Spin Singlet Formation from S = 1/2 Tetrahedral Clusters

Muon spin relaxation ($\mu$SR) and nuclear magnetic resonance (NMR) experiments revealed that the spin singlet state with an excitation gap of $\sim$200 K is realized from $S = 1/2$ Nb$_4$ tetrahedral clusters in a cluster Mott insulator GaNb$_4$S$_8$. The intercluster cooperative phenomenon to the singlet state at $T_\mathrm{S} = 32$ K is triggered by intracluster Jahn-Teller type structural instability developed from $\sim$$3T_\mathrm{S}$. Referring to the lattice symmetry, the formation of Nb$_8$ octamer (Nb$_4$--Nb$_4$ bond) is suggested.