Uniaxial-stress dependence of the first-order Raman spectrum of rutile. I. Experiments

Abstract

We report an investigation of the uniaxial-stress dependence of the first-order Raman spectrum of rutile (Ti${\mathrm{O}}_2$). We find a normal-mode behavior, characterized by an increase in the phonon frequency versus uniaxial compression, for the two Raman modes ${\Gamma }_1$ ($A_{1g}$) and ${\Gamma }_5$ ($E_g$). We deduce two deformation potentials for ${\Gamma }_1$ (in unit of ${\mathrm{cm}}^{-1\mathrm{}}$): $a_1=-610\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $b_1=-820\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and four deformation potentials for ${\Gamma }_5$ (doubly degenerate mode): $a_5=-1170\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $b_5=-1840\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $c_5=+35\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $d_5=-230\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. We find less classical results for ${\Gamma }_3$ ($B_{1g}$): the phonon frequency increases for uniaxial stress parallel to $\overrightarrow{\mathrm{c}}$ but decreases for uniaxial stress parallel to $\overrightarrow{\mathrm{a}}$ ([100] direction) or parallel to ${\overrightarrow{\mathrm{a}}}^{\prime }$ ([110] direction). The corresponding deformation potentials are $a_3=+620\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $b_3=+330\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Within experimental error, all phonon energies displace linearly versus deformation.