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Molecular based spin-1/2 triangular lattice systems such asLiZn$_2$Mo$_3$O$_8$ have attracted research interest. Distortions, defects, andintersite disorder are suppressed in such molecular-based magnets, andintrinsic geometrical frustration gives rise to unconventional and unexpectedground states. Li$_2$$A$Mo$_3$O$_8$ ($A$ = In or Sc) is such a compound wherespin-1/2 Mo$_3$O$_{13}$ clusters in place of Mo ions form the uniformtriangular lattice. Their ground states are different according to the $A$site. Li$_2$InMo$_3$O$_8$ undergoes conventional $120^\circ$ long-rangemagnetic order below $T_\text{N}=12$~K whereas isomorphic Li$_2$ScMo$_3$O$_8$exhibits no long-range magnetic order down to 0.5~K. Here, we report exoticmagnetisms in Li$_2$InMo$_3$O$_8$ and Li$_2$ScMo$_3$O$_8$ investigated by muonspin rotation ($\mu$SR) and inelastic neutron scattering (INS) spectroscopiesusing polycrystalline samples. Li$_2$InMo$_3$O$_8$ and Li$_2$ScMo$_3$O$_8$ showcompletely different behaviors observed in both $\mu$SR and INS measurements,representing their different ground states. Li$_2$InMo$_3$O$_8$ exhibits spinwave excitation which is quantitatively described by the nearest neighboranisotropic Heisenberg model based on the $120^\circ$ spin structure. Incontrast, Li$_2$ScMo$_3$O$_8$ undergoes short-range magnetic order below 4~Kwith quantum-spin-liquid-like magnetic fluctuations down to the basetemperature. Origin of the different ground states is discussed in terms ofanisotropies of crystal structures and magnetic interactions.

Quantum magnetisms in uniform triangular lattices Li2AMo3O8 (A = In, Sc)