  A Fermi liquid with spin-orbit coupling (SOC) is expected to support a new
kind 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}^2=E_F , where
{\Delta} is a characteristic spin-orbit energy splitting and E_F is the Fermi
energy. Such damping is in a 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.
