Spin-Hall effect in a diffusive two-dimensional electron system with spin-orbit coupling under an in-plane magnetic field

It is shown that a finite spin-Hall current can be induced by applying an in-plane magnetic field in a diffusive two-dimensional electron system with the Rashba and Dresselhaus spin-orbit couplings subjected to a dc electric field. The spin-Hall conductivity depends not only on the strength and direction of the magnetic field, but also strongly depends on the form of the scattering potential. It can be negative or positive in the case of remote impurity scattering, but essentially positive in the case of short-range scattering.