Quantum spin liquid and cluster Mott insulator phases in the Mo3O8 magnets

S A Nikolaev,S V Streltsov,I V Solovyev

doi:10.1038/s41535-021-00316-7

Abstract

We unveil the microscopic origin of largely debated magnetism in the Mo3O8 quantum systems. Upon considering an extended Hubbard model at 1/6 filling on the anisotropic kagomé lattice formed by the Mo atoms, we argue that its ground state is determined by the competition between kinetic energy and intersite Coulomb interactions, which is controlled by the trimerisation of the kagomé lattice into the Mo3O13 clusters, and the sign of hopping parameters, specifying the electron localisation at such clusters. Based on first-principles calculations, we show that the strong interaction limit reveals a plaquette charge order with unpaired spins at the resonating hexagons that can be realised in LiZn2Mo3O8, and whose origin is solely related to the opposite signs of intracluster and intercluster hoppings, in contrast to all previous scenarios. On the other hand, both Li2InMo3O8 and Li2ScMo3O8 are demonstrated to fall into the weak interaction limit where the electrons are well localised at the Mo3O13 clusters. While the former is found to exhibit long-range antiferromagnetic order, the latter is more likely to reveal short-range order with quantum spin liquid-like excitations. Our results not only reproduce most of the experimentally observed features of the Mo3O8 systems, but will also help to describe various properties in other quantum cluster magnets.

Highlights

Frustrated quantum systems lie at the core of research activity revolving around a putative quantum spin liquid (QSL) state that displays long-range quantum entanglement, charge fractionalisation and emergent gauge structures[1,2,3,4]
Having considered an extended Hubbard model on the anisotropic kagomé lattice at 1/6 filling as the low-energy model for the Mo3O8 cluster magnets, we showed that it features two different limits: a PCO of resonating hexagons with valence bond condensation and orphan spins, as realised in quantum paramagnet LiZn2Mo3O8, and a cluster Mott insulator with the electrons localised at the kagomé triangles, as revealed in Li2InMo3O8 and Li2ScMo3O8 showing a Néel-type antiferromagnetic order and QSL behaviour, respectively
We demonstrated that their manifestation can be attributed to the trimerisation of the kagomé lattice controlling the competition between kinetic energy and intersite Coulomb interactions and specifying the character of electron localisation at the Mo3O13 clusters, that can help to unravel a largely speculated origin of magnetism in these systems

Summary

INTRODUCTION

Frustrated quantum systems lie at the core of research activity revolving around a putative quantum spin liquid (QSL) state that displays long-range quantum entanglement, charge fractionalisation and emergent gauge structures[1,2,3,4]. Since U is not operative, it is the intersite V and V0 that are responsible for electron localisation leading to a highly degenerate charge ordered state, where each corner-sharing triangle hosts exactly one electron This degeneracy is further lifted by hopping parameters that induce collective tunnelling processes, when the electrons hop either clockwise or counter-clockwise along the T and T 0 bonds stabilising a charge pattern with three electrons at the hexagons, as shown, b. Eq (2) and schematically shown, the resulting ground state of the resonating hexagon is given as a superposition of the plaquette states jAi and jBi, each having valence bonds resonating in the hexagon and leaving one spin unpaired, whose location is smeared out in the hexagon owing to the resonating nature of valence bonds Such an unusual entanglement with dangling spins originates solely from the asymmetry of tunnelling processes that, in turn, facilitates partial singlet pairing between the resonating electrons, while the unpaired spins behave paramagnetically in a thermodynamic limit.

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DISCUSSION

METHODS