Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters

Abstract

Motivated by recent synthetic and theoretical progress we consider magnetism in crystals of multi-nuclear organometallic complexes. We calculate the Heisenberg symmetric exchange and the Dzyaloshinskii-Moriya antisymmetric exchange. We show how, in the absence of spin-orbit coupling, the interplay of electronic correlations and quantum interference leads to a quasi-one dimensional effective spin model in a typical tri-nuclear complex, Mo${}_3$S${}_7$(dmit)${}_3$, despite its underlying three dimensional band structure. We show that both intra- and inter-molecular spin-orbit coupling can cause an effective Dzyaloshinskii-Moriya interaction. Furthermore, we show that, even for an isolated pair of molecules the relative orientation of the molecules controls the nature of the Dzyaloshinskii-Moriya coupling. We show that interference effects also play a crucial role in determining the Dzyaloshinskii-Moriya interaction. Thus, we argue, that multi-nuclear organometallic complexes represent an ideal platform to investigate the effects of Dzyaloshinskii-Moriya interactions on quantum magnets.

This update incorporates the corrections described in a recently submitted erratum. Changes are confined to sections IV.A and B. The conclusions of the paper are unchanged. 12 + 4 pages, 9 figures

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Cited by in corpus (13)

• Interplay of dipoles and spins in $\kappa$-(BEDT-TTF)${}_{2}X$, where $X=$ Hg(SCN)${}_2$Cl, Hg(SCN)${}_2$Br, Cu[N(CN)${}_2$]Cl, Cu[N(CN)${}_2$]Br, and Ag${}_2$(CN)${}_3$
• Spin-orbit coupling in {Mo${}_3$S${}_7$(dmit)${}_3$}
• Spin-$0$ Mott insulator to metal to spin-$1$ Mott insulator transition in the single-orbital Hubbard model on the decorated honeycomb lattice
• Multiple insulating phases due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model
• From quantum anomalous Hall phases to topological metals in interacting decorated honeycomb lattices
• Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes
• Unconventional superconductivity near a flat band in organic and organometallic materials
• Topological superconductivity from doping a triplet quantum spin liquid in a flat band system
• Magnetism and topological phases in an interacting decorated honeycomb lattice with spin-orbit coupling
• A theory of the quantum spin liquid in the hyper-honeycomb metal-organic framework [(C${}_2$H${}_5$)${}_3$NH]${}_2$Cu${}_2$(C${}_2$O${}_4$)${}_3$ from first principles
• Spin molecular-orbit coupling and magnetic properties of the decorated honeycomb layers of Mo3S7(dmit)3 crystals
• Gapless spinons and a field-induced soliton gap in the hyper-honeycomb Cu oxalate framework compound [(C${}_2$H${}_5$)${}_3$NH]${}_2$Cu${}_2$(C${}_2$O${}_4$)${}_3$
• General structure factor and dynamic effects of the Dzyaloshinskii-Moriya interaction in S = 1/2 clusters