The quantum paraelectric behavior of SrTiO_{3} revisited: relevance of the structural phase transition temperature

TL;DR

This paper revisits the quantum paraelectric behavior of SrTiO₃, explaining the crossover in dielectric constant behavior at 10K through the distribution of phonon frequencies and the structural transition temperature.

Contribution

It demonstrates that the dielectric constant crossover in SrTiO₃ is due to the quantum distribution of phonon frequencies and the structural phase transition temperature.

Findings

Crossover in saturation temperatures explained by phonon frequency distribution.

The structural transition temperature influences dielectric behavior.

Quantum distribution of modes accounts for low-temperature dielectric properties.

Abstract

It has been known for a long time that the low temperature behavior shown by the dielectric constant of quantum paraelectric $SrTiO_{3}$ can not be fitted properly by Barrett's formula using a single zero point energy or saturation temperature ($T_{1}$). As it was originally shown [K. A. M\"{u}ller and H. Burkard, Phys. Rev. B {\bf 19}, 3593 (1979)] a crossover between two different saturation temperatures ($T_{1l}$=77.8K and $T_{1h}$=80K) at $T\sim10K$ is needed to explain the low and high temperature behavior of the dielectric constant. However, the physical reason for the crossover between these two particular values of the saturation temperature at $T\sim10K$ is unknown. In this work we show that the crossover between these two values of the saturation temperature at $T\sim10K$ can be taken as a direct consequence of (i) the quantum distribution of frequencies $g(\Omega)\propto\Omega^{2}$ associated with the complete set of low-lying modes and (ii) the existence of a definite maximum phonon frequency given by the structural transition critical temperature $T_{tr}$.