Anomalous Hall effect in ferromagnetic semiconductors with hopping transport

Abstract

We use high-field magnetotransport to examine the relation between the Hall effects and the longitudinal resistance, ${R}_{xx}$, in digitally doped (Ga,Mn)As structures with hopping transport. The ordinary and anomalous Hall resistances, ${R}_{\mathrm{OH}}$ and ${R}_{\mathrm{AH}}$, display sublinear dependences on ${R}_{xx}$, a behavior inconsistent with theories used to interpret data from metallic semiconductor ferromagnets. None of the resistances are simply activated. While ${R}_{\mathrm{OH}}$ is consistently holelike, ${R}_{\mathrm{AH}}$ can have either sign. These results agree qualitatively with aspects of a recently developed model for the Hall effects in the hopping regime.