The Scaling of the Anomalous Hall Effect in the Insulating Regime

Abstract

We develop a theoretical approach to study the scaling of anomalous Hall effect (AHE) in the insulating regime, which is observed to be ${\sigma }_{xy}^{AH}\propto {\sigma }_{xx}^{1.40\sim 1.75}$ in experiments over a large range of materials. This scaling is qualitatively different from the ones observed in metals. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derive a general formula for the anomalous Hall conductivity, and show that it scales with the longitudinal conductivity as ${\sigma }_{xy}^{AH}\sim {\sigma }_{xx}^{\gamma }$ with $\gamma$ predicted to be $1.38\le \gamma \le 1.76$, quantitatively in agreement with the experimental observations. Our result provides a clearer understanding of the AHE in the insulating regime and completes the scaling phase diagram of the AHE.

4 pages, 4 figures, plus the supplementary information. Minor revisions made according to Referee reports

References in corpus (5)

• Anomalous Hall effect
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Anomalous Hall effect in field-effect structures of (Ga,Mn)As
• Anomalous Hall Effect in Magnetite: Universal Scaling Relation Between Hall and Longitudinal Conductivity in Low-Conductivity Ferromagnets
• Scaling relation of the anomalous Hall effect in (Ga,Mn)As

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