Softening and mode crossing of the lowest-frequency A1(transverse-optical) phonon in single-crystal PbTiO3

The polarized Raman spectra of high-quality single-crystal PbTiO3 were measured in the temperature range between 300 and 700 K. The soft-mode behavior of the A1(1TO) (transverse- optical) phonon was observed directly. Above 400 K, however, an intensity transfer between the subpeaks of the A1(1TO) mode was observed, and the line shape of the A1(1TO) mode strongly deviated from the theoretical prediction based on the harmonic approximation in the interatomic potential. In addition, the mode crossing between the A1(1TO) phonon and the E(1LO) (longitudinal optical) phonon was observed. The observed mode crossing behavior clearly supports the assignment of the E(1LO) and A1(1TO) modes, which was originally suggested by Foster and co-workers [Phys. Rev. Lett. 71, 1258 (1993)].