Localization and the anomalous Hall effect in a dirty metallic ferromagnet

We report magnetoresistance measurements over an extensive temperature range (0.1≤T≤100 K) in a disordered ferromagnetic semiconductor (Ga1-x Mnx As). The study focuses on a series of metallic Ga_1-x Mn_x As epilayers that lie in the vicinity of the metal-insulator transition (k _Fl_e∼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 the 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≥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.