Mixing of Acoustic and Soft Optic Modes in Ferroelectric BaTiO3

Experimental results indicate that in the tetragonal ferroelectric phase of BaTi${\mathrm{O}}_3$ the soft optic branches cross the acoustic ones for small wave-vector values. It is shown that this accidental degeneracy is lifted in particular cases (depending on the type and the direction of propagation of degenerate modes) because of coupling between the soft optic and acoustic modes which is of piezoelectric origin. The resulting modes are neither pure elastic nor pure polarization waves. The disperison relations of these mixed modes are calculated in the long-wave limit, and the experimental significance of this effect is discussed.