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

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.

arXiv comment8 pages, 10 figures

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Cited by in corpus (3)

• Interplay between multipolar spin interactions, Jahn-Teller effect and electronic correlation in a $J_{eff}=\frac{3}{2}$ insulator
• Modelling Magnetic Multipolar Phases in Density Functional Theory
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States