Quantum saturation of the order parameter and the dynamical soft mode in quartz

The temperature evolution of the static order parameter of α-quartz and its soft-mode frequencies were determined at temperatures below 300 K. While these parameters follow classic Landau theory at higher temperatures, quantum saturation was found below room temperature with a characteristic quantum temperature of 187 K. A quantitative analysis gave a good agreement with the predictions of a Φ 6 model close to the displacive limit and a rather flat dispersion of the soft-mode branch. No indication of any effect of strong mode–mode coupling on the saturation behaviour was observed.