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

TLDR

The study aims to understand the anomalous metallic state of iron‑pnictide parent compounds from a strong‑coupling perspective, incorporating orbital degrees of freedom. Using an intermediate‑spin Fe²⁺ model, the authors derive a Kugel‑Khomskii spin‑orbital Hamiltonian for the t₂g orbitals, compute its classical phase diagram, and analyze spin‑only and orbital‑only limits to explain phase stability. The resulting frustrated spin‑orbital model predicts a stable spin‑stripe phase with accompanying orbital‑ferro or orbital‑stripe order that breaks in‑plane symmetry, and the calculated magnetic excitation spectra show a reduced ordered moment, suggesting these orbital patterns could be detected by resonant X‑ray diffraction.

Abstract

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 ${\text{Fe}}^{2+}$ 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 in the ordered moment, and point out that the proposed orbital ordering pattern can be measured in resonant x-ray diffraction.