Anomalous Acoustic Dispersion in Centrosymmetric Crystals with Soft Optic Phonons

A careful study of the dispersion of the transverse acoustic phonons and the low-frequency transverse optic phonons in KTa${\mathrm{O}}_3$ has been carried out by inelastic neutron scattering. In addition to the well-known temperature dependence of the optic-mode frequencies, both the acoustic-phonon frequencies and the neutron-scattering cross sections of the TO and TA phonons with q along [100] show a marked temperature dependence. This anomalous behavior is not, however, revealed in ultrasonic velocity measurements. By means of a long-wavelength expansion of the lattice-dynamical equations, we show that these phenomena are the result of quasiharmonic coupling of optic- and acoustic-like excitations. In centrosymmetric crystals, this interaction vanishes as the wave vector q→0, in such a way as to leave the limiting acoustic velocity unaffected. The existence of this interaction suggests the possibility of a soft Brillouin-zone-center optic phonon precipitating an instability in a mode with mixed acoustic-optic character and nonzero wave vector, giving rise to an antiferroelectric (or microtwinned ferroelectric) phase.