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Magnetization, specific heat, and electron spin resonance (ESR) measurementsare carried out to clarify the low-energy excitations for the S = 1/2polyhedral clusters {Mo$_{72}$V$_{30}$} and {W$_{72}$V$_{30}$}. The clustersprovide unique model systems of Kagom\'e network on a quasi-sphere. The linearfield variation of magnetization at low temperatures indicates that the groundstate is singlet for both clusters. The temperature and the magnetic fielddependence of specific heat shows a distinct difference between two clusterswith differing structural symmetries. In {W$_{72}$V$_{30}$} with I$_h$symmetry, the existence of the several tens of low-energy singlet excitedstates below the lowest triplet excited state is revealed. The specific heat ofthe slightly distorted {Mo$_{72}$V$_{30}$} with D$_{5h}$ symmetry leads to adrastic decrease of the singlet contribution, which is consistent with thepartial lifting of the frustration and the decrease of degenerated low-energystates. The singlet excitation existence is confirmed further by thetemperature dependence of the ESR spectra. Comprehensive experimental studieshave demonstrated unique low-energy excitations of the spherical Kagom\'enetworks and their sensitivity to the cluster symmetry.

physical review. b./physical review. b

Evidence of Low-Energy Singlet Excited States in the Spin-1/2 Polyhedral  Clusters {Mo$_{72}$V$_{30}$} and {W$_{72}$V$_{30}$} with Strongly Frustrated  Kagom\'e Networks