Pressure-induced phonon frequency shifts in transition-metal nitrides

We report the experiments on the high-pressure phonon spectra of transition-metal nitrides $\mathrm{HfN}$, $\mathrm{ZrN}$, and $\mathrm{NbN}$, obtained by Raman-scattering measurements. Two pronounced bands, which are related to the acoustic part at low-frequency around $200\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and the optical part at high-frequency around $550\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ of the phonon spectrum, respectively, shift to high-frequency values with increasing pressure. An analysis of the results allows us to reproduce the experimental pressure dependence of the superconducting transition temperature ${T}_{c}$ of $\mathrm{ZrN}$ and $\mathrm{NbN}$. We also predict the pressure effect on ${T}_{c}$ in $\mathrm{HfN}$.