Anomalous low-frequency phonons in ZrB$_{12}$

The influence of pressure and temperature on low-frequency lines (100–300 cm$^{-1}$) in Raman spectra of ZrB$_{12}$ and LuB$_{12}$ single crystals has been investigated. These spectral features have been identified as one-phonon and two-phonon excitations of the acoustic branches of the phonon spectrum. It has been found that the observed spectra of ZrB$_{12}$ single crystals are more structured and indicate the development of phonon anomalies with a decrease in the temperature. Despite the fact that the low-frequency features in the phonon spectrum of ZrB$_{12}$ are characterized by a high value of the isothermal Grüneisen parameter, their isobaric Grüneisen parameter has a negative value. This indicates large contributions from the fourth-order anharmonicity, which significantly exceed the volume effects. The appearance of narrow lines in the frequency range from 155 to 175 cm$^{-1}$ at temperatures $T<$ 100 K suggests the possibility of a structural transition with an incomplete softening of the lattice.