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

Abstract
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.