Theory of Electrical Spin Manipulation in Spin-Orbit Coupling Systems

By associating a spin-orbit interaction with a non-Abelian gauge potential, we theoretically present a spin polarization in a quite general form using an effective Yang-Mills field and a usual electromagnetic field. In this gauge invariant result, we focus on a purely electrically-induced spin contribution. We find that both the inverse spin galvanic effect and the spin Hall effect arise from the same origin, i.e., the SU(2)$\times$U(1) Hall effect. We also discover that a large effective magnetic field of the order of 1T is induced in the Rashba system.