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The magnetic phase diagrams of models for quasi one-dimensional compoundsbelonging to the iron-based superconductors family are presented. Thefive-orbital Hubbard model and the real-space Hartree-Fock approximation areemployed, supplemented by density functional theory to obtain the hoppingamplitudes. Phase diagrams are constructed varying the Hubbard $U$ and Hund $J$couplings and at zero temperature. The study is carried out at electronicdensity (electrons per iron) $n = 5.0$, which is of relevance for the alreadyknown material TlFeSe$_2$, and also at $n = 6.0$, where representativecompounds still need to be synthesized. At $n = 5.0$ there is a clear dominanceof staggered spin order along the chain direction. At $n = 6.0$ and therealistic Hund coupling $J/U = 0.25$, the phase diagram is far richer includinga variety of ``block'' states involving ferromagnetic clusters that areantiferromagnetically coupled, in qualitative agreement with recent DensityMatrix Renormalization Group calculations for the three-orbital Hubbard modelin a different context. These block states arise from the competition betweenferromagnetic order (induced by double exchange, and prevailing at large $J/U$)and antiferromagnetic order (dominating at small $J/U$). The density of statesand orbital compositions of the many phases are also provided.

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