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 localized at the Mo3O13 clusters. While the former is found to exhibit a long-range antiferromagnetic order, the latter is more likely to reveal short-range order with quantum spin liquid-like excitations [1].
We have also studied the electronic structure of Mo trimers in LiZn2Mo3O8 by means of the hard x-ray photoemission spectroscopy. The Mo 3d5/2 core level peak is accompanied by a shoulder on the lower energy side, indicating that the shoulder and main peaks are derived from Mo3+ and Mo4+ species in the trimers being a direct experimental evidence of the Mo3+/Mo4+ charge fluctuations due to formation of molecular orbitals or intersite Coulomb interaction [2,3]. Importance of the spin-orbit coupling on magnetic properties (and in particular on anisotropy of the exchange interaction) of Mo3O8 quantum systems will be also discussed.
We will also discuss possibility of a spin-liquid state realization in various Kitaev materials.
The work is supported by the grant RSF 23-12-00159.
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