Molecular spin-liquid state in spin-3/2 frustrated spinel HgCr$_2$O$_4$

A hexamer-type spin excitation seen in spinel chromates $A$Cr$_2$O$_4$ ($A$ = Mg, Zn, or Cd) is the representative spin-liquid-like state caused by geometrical frustration. To clarify an origin of the state, we comparatively studied spin excitations in an isomorphic material HgCr$_2$O$_4$ by inelastic neutron scattering, and observed a different molecular-type excitation. Numerical analyses performed using model Hamiltonians suggest that these two types of spin excitations originate from a spin-3/2 molecular singlet hidden in a magnetically ordered phase. The difference between the molecular types is explained by the difference in the kind of exchange interactions occurring in the chromates.