Impact of Oxidation State on the Valence-bond-glass Physics in the lithium-intercalated Mo${}_3$O${}_8$ Cluster Mott Insulators

We have successfully synthesized four Mo${}_3$O${}_8$-type cluster Mott insulators (CMI) by intercalating lithium into nonmagnetic precursors to regulate the Mo${}_3$ cluster valence. The resulting materials are Li${}_{1+x}$$R$Mo${}_3$O${}_8$ ($R$ = Sc, Y, Lu) and Li${}_x$Zn${}_2$Mo${}_3$O${}_8$. Our magnetic susceptibility measurements revealed that these materials display characteristics akin to a valence bond glass state and suggest the presence of short-range ordering when the Mo${}_3$ cluster valence approximates its ideal value. These findings challenge the prevailing belief that the plaquette charge ordering state is an inherent feature of Mo${}_3$O${}_8$-type CMI. Instead, they underscore the importance of Mo${}_3$ cluster valence in determining the physical properties of these systems. These insights furnish a fresh understanding of the Mo${}_3$O${}_8$-type CMI and open new research opportunities in highly frustrated magnetism.