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We calculate the magnetic and quasiparticle excitation spectra of anitinerant $J_1-J_2$ model for iron pnictides. In addition to an acousticspin-wave branch, the magnetic spectrum has a second, optical branch, resultingfrom the coupled four-sublattice magnetic structure. The spin-wave velocity hasalso a planar directional anisotropy, due to the collinear/stripedantiferromagnetism. Within the magnetically ordered phase, the quasiparticlespectrum is composed of two Dirac cones, resulting from the folding of themagnetic Brillouin zone. We discuss the relevance of our findings to theunderstanding of both neutron scattering and photoemission spectroscopy resultsfor SrFe$_{2}$As$_{2}$.

Magnetic and Quasiparticle Excitation Spectra of an Itinerant $J_1-J_2$ Model for Iron Pnictide Superconductors