Orbital Dzyaloshinskii-Moriya Exchange Interaction

TL;DR

This paper introduces a novel orbital exchange interaction resembling the Dzyaloshinskii-Moriya interaction, derived from superexchange calculations in multi-orbital models with broken inversion symmetry, revealing complex orbital phases.

Contribution

It develops a superexchange framework for orbital interactions with symmetry-breaking electric fields, uncovering a new orbital Dzyaloshinskii-Moriya-like exchange term and rich phase diagrams.

Findings

Identification of a new orbital exchange term similar to Dzyaloshinskii-Moriya interaction.

Prediction of complex orbital phases including spiral and nematic orders.

Evidence for robust chiral-orbital order in spinful two-orbital models.

Abstract

Superexchange calculation is performed for multi-orbital band models with broken inversion symmetry. Orbital-changing hopping terms allowed by the symmetry breaking electric field lead to a new kind of orbital exchange term closely resembling the Dzyaloshinskii-Moriya spin exchange. The final superexchange Hamiltonian in two dimensions is expressed in terms of Gell-Mann matrices that break down as three spin operators and five nematic (quadrupole) order operators. Mean-field phase diagram exhibits a rich structure including anti-ferro-orbital, ferro-orbital, and both single and multiple spiral-orbital phases. Superexchange calculation for spinful, two-orbital model also strongly suggests a robust chiral-orbital order in the ground state.