Orbital ordering induces structural phase transition and the resistivity anomaly in iron pnictides

We attribute the structural phase transition (SPT) in the parent compounds of the iron pnictides to orbital ordering. Due to the anisotropy of the $d_{xz}$ and $d_{yz}$ 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 stripelike antiferromagnetism and anisotropy of the magnetic exchange couplings. This model is quantitatively consistent with available experimental observations.

Figure 1

(Color online) (a) Equal numbers of $d_{xz}$ and $d_{yz}$ with a square lattice configuration. (b) Entirely $d_{yz}$ state with $a<b$. (c) Entirely $d_{xz}$ state with $a>b$. (d) Relative energy difference $\Delta$ between configurations (a) and (b), or (c), as a function of lattice distortion $\delta$. (Inset: an Ising-type transition where the order parameter $M$ is defined as the difference between the numbers of occupied $d_{xz}$ and $d_{yz}$ orbitals.)

Figure 2

(a) A schematic of a double-well potential as the classical analog of the two-level system. (b) Two types of scattering processes between the itinerant electrons and the localized states. $V^z$: diagonal scattering and $V^x$: off-diagonal scattering.

Figure 3

(Color online) (a) scaling of the coupling constants $v^i$ with respect to bandwidth $D$. (b) Energy gap and resistivity as a function of temperature $T$. (The experimental data of resistivity are extracted from Ref. 2.) Setting the resistivity at $T=150K$ of our model equal to that of the experiment was the only fitting parameter.

Figure 4

(Color online) Different possible spin configurations on a distorted lattice with $a<b$, which corresponds to the case that $d_{yz}$ is the majority orbital.