Elastic Anomaly and Phase Transition of BaTi${\mathrm{O}}_3$

The acoustic-phonon velocities of a single crystal of BaTi${\mathrm{O}}_3$ have been measured as a function of pressure up to 8 GPa, including the transition pressure $p_c=2.35\mathrm{}$ GPa, by means of Brillouin scattering technique. Only one elastic eigenmode shows an anomalous decrease on approaching $p_c$ and the elastic anisotropy increases. The elastic anomaly of cubic BaTi${\mathrm{O}}_3$ is interpreted well by introducing a new tensorial order parameter which describes the anisotropy. The cubic-to-tetragonal phase transition in BaTi${\mathrm{O}}_3$ is shown to be triggered by the fluctuation of the anisotropy, not the polarization itself.