Electric-field-induced long-lived spin excitations in two-dimensional spin-orbit coupled systems

Rigorous coupled spin-charge drift-diffusion equations are derived from quantum-kinetic equations for the spin-density matrix that incorporate effects due to k-linear spin-orbit interaction, an electric field, and the elastic scattering on nonmagnetic impurities. The explicit analytical solution for the induced magnetization exhibits a pole structure, from which the dispersion relations of spin excitations are identified. Applications of the general approach refer to the excitation of long-lived field-induced spin waves by optically generated spin and charge patterns for a planar and cylindrical geometry. This approach transfers methods known in the physics of space-charge waves to the treatment of long-lived spin eigenmodes that appear in planar and nonplanar two-dimensional electron systems with spin-orbit interaction. In addition, the amplification of an oscillating electric field by spin injection is demonstrated.