Cluster Mott insulators and two Curie-Weiss regimes on an anisotropic kagome lattice

Motivated by recent experiments on the quantum-spin-liquid candidate material ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, we study a single-band extended Hubbard model on an anisotropic kagome lattice with the $\frac{1}{6}$ electron filling. Due to the partial filling of the lattice, the intersite repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters rather than at lattice sites. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. The nature of charge excitations in cluster Mott insulators can be quite different from conventional Mott insulator and we show that there exists a cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only $\frac{1}{3}$ of the total spinon excitations are magnetically active. Based on these results, we propose that the two Curie-Weiss regimes of the spin susceptibility in ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.