Magnetic States of the Two-Leg Ladder Alkali Metal Iron Selenides $A$Fe$_2$Se$_3$

TL;DR

This study uses theoretical models to confirm the stability of the block-AFM magnetic state in BaFe$_2$Se$_3$ and explores other competing magnetic phases, aligning with experimental findings and providing insights into their electronic and magnetic properties.

Contribution

The paper demonstrates the stability of the block-AFM state in two-leg ladder selenides using realistic models and explores other magnetic phases under doping and pressure.

Findings

Block-AFM state is stable at realistic electronic densities.

The CX state is close in energy and stable under doping.

Multiple competing magnetic phases can be stabilized experimentally.

Abstract

Recent neutron scattering experiments addressing the magnetic state of the two-leg ladder selenide compound BaFe$_2$Se$_3$ have unveiled a dominant spin arrangement involving ferromagnetically ordered 2$\times$2 iron-superblocks, that are antiferromagnetically coupled among them (the "block-AFM" state). Using the electronic five-orbital Hubbard model, first principles techniques to calculate the electronic hopping amplitudes between irons, and the real-space Hartree-Fock approximation to handle the many-body effects, here it is shown that the exotic block-AFM state is indeed stable at realistic electronic densities close to $n \sim 6.0$. Another state (the "CX" state) with parallel spins along the rungs and antiparallel along the legs of the ladders is close in energy. This state becomes stable in other portions of the phase diagrams, such as with hole doping, as also found experimentally via neutron scattering applied to KFe$_2$Se$_3$. In addition, the present study unveils other competing magnetic phases that could be experimentally stabilized varying either $n$ chemically or the electronic bandwidth by pressure. Similar results were obtained using two-orbital models, studied here via Lanczos and DMRG techniques. A comparison of the results obtained with the realistic selenides hoppings amplitudes for BaFe$_2$Se$_3$ against those found using the hopping amplitudes for pnictides reveals several qualitative similarities, particularly at intermediate and large Hubbard couplings.