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 Δ¯2/E(F), where Δ¯ 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.