Raman Scattering from the Soft Optic Mode in Ferroelectric Crystals

Abstract

A microscopic description of Raman scattering from the soft ferroelectric mode in the class of oxygen-octahedra ferroelectrics is presented. By relating energy-band shifts produced by critical point polarization fluctuations to fluctuations in the optical dielectric constant tensor we are able to calculate the magnitude of the soft mode Raman scattering efficiency. The polarization-induced energy-band shifts are described using a polarization potential tensor which relates these shifts to the square of the total crystal polarization. The magnitude of the polarization potential is found to be essentially the same in all oxygen-octahedra ferroelectrics based on a straightforward connection between this quantity and the clamped quadratic electro-optic coefficients. Theoretical estimates are also available from energy-band calculations from which we conclude that modulation of the pdπ energy overlap integral by the soft mode polarization fluctuations leads to the electron-phonon interaction observed in Raman scattering. We find further that the strength of the interaction depends only on the dielectric quantity κ^SP_S ², where κ^S is the relevant static dielectric constant, and P_S is the crystal spontaneous polarization.

The polarization fluctuation model can also be used to calculate the soft mode Raman line-shape. Based on the Nyquist theorem combined with a classical damped harmonic oscillator description of the soft mode, we obtain the Raman lineshape in the presence of phonon damping.