Theory of electronic magnetoelectric coupling in $d^5$ Mott insulators

TL;DR

This paper develops a theoretical framework for understanding magnetoelectric effects in $d^5$ Mott insulators, explaining recent terahertz spectroscopy results in $ ext{RuCl}_3$ by deriving electric polarization mechanisms from a Hubbard model with strong spin-orbit coupling.

Contribution

The paper introduces a detailed theory for electronic magnetoelectric coupling in $d^5$ Mott insulators, including explicit calculations of polarization operators and mechanisms for different geometries.

Findings

Derived polarization mechanisms for edge-sharing and corner-sharing geometries.

Calculated coupling constants using perturbation theory and exact diagonalization.

Explained the strong electric-dipole contribution observed in $ ext{RuCl}_3$ terahertz measurements.

Abstract

Motivated by recent terahertz (THz) spectroscopy measurements in $\alpha$-RuCl$_3$, we develop a theory for magnetoelectric (ME) effects in Mott insulators of $d^5$ transition metal ions in an octahedral crystal field. For $4d$ and $5d$ compounds, the relatively wide-spread orbitals favor charge fluctuations of localized electrons to neighboring ions and a significant ME effect from electronic mechanisms is expected. From a three-orbital Hubbard model with strong spin-orbit coupling, we derive the mechanisms for the electric polarization originating from virtual hopping of the localized holes carrying the spins. We consider the electric polarization generated by pairs of spin operators on nearest neighbor bonds with either an edge-sharing geometry (i.e., two ligands are shared) or a corner-sharing geometry (i.e., one ligand is shared). The allowed couplings are first derived using a symmetry approach. Then, we explicitly calculate the coupling constants and evaluate the effective polarization operator in the ground state manifold using perturbation theory and exact diagonalization. The results are relevant when considering the THz optical conductivity of magnetic systems such as some perovskite iridates or Kitaev materials. In particular, they help explain the recent THz optical measurements of $\alpha$-RuCl$_{3}$ for which the electric-dipole-induced contribution has been shown to be strong.