Magnetic versus hyperfine field in the anomalous Hall effect

The anomalous Hall effect (AHE) in nonmagnetic semiconductors is considered in the presence of the hyperfine field. The results obtained are essentially equivalent to those without the hyperfine field except for the appropriate modification of the electronic spin polarisation. Our calculation shows that it should be possible to observe the contact hyperfine interaction driven AHE in bulk semiconductors. The role of the hyperfine field is to leave the electronic spin polarisation constant and to enhance the splitting of the conduction band, thus competing with the applied external magnetic field in creating the magnetisation of the carriers. As an example, a quantitative calculation for InSb is presented.