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Collective spin mode in a multi-component system of coupled itinerant and localized electrons

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.