  We study collective spin excitations of a magnetically ordered state in a
multi-component system composed of both itinerant electrons and local moments.
Here the induced spin-density-wave (SDW) ordering of itinerant electrons and
the collinear antiferromangetic (AF) ordering of local moments are locked
together via a Hund's rule coupling. We show that the Goldstone theorem still
holds at the RPA level with the gapless spin wave protected inside the small
SDW gap of itinerant electrons, which, however, is fragile in the presence of
ion-anisotropy. A gapped out-of-phase spin mode extending over a much wider
energy scale above the SDW gap is found to be more robust against the
ion-anisotropy, which is mainly contributed by the local moment fluctuations.
While the scattering between the Goldstone mode and itinerant electrons
diminishes within the SDW gap, the out-of-phase mode will strongly interact
with itinerant electrons and thus dominate the spin and charge dynamics in such
an ordered phase. Possible relevance of such a model to the iron-pnictides will
be also discussed.
