Accurate determination of the far-infrared dispersion in SrTiO3by hyper-Raman spectroscopy

We use the fluctuation-dissipation theorem to relate the hyper-Raman scattering efficiency of transverse and longitudinal-optical phonons to the infrared dielectric function $\epsilon \left(\Omega \right)={\epsilon }^{\prime }\left(\Omega \right)+i{\epsilon }^{\prime \prime }\left(\Omega \right)$. The relation is applied to SrTi${\mathrm{O}}_3$ at room temperature in order to clarify the discrepancies between various far-infrared reflectivity studies. We take advantage of the hyper-Raman selection rules allowing the observation of Raman-forbidden modes. ${\epsilon }^{\prime \prime }\left(\Omega \right)$ is derived from accurately measured hyper-Raman lines and combined with compatible infrared reflectivity data to give ${\epsilon }^{\prime }\left(\Omega \right)$. Below 100 ${\mathrm{cm}}^{-1\mathrm{}}$ the dielectric dispersion can be adequately described by a classical dispersion formula with a quasiharmonic-oscillator frequency of 87.9 ${\mathrm{cm}}^{-1\mathrm{}}$ and a single damping constant of 23.7 ${\mathrm{cm}}^{-1\mathrm{}}$. This approximation fails above 100 ${\mathrm{cm}}^{-1\mathrm{}}$.