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

TL;DR

This study investigates the localization effects and anomalous Hall effect in disordered ferromagnetic semiconductors near the metal-insulator transition, revealing temperature-dependent quantum corrections and mechanisms.

Contribution

It provides new insights into the temperature-dependent behavior of conductivity and Hall effects, supporting the side-jump mechanism in a 'dirty' ferromagnetic metal near the transition.

Findings

Longitudinal conductivity shows a T^{1/3} dependence at low T.

Anomalous Hall conductivity exhibits universal behavior at low T.

Quantum corrections are absent in the Hall conductivity at low T.

Abstract

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.