Study of the magnetic state of K$_{0.8}$Fe$_{1.6}$Se$_2$ using the five-orbital Hubbard model in the Hartree-Fock approximation

TL;DR

This study uses a five-orbital Hubbard model in the Hartree-Fock approximation to analyze the magnetic state of K$_{0.8}$Fe$_{1.6}$Se$_2$, revealing an insulating phase with a specific spin pattern consistent with experimental observations.

Contribution

It introduces a detailed phase diagram for the five-orbital Hubbard model, capturing magnetic states and local tendencies aligned with experimental and Lanczos results.

Findings

Identifies an insulating state with a 2x2 ferromagnetic plaquette pattern.

Magnetic moments around 3μ_B/Fe match experimental data.

Reveals multiple phases consistent with phenomenological models.

Abstract

Motivated by the recent discovery of Fe-based superconductors close to an antiferromagnetic insulator in the experimental phase diagram, here the five-orbital Hubbard model (without lattice distortions) is studied using the real-space Hartree-Fock approximation, employing a 10x10 Fe cluster with Fe vacancies in a $\sqrt{5}x\sqrt{5}$ pattern. Varying the Hubbard and Hund couplings, and at electronic density $n$=6.0, the phase diagram contains an insulating state with the same spin pattern as observed experimentally, involving 2x2 ferromagnetic plaquettes coupled with one another antiferromagnetically. The presence of local ferromagnetic tendencies is in qualitative agreement with Lanczos results for the three-orbital model also reported here. The magnetic moment ~ 3$\mu_B$/Fe is in good agreement with experiments. Several other phases are also stabilized in the phase diagram, in agreement with recent calculations using phenomenological models.