Nearly unfrustrated stripe antiferromagnetism in the pnictides as a consequence of orbital ordering induced by degenerate double exchange

We propose a local-itinerant theory to explain the anisotropic electronic and magnetic properties of the iron pnictides. The localized spins are described by an isotropic, strongly frustrated $J_1$-$J_2$ Heisenberg model, forming a $(\pi,0)$ stripe antiferromagnetic ground state. We further introduce a strong Hund's coupling between the local moments and the itinerant bands of the degenerate $d_{xz}$ and $d_{yz}$ orbitals. Due to the kinetic energies gained by hopping along the ferromagnetic direction, the electrons form an orbitally ordered nematic state. By calculating the spin-wave dispersion in the presence of both superexchange and double exchange, we find that the orbital order leads to a stabilization of the stripe antiferromagnetism and to a dramatic increase of the spin-wave energies at $(\pi,\pi)$ of the competing N\'eel order. The spectra are in good agreement with recent neutron scattering data and suggest a strong anisotropy of the magnetic exchanges on the level of an effective spin-only model.