  We derive the spin-wave dynamics of a magnetic material from the
time-dependent spin density functional theory in the linear response regime.
The equation of motion for the magnetization includes, besides the static spin
stiffness, a "Berry curvature" correction and a damping term. A gradient
expansion scheme based on the homogeneous spin-polarized electron gas is
proposed for the latter two quantities, and the first few coefficients of the
expansion are calculated to second order in the Coulomb interaction.
