Localization and the Anomalous Hall Effect in a "Dirty" Metallic Ferromagnet

Abstract

We report magnetoresistance measurements over an extensive temperature range (0.1 K $\le T\le$ 100 K) in a disordered ferromagnetic semiconductor (\gma). The study focuses on a series of metallic \gma~ epilayers that lie in the vicinity of the metal-insulator transition ($k_F{l}_e\sim 1$). At low temperatures ($T<4$ K), we first confirm the results of earlier studies that the longitudinal conductivity shows a $T^{1/3}$ dependence, consistent with quantum corrections from carrier localization in a ``dirty'' metal. In addition, we find that the anomalous Hall conductivity exhibits universal behavior in this temperature range, with no pronounced quantum corrections. We argue that observed scaling relationship between the low temperature longitudinal and transverse resistivity, taken in conjunction with the absence of quantum corrections to the anomalous Hall conductivity, is consistent with the side-jump mechanism for the anomalous Hall effect. In contrast, at high temperatures ($T\gtrsim 4$ K), neither the longitudinal nor the anomalous Hall conductivity exhibit universal behavior, indicating the dominance of inelastic scattering contributions down to liquid helium temperatures.

Revised version of original submission. To appear in Phys. Rev. B

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• Unconventional temperature dependence of the anomalous Hall effect in HgCr2Se4
• Temperature Dependence of the Anomalous Hall Effect from Electron Interactions
• Thermodynamic and thermoelectric properties of (Ga,Mn)As and related compounds
• Does carrier localization affect the anomalous Hall effect?