Damping of the softE-symmetry phonon in lead titanate

The frequency and temperature dependence of the phonon damping function γ(ω,T) of the soft E-symmetry phonon in PbTiO₃ has been determined using Raman scattering. From 40^∘{}K to room temperature the frequency of the lowest E mode, ω₀(T), is nearly constant and permits the temperature dependence of γ to be measured at constant frequency. Below room temperature, γ(ω₀,T) is proportional to the absolute temperature T and extrapolates to zero damping at $T=0$. The frequency dependence of γ(ω,Tᵣₘ) 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 cm^-1. Below the ferroelectric phase transition at 766^∘{}K, it is shown that the apparent divergence of γ(ω₀(T)) as T→Tc^- results mainly from this frequency dependence and a nearly linear dependence on temperature. At fixed frequency, γ(ω,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.