Chiral spin resonance and spin-Hall conductivity in the presence of the electron-electron interactions.

We discuss the electron spin resonance in two-dimensional electron gas at zero external magnetic field. This spin resonance is due to the transitions between the electron states, which are split by the spin-orbit (SO) interaction, and is termed as the chiral spin resonance (CSR). It can be excited by the in-plane component of the electric field of microwave radiation. We show that there exists an inherent relationship between the spin-Hall conductivity and the CSR in a system with the SO interaction. Since in the presence of the SO-interaction spin is not conserved, the electron-electron interaction renormalizes the spin-Hall conductivity as well as the frequency of the CSR. The effects of the electron interaction in systems with the SO interaction are analyzed both phenomenologically and microscopically.