High-pressure Raman study of zone-center phonons in PbTiO3

A complete study of the $\overrightarrow{\mathrm{k}}=\overrightarrow{0}$ optical phonons of the ferroelectric tetragonal PbTi${\mathrm{O}}_3$ as a function of hydrostatic pressure has been carried out using Raman spectroscopy. The coalescence, to the same frequency, of the high-energy [$A_1\left(\mathrm{TO}\right)$, $E\left(\mathrm{TO}\right)$] pairs of phonons in the ferroelectric phase and the disappearance of the first-order Raman lines in the cubic phase has enabled us to determine the transition pressure $P_c$, as well as the second-order character of the phase transition. Our results also suggest the existence of a tricritical point in the ($P$,$T$) phase diagram. Using the Liddane-Sachs-Teller relation we calculate the static dielectric constant as a function of pressure and compare the results with previous dielectric measurements. Moreover, we discuss the soft phonons, their damping, and their behavior near the phase transition. It is found that the soft $E\left(\mathrm{TO}\right)$ phonon damping function is nearly constant over a wide frequency range and that it appears to diverge near the phase transition.