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We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic(Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping ofholes between localized states in the impurity band. We show that themicroscopic origin of the anomalous Hall conductivity in this system can beattributed to a phase that a hole gains when hopping around closed-loop pathsin the presence of spin-orbit interactions and background magnetization of thelocalized Mn moments. Mapping the problem to a random resistor network, wederive an analytic expression for the macroscopic anomalous Hall conductivity$\sigma_{xy}^{AH}$. We show that $\sigma_{xy}^{AH}$ is proportional to thefirst derivative of the density of states $\varrho(\epsilon)$ and thus can beexpected to change sign as a function of impurity band filling. We also showthat $\sigma_{xy}^{AH}$ depends on temperature as the longitudinal conductivity$\sigma_{xx}$ within logarithmic accuracy.Comment: 4 pages, 1 eps figure, final versio

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime