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

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

2008-08-15

arxiv.org/abs/0808.2079v2

Phys. Rev. B 82, 035205 (2010)

Physics

Condensed Matter

Materials Science

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

Scientific paper

10.1103/PhysRevB.82.035205

We report magnetoresistance measurements over an extensive temperature range (0.1 K $\leq T \leq$ 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.

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