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We present a microscopic calculation of magnetization damping for a magnetic"toy model." The magnetic system consists of itinerant carriers coupledantiferromagnetically to a dispersionless band of localized spins, and themagnetization damping is due to coupling of the itinerant carriers to a phononbath in the presence of spin-orbit coupling. Using a mean-field approximationfor the kinetic exchange model and assuming the spin-orbit coupling to be ofthe Rashba form, we derive Boltzmann scattering integrals for the distributionsand spin coherences in the case of an antiferromagnetic exchange splitting,including a careful analysis of the connection between lifetime broadening andthe magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extractdephasing and magnetization times T_1 and T_2 from initial conditionscorresponding to a tilt of the magnetization vector, and draw a comparison tophenomenological equations such as the Landau-Lifshitz or the Gilbert damping.We also analyze magnetization precession and damping for this system includingan anisotropy field and find a carrier mediated dephasing of the localized spinvia the mean-field coupling.

Magnetization dynamics and damping due to electron-phonon scattering in a ferrimagnetic exchange model