A Green function technique is used to study the anharmonic spin-phonon
and phonon-phonon interaction effects on optical phonon modes and spi
n-wave excitations in ferromagnetic semiconductors. The cubic spinels
have been investigated because the magnetostriction of these compounds
is small and the direct contribution of spin ordering to the phonon m
odes can be clearly observed. The phonon and spin-wave energy and damp
ing are evaluated for the first time beyond the random-phase approxima
tion. The temperature dependence of these quantities is discussed and
is found to be in good agreement with the experimental data.