Electric-Field-Induced Raman Scattering in SrTiO3and KTaO3

Abstract

In their paraelectric phases, SrTi${\mathrm{O}}_{3}$ and KTa${\mathrm{O}}_{3}$ crystallize in the cubic perovskite structure (space group ${{O}_{h}}^{1}$) in which the first-order Raman effect is forbidden. We discuss here experiments in which first order Raman scattering has been induced by the application of an external electric field that serves to remove the center of inversion symmetry of the crystals. An electric field applied along a $〈001〉$ direction induces a ${C}_{4v}$ symmetry in the crystal and renders all the phonons first-order Raman-active. We have studied induced scattering from all four TO phonons in SrTi${\mathrm{O}}_{3}$ and from three TO phonons in KTa${\mathrm{O}}_{3}$ at temperatures between 8 and 300\ifmmode^\circ\else\textdegree\fi{}K and with electric fields between 0.2 to 15 kV/cm. Most attention was given to the lowest-frequency TO phonon---the "soft" or "ferroelectric" mode---whose striking decrease in frequency as the temperature is lowered signals the lattice instability associated with the ferroelectric phase transition. Detailed investigations were also made of the electric field dependence of the soft-mode frequencies in both materials. At 8\ifmmode^\circ\else\textdegree\fi{}K this frequency in SrTi${\mathrm{O}}_{3}$ increases from 10 ${\mathrm{cm}}^{\ensuremath{-}1}$ at zero field to 45 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 12 kV/cm. Similar behavior is observed in KTa${\mathrm{O}}_{3}$. From this behavior we infer values for the nonlinear dielectric response coefficients of the crystals. Some discussion is given of the large discrepancies between the soft-mode linewidths that we observe and those previously obtained from infrared (IR) reflectivity experiments. At 80\ifmmode^\circ\else\textdegree\fi{}K in SrTi${\mathrm{O}}_{3}$ the Raman and IR measurements yield values of 3 and 61.7 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. Additional topics considered include relative electric-field-induced scattering cross sections for the various phonon modes, and the temperature dependence of the soft-mode linewidth. Finally, the question of anomalous first-order Raman scattering in the intrinsic spectrum of SrTi${\mathrm{O}}_{3}$, recently reported by several authors, is considered in the light of the field-induced first-order Raman scattering.