The Scaling of the Anomalous Hall Effect in the Insulating Regime

Details The Scaling of the Anomalous Hall Effect in the Insulating Regime The Scaling of the Anomalous Hall Effect in the Insulating Regime

2011-04-08

arxiv.org/abs/1104.1473v2

Phys. Rev. B 84, 165304 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevB.84.165304

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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