Damping of the softE-symmetry phonon in lead titanate

Abstract

The frequency and temperature dependence of the phonon damping function $\ensuremath{\gamma}(\ensuremath{\omega},T)$ of the soft $E$-symmetry phonon in PbTi${\mathrm{O}}_{3}$ has been determined using Raman scattering. From 40\ifmmode^\circ\else\textdegree\fi{}K to room temperature the frequency of the lowest $E$ mode, ${\ensuremath{\omega}}_{0}(T)$, is nearly constant and permits the temperature dependence of $\ensuremath{\gamma}$ to be measured at constant frequency. Below room temperature, $\ensuremath{\gamma}({\ensuremath{\omega}}_{0},T)$ is proportional to the absolute temperature $T$ and extrapolates to zero damping at $T=0$. The frequency dependence of $\ensuremath{\gamma}(\ensuremath{\omega},{T}_{\mathrm{rm}})$ was determined at room temperature using near-forward Raman scattering from polaritons. New results are obtained by reanalyzing previously reported data. The damping is found to increase for decreasing polariton frequencies down to about 53 ${\mathrm{cm}}^{\ensuremath{-}1}$. Below the ferroelectric phase transition at 766\ifmmode^\circ\else\textdegree\fi{}K, it is shown that the apparent divergence of $\ensuremath{\gamma}({\ensuremath{\omega}}_{0}(T))$ as $T\ensuremath{\rightarrow}{T}_{c}^{\ensuremath{-}}$ results mainly from this frequency dependence and a nearly linear dependence on temperature. At fixed frequency, $\ensuremath{\gamma}(\ensuremath{\omega},T)$ is proportional to the absolute temperature although smaller nonlinear contributions cannot be ruled out. This linear temperature dependence indicates that the dominant damping mechanism for the soft $E$ mode is due to cubic anharmonicity in the lattice potential. These results are interpreted in terms of the model described by Cowley for phase transitions arising from anharmonic decay. A review of experimental results concerning the temperature dependence of the damping of soft modes in related materials is included.