Raman scattering in ZrB$_{12}$ cage glass

High-precision measurements of the Hall effect and Raman scattering have been performed for single crystals of ZrB$_{12}$ superconductor in the wide temperature range of $5$–$300$ K. For ZrB$_{12}$, the boson peak with $\omega_{\mathrm{max}} \sim 100$ cm$^{-1}$ has been observed for the first time within the low-frequency range of the Raman spectrum $I(\omega)$. The sizes of vibrational clusters with the correlation length ranging from $25$ to $35$ Å are estimated. The relation between the renormalization of the low-frequency density of vibrational states accompanying the transition to the cage-glass phase ($T^*\sim90$ K) and the enhancement of superconductivity in ZrB$_{12}$ is discussed.