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 superconductors 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 varying the Hubbard $U$ and Hund $J$ couplings and 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 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 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.