Spin dynamics in the generalized ferromagnetic Kondo model for manganites

Dynamical spin susceptibility is calculated for the generalized ferromagnetic Kondo model which describes itinerant $e_g$ electrons interacting with localized $t_{2g}$ electrons with antiferromagnetic coupling. The calculations done in the mean field approximation show that the spin-wave spectrum of the system in ferromagnetic state has two branches, acoustic and optic ones. Self-energy corrections to the spectrum are considered and the acoustic spin-wave damping is evaluated.