Intrinsic anomalous Hall conductivity of GaMnAs solely governed by the carrier concentration

In the core of quantum Hall effect, intrinsic anomalous Hall effect (AHE), and intrinsic spin Hall effect lies the Berry phase, a quantum mechanical phase associated with an adiabatic change of the system. However, experimental evidences supporting this new recognition are scarce in three-dimensional systems. We report here that the anomalous Hall conductivity of metallic GaMnAs samples, when properly scaled by the carrier concentration, remains constant regardless of the ferromagnetic transition temperature from 50 to 160 K. In addition, the constant agrees with the theoretical prediction quite well. These qualitative and quantitative agreements support the idea of intrinsic AHE originated from momentum-space Berry phase firmly. Furthermore, the tunability of intrinsic AHE in the diluted magnetic semiconductors can be utilized in the semiconductor spintronics applications.