Evidence of Low-Energy Singlet Excited States in the Spin-1/2 Polyhedral Clusters {Mo₇₂V₃₀} and {W₇₂V₃₀} with Strongly Frustrated Kagom\'e Networks

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