Crystal symmetry and magnetic order in iron pnictides: A tight-binding Wannier function analysis

To perform a local-orbital analysis of electronic and magnetic interactions, we construct the Wannier functions (WFs) of the $\text{Fe}3d$ orbitals in the parent compound of the recently discovered iron-pnictide superconductors, LaFeAsO, and a comparison material LaFePO. Comparing the WFs for the stripe antiferromagnetic order with those for no magnetic order, the difference is a significant spreading (delocalization) of specifically the $d_{xy}$ and $d_{xz}$ (but not $d_{yz}$) WFs, where parallel Fe spins lie along the $x$ direction. The WF basis gives a tight-binding representation of the first-principles, density-functional based Fe-derived bands. Comparing hopping parameters, it is found that changes due to stripe antiferromagnetism, even if it is weak, enables more isotropic hopping involving spin-majority electrons in the $\text{Fe}3d_{xz}$ (but not the $3d_{yz}$) orbital. This change, counterintuitively, actually reinforces electronic anisotropy. Further insight is gained by comparing the WFs of LaFeAsO and LaFePO, identifying how the difference in WFs is related to the difference in hopping integrals and showing how the pnictide atom is influential in forming the stripe antiferromagnetism. Kinetic-energy considerations suggest that orbital fluctuation, in addition to spin fluctuation, may contribute to the decrease in observed ordered moment compared to the calculated values.

Figure 1

(Color online) LaFeAsO band structure with highlighted $\text{Fe}3d_{yz}$ and $\text{Fe}3d_{xz}$ fatband characters in the NM (top panel) and ${\text{Q}}_M$ AFM (bottom panel) phases. Compared to the NM phase, the $\text{Fe}3d_{xz}$ bands near Fermi level in the ${\text{Q}}_M$ AFM phase, especially along $\Gamma \text{-X}$ and $\Gamma \text{-Y}$ directions, change dramatically due to the formation of the stripe antiferromagnetism with large ordered Fe magnetic moment of $1.9{\mu }_B$.

Figure 2

(Color online) LaFePO band structure with highlighted $\text{Fe}3d_{yz}$ and $\text{Fe}3d_{xz}$ fatband characters in the NM (top panel) and ${\text{Q}}_M$ AFM (bottom panel) phase. Compared to LaFeAsO, the $\text{Fe}3d_{xz}$ bands near Fermi level in the ${\text{Q}}_M$ AFM phase change less significantly from the NM phase, due to the relatively small ordered Fe magnetic moment of $0.5{\mu }_B$.

Figure 3

(Color online) Possible orbital orderings of iron in iron pnictides. Left panel: both (a) and (b) form the ${\text{Q}}_M$ AFM ordering. However, (a) is favored because it gains more kinetic energy from nearest-neighbor hoppings according to second-order perturbation theory (see text). Right panel (from top to bottom) shows the simplified symbols for $\text{Fe}3d_{yz}$ and $\text{Fe}3d_{xz}$ orbitals, the chosen $x$ and $y$ directions, up arrows for spin-up electrons and down arrows for spin-down electrons, where black arrows (inside the vertical ellipses) for $3d_{yz}$ orbital and red arrows (outside the vertical ellipses) for $3d_{xz}$ orbital.

Figure 4

(Color online) LaFeAsO Wannier functions of $\text{Fe}3d$ orbitals in the NM phase (top panel) and those for the majority spin in ${\text{Q}}_M$ AFM phase (bottom panel). The Wannier functions of $\text{Fe}3d$ orbitals for the minority spin in the ${\text{Q}}_M$ AFM phase remain almost the same as in the NM phase. The important difference to be observed is that in the ${\text{Q}}_M$ AFM phase, the (majority-spin) Wannier functions of $3d_{xz}$ and $3d_{xy}$ orbitals (and only these) are more extended, with much increased density at neighboring As sites. The isosurface has the same value (density) in each panel.