Anharmonicity of the lowest-frequencyA1(TO) phonon inPbTiO3

Detailed Raman studies of the optical phonons in high-quality single-crystal ${\mathrm{PbTiO}}_3$ indicate that the mode energies and symmetry assignments in the literature [G. Burns and B. Scott, Phys. Rev. B 7, 3088 (1973)] must be revised. In this study, all k≃0 optical-phonon modes are directly observed and are shown to obey rigorously the Raman selection rules. The angular dependence of the phonon frequencies indicates that the energy of the lowest-frequency ${\mathit{A}}_1$(TO) mode is higher than the energy of the lowest-frequency E(LO) mode at 300 K. This indicates that these two k≃0 modes will cross at elevated temperature. The ${\mathit{A}}_1$(TO) mode exhibits an anomalous line shape, which we attribute to the anharmonic nature of the lattice. The phonon frequencies determine the clamped dielectric constants, ${\mathrm{\varepsilon }}_{\mathit{a}}$(0) and ${\mathrm{\varepsilon }}_{\mathit{c}}$(0), using the Lydanne-Sachs-Teller relation. These values, when compared to those obtained from impedance measurements, indicate no dielectric dispersion in ${\mathrm{PbTiO}}_3$ between the MHz region and the Raman region.