Orbital order and spontaneous orthorhombicity in iron pnictides

A growing list of experiments show orthorhombic electronic anisotropy in the iron pnictides, in some cases at temperatures well above the spin-density-wave transition. These experiments include neutron scattering, resistivity and magnetoresistance measurements, and a variety of spectroscopies. We explore the idea that these anisotropies stem from a common underlying cause: orbital order manifest in an unequal occupation of $d_{xz}$ and $d_{yz}$ orbitals, arising from the coupled spin-orbital degrees of freedom. We emphasize the distinction between the total-orbital occupation (the integrated density of states), where the order parameter may be small and the orbital polarization near the Fermi level which can be more pronounced. We also discuss light-polarization studies of angle-resolved photoemission and demonstrate how x-ray absorption linear dichroism may be used as a method to detect an orbital-order parameter.

Figure 1

(Color online) (a) Resistivity anisotropy $\Delta \rho /\rho$ and (b) orbital polarization $⟨\delta n⟩$ as a function of the effective energy splitting ${\Delta }_{\text{eff}}$ between the $d_{xz}/d_{yz}$ orbitals calculated from the five-band model. (c) Anisotropy in the density of states with ${\Delta }_{\text{eff}}=0.1\text{eV}$; the arrow indicates the Fermi level at zero doping $x=0$. (d) $\Delta \rho /\rho$ and $⟨\delta n⟩$ versus the chemical potential $\mu$. Depending on the value of $\mu$, a substantial $\Delta \rho$ could result from a modest $⟨\delta n⟩$.

Figure 2

(Color online) (a) $A\left(\mathbf{k},\omega =E_F\right)$ in the paramagnetic phase plotted in the one Fe unit-cell BZ; the green box indicates the true two Fe unit-cell BZ. (b) $A\left(\mathbf{k},\omega =E_F\right)$ in the SDW phase; the blue box indicates the true four Fe unit-cell BZ. The shadow bands give rise to only weak spectral weight. (c) $A\left(\mathbf{k},\omega =E_F\right)$ in the SDW phase with orbital ordering $\left({\Delta }_{\text{eff}}=0.1\text{eV}\right)$. [(d)–(f)] The $d_{xz}$ projected spectral functions with SDW and various strength of orbital ordering. [(g)–(i)] Similar plots for the $d_{yz}$ orbital. When the SDW field is accompanied by a partial orbital ordering, the outer (inner) pocket is dominated by $d_{xz}$ $\left(d_{yz}\right)$ orbitals. All the plots are broadened with a 10 meV Lorentzian.

Figure 3

(Color online) (a) The $\text{Fe}{L}_3$-edge XAS for $x$ and $y$ polarization from FEFF calculation for ${\text{BaFe}}_2{\text{As}}_2$ in the low temperature $T=20\text{K}$ orthorhombic phase. The LD signal $\left(I_x-I_y\right)$ is multiplied by a factor of ten. (b) Atomic multiplet calculation with solely orbital ordering ${\Delta }_{\text{eff}}=0.1\text{eV}$ for $L_3$-edge XAS. In both cases, a $\sim 3\mathrm{\%}$ LD signal results. The structure distortion would saturate at low $T$ but the orbital polarization is expected to increase with decreasing $T$.