Orbital-weight redistribution triggered by spin order in the pnictides

The one-particle spectral function and its orbital composition are investigated in a three-orbital model for the undoped parent compounds of the iron-based superconductors. In the realistic parameter regime, where results fit experimental data best, it is observed that the magnetization in the $xz$ and $yz$ orbitals are markedly different and the Fermi surface presents mostly $xz$ character, as recently observed in photoemission experiments [T. Shimojima et al., Phys. Rev. Lett. 104, 057002 (2010)]. Since the ferro-orbital order in this regime is at most a few percent, these results are mainly driven by the magnetic order. An analogous analysis for a five-orbital model leads to similar conclusions.

Figure 1

(Color online) Density of states of the $xz$ and $yz$ orbitals in the $\left(\pi ,0\right)$-AF phase of the three-orbital model at $U=0.7$ and $J=U/4$. For these values of $U$ and $J$, the orbital densities are $n_{xz}=n_{xz,\uparrow }+n_{xz,\downarrow }=1.590\approx n_{yz}=1.586$, and the magnetizations $m_{xz}=n_{xz,\uparrow }-n_{xz,\downarrow }=0.04⪡m_{yz}=0.15$. For $U=0$, $N\left(\omega \right)$ is identical for both orbitals (solid line). A Gaussian broadening with $\sigma =0.005$ was used. The inset illustrates the $\left(\pi ,0\right)$-AF order considered here and the $xz$, $yz$, and $xy$ orbitals (left to right).

Figure 2

(Color online) Contributions of the (a) $xz$ and (b) $yz$ orbitals to the Fermi surface for the three-orbital model at the same parameters as in Fig. 1. (c) and (d) show the superpositions of $xz$ and $yz$ as they would be expected to appear in the $s$ and $p$ polarizations, see text. The FS also has a small weight in the $xy$ orbital at the “tip” of the electron pocket (not shown).

Figure 3

(Color online) Orbital-dependent (a) magnetizations (in ${\mu }_{\text{B}}$) and (b) electronic densities of the five-orbital model varying the strength of the Coulomb repulsion $U$, at $J=U/4$. In (a), the total magnetization is also given. The gray area denotes the regime with small ordered magnetic moment and almost no FO order. Its lower boundary is given by the onset of a finite ordered moment. Since orbital order develops more gradually, its upper boundary was defined as the inflection point of the orbital densities, which coincides well with an inflection point in the magnetization.

Figure 4

(Color online) One-particle spectral function $A\left(\mathbf{k},\omega \right)$ for (a) the AF metal without orbital order and (b) the AF metal with moderate FO order at $U=1.6$. In (a), for $U=1.35$ and $J=U/4$, the total staggered magnetization is $m_{\text{tot}}=0.55{\mu }_{\text{B}}$, and the orbital contributions of the $xz$ and $yz$ orbitals are $m_{xz}=0.08{\mu }_{\text{B}}$ and $m_{yz}=0.18{\mu }_{\text{B}}$. The difference in the densities is $n_{xz}-n_{yz}=0.032$. In (b), for $U=1.6$ and $J=0.4$, $m_{\text{tot}}=2.52{\mu }_{\text{B}}$, $m_{xz}=0.37{\mu }_{\text{B}}$, and $m_{yz}=0.65{\mu }_{\text{B}}$; the difference in the densities is $n_{xz}-n_{yz}=0.26$. The thin black lines give the uncorrelated bands at $U=0$.