Antiferromagnetic Order in Multiband Hubbard Models for Iron Pnictides

We investigate multiband Hubbard models for the three iron $3d$ $t_{2g}$ bands and the two iron $3d$ $e_g$ bands in LaOFeAs by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Hartree-Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree-Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hund’s-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron $e_g$ electrons polarize the $t_{2g}$ electrons and they substantially contribute to the ordered moment.

Figure 1

Orbital densities in GT (full symbols) and in DMFT [6] (open symbols) as a function of $U=4J$ for the simplified local Hamiltonian ${\widehat{H}}_C={\widehat{H}}_C^{(1)}$; see (2).

Figure 2

Local charge distribution (a) and spin distribution (b) for the paramagnetic optimized Gutzwiller wave function (GT) for $U=2.6\mathrm{eV}$, $J=0.4\mathrm{eV}$ (left columns) and for the paramagnetic Hartree-Fock (HF) wave function (right columns), which is identical to the noninteracting Fermi-gas state.

Figure 3

Magnetic moments in the five-band model in Hartree-Fock (HFT) and Gutzwiller theory as a function of $J$ for $U=2.2,2.6,3.0\mathrm{eV}$.

Figure 4

Magnetic moments for the three-band model as a function of $J$ for $U=2.2,2.6,3.0\mathrm{eV}$. Full symbols, GT with the full local interaction ${\widehat{H}}_C={\widehat{H}}_C^{(1)}$ (2); open symbols, GT with density-interactions only, ${\widehat{H}}_C={\widehat{H}}_C^{\mathrm{dens}}$, cf. 18.