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.

我们揭示了Mo ₃ O ₈量子系统中引起广泛争议的磁性的微观起源。考虑到在1/6处填充由Mo原子形成的各向异性Kagomé晶格的扩展Hubbard模型时，我们认为其基态是由动能和站点间库仑相互作用之间的竞争决定的，而竞争是由Kagomé的三聚作用控制的。晶格形成Mo ₃ O ₁₃簇，以及跳跃参数的符号，指定了电子在这些簇上的位置。基于第一性原理计算，我们表明强相互作用极限揭示了在LiZn ₂ Mo中可以实现的共振六边形上不成对自旋的球状电荷顺序₃ O ₈，与所有以前的情况相比，其起源仅与集群内和集群间跳变的相反符号有关。另一方面，证明了Li ₂ InMo ₃ O ₈和Li ₂ ScMo ₃ O ₈都落入弱相互作用极限，在弱相互作用极限中，电子很好地定位在Mo ₃ O ₁₃簇上。虽然发现前者表现出远距离的反铁磁顺序，但后者更可能在量子自旋液体状激发下显示近距离的顺序。我们的结果不仅重现了Mo ₃ O的大多数实验观察到的特征_8个系统，但也将有助于描述其他量子簇磁体中的各种特性。