Intrinsic Damping of Collective Spin Modes in a Two-Dimensional Fermi Liquid with Spin-Orbit Coupling

A Fermi liquid with spin-orbit coupling (SOC) is expected to support a new set of collective modes: oscillations of magnetization in the absence of the magnetic field. We show that these modes are damped by the electron-electron interaction even in the limit of an infinitely long wavelength (q = 0). The linewidth of the collective mode is on the order of (Delta) over bar (2)/E-F, where (Delta) over bar is a characteristic spin-orbit energy splitting and E-F is the Fermi energy. Such damping is in stark contrast to known damping mechanisms of both charge and spin collective modes in the absence of SOC, all of which disappear at q = 0, and arises because none of the components of total spin is conserved in the presence of SOC.