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

Abstract

We use the fluctuation-dissipation theorem to relate the hyper-Raman scattering efficiency of transverse and longitudinal-optical phonons to the infrared dielectric function $\ensuremath{\epsilon}(\ensuremath{\Omega})={\ensuremath{\epsilon}}^{\ensuremath{'}}(\ensuremath{\Omega})+i{\ensuremath{\epsilon}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\Omega})$. 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. ${\ensuremath{\epsilon}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\Omega})$ is derived from accurately measured hyper-Raman lines and combined with compatible infrared reflectivity data to give ${\ensuremath{\epsilon}}^{\ensuremath{'}}(\ensuremath{\Omega})$. Below 100 ${\mathrm{cm}}^{\ensuremath{-}1}$ the dielectric dispersion can be adequately described by a classical dispersion formula with a quasiharmonic-oscillator frequency of 87.9 ${\mathrm{cm}}^{\ensuremath{-}1}$ and a single damping constant of 23.7 ${\mathrm{cm}}^{\ensuremath{-}1}$. This approximation fails above 100 ${\mathrm{cm}}^{\ensuremath{-}1}$.