Dzyaloshinskii-Moriya Interaction between Multipolar Moments in $5d^1$ Systems

TL;DR

This paper introduces a new form of Dzyaloshinskii-Moriya interactions acting on high-rank multipolar moments in 5d^1 systems with broken inversion symmetry, revealing their dependence on lattice structure and spin-orbit coupling.

Contribution

It proposes and numerically demonstrates the existence of DM interactions for multipolar moments in 5d^1 systems, a novel extension beyond conventional spin interactions.

Findings

DM interactions for multipoles have finite expectation values.

Dependence of DM interactions on lattice structure and spin-orbit coupling is significant.

Perturbative analysis explains the behavior in different spin-orbit coupling regimes.

Abstract

We propose a new type of Dzyaloshinskii-Moriya (DM) interactions which act on high-rank multipolar moments such as quadrupolar and octupolar moments. Here we consider 5d1 systems with broken spatial inversion symmetry, where the interplay of electron correlation, the spin-orbit coupling, and inversion symmetry breaking plays a crucial role. Using a numerical diagonalization on a two-site multiorbital Hubbard model, we reveal that anti-symmetric products of multipole operators have finite expectation values, indicating the existence of DM interactions for multipoles. We also find that the spin-orbit coupling dependences of DM interactions for multipoles are significantly different depending on the lattice structure. Finally, we discuss the numerical results for small and large spin-orbit coupling region by using perturbative analysis.