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arXiv · 1104.1473

The Scaling of the Anomalous Hall Effect in the Insulating Regime

Xiong-Jun Liu·Xin Liu·Jairo Sinova
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Abstract

We develop a theoretical approach to study the scaling of anomalous Hall effect (AHE) in the insulating regime, which is observed to be $\sigma_{xy}^{AH}\propto\sigma_{xx}^{1.40\sim1.75}$ 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 $1.38\leq\gamma\leq1.76$, 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.

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Xiong-Jun Liu, Xin Liu, Jairo Sinova. 2011-04-08. The Scaling of the Anomalous Hall Effect in the Insulating Regime. https://doi.org/10.1103/physrevb.84.165304

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