The high-frequency elastic constants of SrTiO3in the quantum paraelectric regime

The velocities of acoustic modes have been measured on SrTiO3 by Brillouin and neutron scattering. Anomalies are detected at or below T q, the temperature that marks the onset of the quantum paraelectric regime. It is shown quantitatively that the square of the polarization plays an important role below T q. The dependence on the wavevector square which is found for some of the anomalies indicates the importance of coupling terms proportional to the gradient of the polarization.