Spin-orbital frustrations and anomalous metallic state in iron-pnictide superconductors

We develop an understanding of the anomalous metal state of the parent compounds of recently discovered iron based superconductors starting from a strong coupling viewpoint, including orbital degrees of freedom. On the basis of an intermediate-spin (S=1) state for the Fe^{2+} ions, we derive a Kugel-Khomskii spin-orbital Hamiltonian for the active t_{2g} orbitals. It turns out to be a highly complex model with frustrated spin and orbital interactions. We compute its classical phase diagrams and provide an understanding for the stability of the various phases by investigating its spin-only and orbital-only limits. The experimentally observed spin-stripe state is found to be stable over a wide regime of physical parameters and can be accompanied by three different types of orbital orders. Of these the orbital-ferro and orbital-stripe orders are particularly interesting since they break the in-plane lattice symmetry -- a robust feature of the undoped compounds. We compute the magnetic excitation spectra for the effective spin Hamiltonian, observing a strong reduction of the ordered moment, and point out that the proposed orbital ordering pattern can be measured in resonant X-ray diffraction.