  Starting from the Dirac-Kohn-Sham equation we derive the relativistic
equation of motion of spin angular momentum in a magnetic solid under an
external electromagnetic field. This equation of motion can be written in the
form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external
magnetic field, and leads to a more general magnetization dynamics equation for
a general time-dependent magnetic field. In both cases with an electronic
spin-relaxation term which stems from the spin-orbit interaction. We thus
rigorously derive, from fundamental principles, a general expression for the
anisotropic damping tensor which is shown to contain an isotropic Gilbert
contribution as well as an anisotropic Ising-like and a chiral,
Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation
tensor comprises furthermore both electronic interband and intraband
transitions. We also show that when the externally applied electromagnetic
field possesses spin angular momentum, this will lead to an optical spin torque
exerted on the spin moment.
