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

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 ${\sigma }_{xy}^{\mathrm{AHE}}$ and the longitudinal conductivity ${\sigma }_{xx}$ over several orders of magnitude, a universal scaling relation ${\sigma }_{xy}^{\mathrm{AHE}}\propto {\sigma }_{xx}^{\alpha }$ 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.

4 pages, 4 figures

References in corpus (16)

• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Anomalous Hall effect in ferromagnetic semiconductors
• Universal Scaling Behavior of Anomalous Hall Effect and Anomalous Nernst Effect in Itinerant Ferromagnets
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Topological Nature of Anomalous Hall Effect in Ferromagnet
• Linear magnetization dependence of the intrinsic anomalous Hall effect
• Scaling of the anomalous Hall effect in Sr${}_{1-x}$Ca${}_x$RuO${}_3$
• Charge Transport in Manganites: Hopping Conduction, the Anomalous Hall Effect and Universal Scaling
• Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime
• Hall Resistivity and Dephasing in the Quantum Hall Insulator
• Epitaxy of Fe3O4 on Si(001) by pulsed laser deposition using a TiN/MgO buffer layer
• Berry's phase contribution to the anomalous Hall effect of gadolinium
• Sub-unit cell layer-by-layer growth of Fe3O4, MgO, and Sr2RuO4 thin films

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