Vacancy Driven Orbital and Magnetic Order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$

TL;DR

This study explores how Fe vacancy ordering influences orbital and magnetic properties in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$, revealing enhanced correlations, orbital order, and a novel inverse relation between orbital polarization and magnetic moments.

Contribution

It introduces a three-orbital model showing vacancy order induces orbital order and magnetic phases, and predicts doping-driven spin and orbital state transitions.

Findings

Vacancy order enhances electron correlations and magnetic moments.

Orbital degeneracy is broken, leading to orbital order.

Doping induces a transition from high-spin to low-spin states.

Abstract

We investigate the effects of the $\sqrt{5}\times\sqrt{5}$ Fe vacancy ordering on the orbital and magnetic order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$ using a three-orbital ($t_{2g}$) tight-binding Hamiltonian with generalized Hubbard interactions. We find that vacancy order enhances electron correlations, resulting in the onset of a block antiferromagnetic phase with large moments at smaller interaction strengths. In addition, vacancy ordering modulates the kinetic energy differently for the three $t_{2g}$ orbitals. This results in a breaking of the degeneracy between the $d_{xz}$ and $d_{yz}$ orbitals on each Fe site, and the onset of orbital order. Consequently, we obtain a novel inverse relation between orbital polarization and the magnetic moment. We predict that a transition from high-spin to low-spin states accompanied by a crossover from orbitally-disordered to orbitally-ordered states will be driven by doping the parent compound with electrons, which can be verified by neutron scattering and soft X-ray measurements.