Frequency dependence of induced spin polarization and spin current in quantum wells

Dynamic response of two-dimensional electron systems with spin-orbit interaction is studied theoretically on the basis of quantum kinetic equation, taking into account elastic scattering of electrons. The spin polarization and spin current induced by the applied electric field are calculated for the whole class of electron systems described by p-linear spin-orbit Hamiltonians. The absence of nonequilibrium intrinsic static spin currents is confirmed for these systems with arbitrary (nonparabolic) electron energy spectrum. Relations between the spin polarization, spin current, and electric current are established. The general results are applied to the quantum wells grown in [001] and [110] crystallographic directions, with both Rashba and Dresselhaus types of spin-orbit coupling. It is shown that the existence of the fixed (momentum-independent) precession axes in [001]-grown wells with equal Rashba and Dresselhaus spin velocities or in symmetric [110]-grown wells leads to vanishing spin polarizability at arbitrary frequency omega of the applied electric field. This property is explained by the absence of Dyakonov-Perel-Kachorovskii spin relaxation for the spins polarized along these precession axes. As a result, a considerable frequency dispersion of spin polarization at very low omega in the vicinity of the fixed precession axes is predicted. Possible effects of extrinsic spin-orbit coupling on the obtained results are discussed.