Interplay between Carrier Polarization, Spin-Orbit Coupling and Exchange Field on Anomalous Hall Conductivity in the Presence of Magnetic Impurity in Mn Doped GaAs

We develop a model Hamiltonian to treat anomalous Hall conductivity in dilute magnetic semiconductor (DMS) of type (III, Mn, V) considering the impurity potentials (potential due to interaction of spin of carriers with localized spin of dopant (Mn) and coulomb like potential). Using equation of motion in Green function together with Quantum Kubo-formula of conductivity, the anomalous Hall conductivity is calculated as function of spin-orbit coupling, exchange field and carrier polarization. The calculated result shows that at low impurity concentration, the interplay between spin polarization of carriers, spin-orbit coupling and exchange fields is crucial for existence of anomalous Hall conductivity. The monotonic increment of anomalous Hall conductivity with exchange field is observed for strong spin-orbit coupling limit. In weak spin-orbit coupling limit, the magnitude of anomalous Hall conductivity increases parabolically with the spin-orbit coupling. Our results provide an important basis for understanding the interplay between the spin polarization, spin-orbit coupling, and exchange field on anomalous Hall conductivity at low impurity concentration. The findings are also a key step to realize dissipationless quantum transport without external magnetic field.