variations, bridging metallic and hopping transport regimes.

Contribution

It demonstrates a universal scaling law for the anomalous Hall effect in low-conductivity ferromagnets, applicable across different transport mechanisms and material conditions.

Findings

Universal scaling relation $\sigma_{xy}^{ m AHE} \propto \sigma_{xx}^{1.69}$ found

Scaling relation holds across various orientations, compositions, and strain states

Relation is consistent with theories for metallic and hopping conduction regimes

Abstract

The anomalous Hall effect (AHE) has been studied systematically in the low-conductivity ferromagnetic oxide Fe$_{3-x}$Zn$_x$O$_4$ with $x = 0$, 0.1, and 0.5. We used (001), (110), and (111) oriented epitaxial Fe$_{3-x}$Zn$_x$O$_4$ 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 $\sigma_{xy}^{\rm AHE}$ and the longitudinal conductivity $\sigma_{xx}$ over several orders of magnitude, a universal scaling relation $\sigma_{xy}^{\rm AHE} \propto \sigma_{xx}^{\alpha}$ with $\alpha = 1.69 \pm 0.08$ 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.