Spontaneous Polarization of BaTiO_3 at Low Temperatures

The pressure-temperature phase diagram of BaTiO3 was investigated by using a modification of the standard Landau potential to take account of quantum saturation of the order parameter. At low temperatures, each phase boundary bends sharply down, and this non-linear behavior is associated with quantum mechanical effects. Saturation temperatureθs characterizes the extent of quantum mechanical, and is related to the extent to which changes in the hard phonon modes influence the transition mechanism.