Anomalous Hall effect in field-effect structures of (Ga,Mn)As

The anomalous Hall effect in metal-insulator-semiconductor structures having thin (Ga,Mn)As layers as a channel has been studied in a wide range of Mn and hole densities changed by the gate electric field. Strong and unanticipated temperature dependence, including a change of sign, of the anomalous Hall conductance $\sigma_{xy}$ has been found in samples with the highest Curie temperatures. For more disordered channels, the scaling relation between $\sigma_{xy}$ and $\sigma_{xx}$, similar to the one observed previously for thicker samples, is recovered.