Effect of spin-conserving scattering on Gilbert damping in ferromagnetic semiconductors

The Gilbert damping in ferromagnetic semiconductors is theoretically investigated based on the $s$-$d$ model. In contrast to the situation in metals, all the spin-conserving scattering in ferromagnetic semiconductors supplies an additional spin relaxation channel due to the momentum dependent effective magnetic field of the spin-orbit coupling, thereby modifies the Gilbert damping. In the presence of a pure spin current, we predict a new contribution due to the interplay of the anisotropic spin-orbit coupling and a pure spin current.