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

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