Quantum Paraelectric States in SrTiO₃and KTaO₃: Barrett Model, Vendik Model, and Quantum Criticality

The dielectric constants of the quantum paraelectrics SrTiO3 and KTaO3 are measured between 4 and 325 K. Their temperature dependences are analyzed on the basis of the Barrett and Vendik models. The former model deals with a ferroelectric optical mode coupled with other optical modes, whereas the latter deals with the mode coupled with acoustic modes. In addition, the latter contains a measure of the density of defects and inhomogeneity. The dielectric constants at low temperatures can be accurately described using Vendik’s formula; however, they cannot be accurately described using Barrett’s formula, even after the introduction of a measure of the density of defects and inhomogeneity. A critical quantum paraelectric region has been introduced recently between a classical region and a quantum paraelectric one. We point out that the critical region is where a low-temperature approximation is well realized for the model with the coupling between the ferroelectric and acoustic modes.