A soft optic phonon which is neither Raman nor infrared active has been directly observed for the first time in the higher-symmetry phase above $T_a$ (221.5 K) of hexagonal BaTi${\mathrm{O}}_3$ by an experiment of hyper-Raman scattering. The underdamped feature of the soft-phonon mode even close to $T_a$ allows one to determine unambiguously both the frequency and the damping constant as a function of temperature. It is found that the soft-mode frequency obeys the Landau-Cochran theory in contrast with the nonclassical behavior below $T_a$ which was previously found by a Raman scattering experiment. Furthermore, the second-harmonic-generation observation indicates that the crystal structure below $T_a$ should be of acentric symmetry, which is closely related with the ferroelastic nature of the phase transition at $T_a=74\mathrm{}$ K.

• Received 9 June 1988

DOI:https://doi.org/10.1103/PhysRevB.38.6352