Motivated by recent developments in the study of quasi-one-dimensional iron systems with ${\mathrm{Fe}}^{2+}$, we comprehensively study an ${\mathrm{Fe}}^{3+}$ chalcogenide chain system. Based on first-principles calculations, the ${\mathrm{Fe}}^{3+}$ chain has a similar electronic structure to that discussed before for the ${\mathrm{Fe}}^{2+}$ chain, because of the similar $\mathrm{Fe}{X}_4$ ($X=\mathrm{S}$ or Se) tetrahedron-chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation $U/W$ region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons ($U$ is the on-site Hubbard repulsion, while $W$ is the electronic bandwidth) based on the orbital-selective behavior observed in the charge fluctuations. Furthermore, we do not observe any obvious pairing tendency in the ${\mathrm{Fe}}^{3+}$ chain in the electronic-correlation $U/W$ region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the ${\mathrm{Fe}}^{3+}$ systems. Our results clearly establish the similarities and differences between ${\mathrm{Fe}}^{2+}$and ${\mathrm{Fe}}^{3+}$ iron chains, as well as iron ladders.

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• Density matrix renormalization group
• Electronic structure
• Magnetism
• 1-dimensional spin chains
• 1-dimensional systems
• Iron-based superconductors
• Magnetic systems
• Strongly correlated systems
• First-principles calculations
• Hubbard model