Magnetic states of the five-orbital Hubbard model for one-dimensional iron-based superconductors

The magnetic phase diagrams of models for quasi-one-dimensional compounds belonging to the iron-based-superconductor family are presented. The five-orbital Hubbard model and the real-space Hartree--Fock approximation are employed, supplemented by density functional theory to obtain the hopping amplitudes. Phase diagrams are constructed by varying the Hubbard $U$ and Hund $J$ couplings at zero temperature. The study is carried out at electronic density (electrons per iron) $n=5.0$, which is of relevance for the already-known material ${\mathrm{TlFeSe}}_{2}$, and also at $n=6.0$, where representative compounds still need to be synthesized. At $n=5.0$ there is a clear dominance of staggered spin order along the chain direction. At $n=6.0$ and with the realistic Hund coupling $J/U=0.25$, the phase diagram is far richer, including a variety of ``block'' states involving ferromagnetic clusters that are antiferromagnetically coupled, in qualitative agreement with recent density matrix renormalization group calculations for the three-orbital Hubbard model in a different context. These block states arise from the competition between ferromagnetic order (induced by double exchange and prevailing at large $J/U$) and antiferromagnetic order (dominating at small $J/U$). The density of states and orbital compositions of the many phases are also provided.