We attribute the structural phase transition (SPT) in the parent compounds of the iron pnictides to orbital ordering. Due to the anisotropy of the dxz and dyz orbitals in the xy plane, a ferro-orbital ordering makes the orthorhombic structure more energetically favorable, thus inducing the SPT. In this orbital-ordered system, the sites with orbitals that do not order have higher energies. Scattering of the itinerant electrons by these localized two-level systems causes a resistivity anomaly upon the onset of the SPT. The proposed orbital ordering also leads to the stripe-like anti-ferromagnetism and anisotropy of the magnetic exchanges. This model is quantitatively consistent with available experimental observations.

The magnetic excitations of the iron pnictides are explained within a degenerate double-exchange model. The local-moment spins are coupled by superexchanges J1 and J2 between nearest and next-nearest neighbors, respectively, and interact with the itinerant electrons of the degenerate dxz and dyz orbitals via a ferromagnetic Hund exchange. The latter stabilizes (π, 0) stripe antiferromagnetism due to emergent ferro-orbital order and the resulting kinetic energy gain by hopping preferably along the ferromagnetic spin direction. Taking the quantum nature of the spins into account, we calculate the magnetic excitation spectra in the presence of both, super-and doubleexchange. A dramatic increase of the spin-wave energies at the competing Néel ordering wave vector is found, in agreement with recent neutron scattering data. The spectra are fitted to a spin-only model with a strong spatial anisotropy and additional longer ranged couplings along the ferromagnetic chains. Over a realistic parameter range, the effective couplings along the chains are negative corresponding to unfrustrated stripe antiferromagnetism.

Recent experimental developments in the iron pnictides have unambiguously demonstrated the existence of in-plane electronic anisotropy in the absence of the long-range magnetic order. Such anisotropy can arise from orbital ordering, which is described by an energy splitting between the two otherwise degenerate dxz and dyz orbitals. Including this phenomenological orbital order into a fiveorbital Hubbard model, we obtain the mean-field solutions where the magnetic order is determined self-consistently. Despite sensitivity of the resulting states to the input parameters, we find that a weak orbital order that places the dyz orbital slightly higher in energy than the dxz orbital combined with intermediate on-site interactions produces band dispersions that are compatible with the photoemission results. In this regime, the stripe antiferromagnetic order is further stabilized and the resistivity displays the observed anisotropy. We also calculate the optical conductivity and show that it agrees with the temperature evolution of the anisotropy seen experimentally.

We use inelastic neutron scattering to study spin waves in the antiferromagnetic ordered phase of iron pnictide NaFeAs throughout the Brillouin zone. Comparing with the well-studied AFe 2 As 2 (A ¼ Ca, Sr, Ba) family, spin waves in NaFeAs have considerably lower zone boundary energies and more isotropic effective in-plane magnetic exchange couplings. These results are consistent with calculations from a combined density functional theory and dynamical mean field theory and provide strong evidence that pnictogen height controls the strength of electron-electron correlations and consequently the effective bandwidth of magnetic excitations.

Motivated by recent neutron scattering experiments in Fe-based superconductors, we study how the magnetic resonance in the superconducting state is affected by the simultaneous presence of either static or fluctuating magnetic orders using the random phase approximation. We find that for the underdoped materials with coexisting superconducting and antiferromagnetic orders, spin rotational symmetry is explicitly broken at the ordering momentum Q1 = (π, 0). Only the longitudinal susceptibility exhibits the resonance mode, whereas a spin-wave Goldstone mode develops in the transverse component. Meanwhile, at the frustrated momentum Q2 = (0, π), the susceptibility becomes isotropic in spin space and the magnetic resonance exists for both components. Furthermore, the resonance energies at Q1 and Q2 have distinct scales, which provide a natural explanation for the recently observed double resonance peaks. In addition, we show that near optimal doping the existence of strong magnetic fluctuations, which are modeled here via a Gaussian mode, can still induce the spin anisotropy in the magnetic susceptibility.