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We argue that salient experimental features of the magnetic excitations inthe SDW phase of iron-based superconductors can be understood within anitinerant model. We identify a minimal itinerant model and use a multi-band RPAtreatment of the dynamical spin susceptibility. Weakly-damped spin-waves arefound near the ordering momentum and it is shown how they dissolve into theparticle-hole continuum. We show that ellipticity of the electron bandsaccounts for the anisotropy of the spin waves along different crystallographicdirections and the gap at the momentum conjugated to the ordering one. We arguethat our theory agrees well with the neutron scattering data.

Theory of itinerant magnetic excitations in the SDW phase of iron-based superconductors