Soft Ferroelectric Modes in Lead Titanate

The ferroelectric phase transition in PbTi${\mathrm{O}}_3$ has been investigated by the neutron inelastic scattering technique. As is the case with BaTi${\mathrm{O}}_3$, the soft optic mode at the zone center condenses when the temperature is lowered to the Curie point at 490°C. In contrast to BaTi${\mathrm{O}}_3$, however, the lowest transverse optic modes along [100] are well defined (not overdamped), except for the phonons with very small $q$ values. When this optic branch approaches the acoustic branch near the Curie temperature, effects of the "coupling" are clearly observed. Intensities of the soft modes were measured at several zone centers in the ferroelectric phase. Observed values are in qualitative agreement with calculations based upon the mode motions deduced from the atomic positions in the ferroelectric phase.