Evidence of low-energy singlet excited states in the spin- 1 2 polyhedral clusters { M o 72 V 30 } and { W 72 V 30 } with strongly frustrated kagome 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 ${\mathrm{M}{\mathrm{o}}_{72}{\mathrm{V}}_{30}}$ and ${{\mathrm{W}}_{72}{\mathrm{V}}_{30}}$. The clusters provide unique model systems of a kagom\'e network on a quasisphere. 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 the two clusters with differing structural symmetries. In ${{\mathrm{W}}_{72}{\mathrm{V}}_{30}}$ with ${I}_{\mathrm{h}}$ symmetry, the existence of several tens of low-energy singlet excited states below the lowest triplet excited state is revealed. The specific heat of the slightly distorted ${\mathrm{M}{\mathrm{o}}_{72}{\mathrm{V}}_{30}}$ with ${D}_{5\mathrm{h}}$ 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.