Light-scattering investigation of the ferroelectric transition in lead germanate

A series of light-scattering investigations has been performed on lead germanate (${\mathrm{Pb}}_5$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{11}$) near the second-order ferroelectric transition at $T_c=451\mathrm{}$ K. In the vicinity of $T_c$ the overdamped soft mode is observed to evolve into a superposition of central peaks. A high-frequency wing of width 75 GHz (half-width at half-maximum) is observed, together with a weakly diverging dynamic singular central peak. The observed width of this singular component is as low as 4 GHz near $T_c$. The weak divergence of the integrated intensity of this dynamic central peak is consistent with a logarithmic dependence on ($T_c-T$). It is proposed that the dynamic central component is related to soft-mode interactions with phonon-density fluctuations. In addition, a much narrower central component of width less than 0.002 GHz is observed whose intensity diverges strongly near $T_c$. Combined with previous autocorrelation spectra of this spectral feature, our observations confirm that this component of the central peak is indeed elastic. The intensity of the elastic peak is found to exhibit a power-law divergence on both sides of $T_c$. This divergence is far stronger than expected from either mean-field theory or renormalization-group calculations for a pure uniaxial ferroelectric. Static symmetry-breaking defects are suggested as the cause of the elastic central component. The dynamic-central-peak line shape is attributed to a relaxing-soft-mode self-energy arising from phonon-density fluctuations and is influenced by the piezoelectric coupling of the soft mode to the longitudinal-acoustical phonons. We present detailed Brillouin measurements on the LA frequency and damping, displaying the expected anomalies. A coupled-mode analysis of these spectra is presented which properly accounts for the dynamic-peak line shape, and the LA-phonon anomalies over the entire range of temperature are studied. The relaxation frequency of the soft-mode self-energy is found to be 29 GHz. The presence of defects is shown to be unimportant to the shape of the dynamic peak for $t\equiv \frac{(T_c-T)}{T_c}>{10}^{-3\mathrm{}}$, but possible smearing of $T_c$ prevents us from drawing quantitative conclusions regarding the critical dynamics for $t<\mathrm{}{10}^{-3\mathrm{}}$.