Exchange Constants and Neutron Spectra of Iron Pnictide Materials

We show that the neutron scattering spectra observed in CaFe${}_2$As${}_2$ by Zhao et al (arXiv:0903.2686v1) and the highly unusual spatially anisotropic exchange constants in the iron pnictides derived by Han et al (Phys. Rev. Lett. 102, 107003 (2009)), using electronic structure calculations, can be explained by assuming a role for orbital order in these materials. We write down a simple model Hamiltonian with tertagonal symmetry, whose spin-wave spectra describes the observed dispersion relations. We further argue that these materials have orbital selective Mott transition, which is driven by superexchange between neighboring iron atoms. We suggest that reduced spin and quasi-one dimensionality and not frustration are responsible for the reduced moments in these materials.