Interplay of orbital and spin ordering in the iron pnictides

A number of recent experiments exhibit electronic anisotropy in the iron pnictides, and there is a growing body of experimental evidence that its origin is related to orbital ordering in Fe d_{xz} and d_{yz} orbitals. We examine this problem in the parent compounds of the iron pnictides by a combination of ab initio band theory calculations, phenomenological Ginzburg-Landau theory of coupled orbital and magnetic order parameters, and a microscopic mean-field study of the Kugel-Khomskii model. We find that orbital ordering is sufficient to explain a number of key experimental observations, in particular a linear correlation between the orthorhombic lattice distortion and the magnetic ordered moment. We predict that orbital polarization should scale as a square of magnetic moment close to T_N. Mediated by orbital polarization, the effective spin-spin exchange interactions develop anisotropy in the ab-plane, in accord with recent neutron scattering measurements.