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

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

2006-03-13

arxiv.org/abs/cond-mat/0603354v1

Physical Review B 72, 092103 (2005)

Physics

Condensed Matter

Materials Science

8 pages, 3 figures

Scientific paper

10.1103/PhysRevB.72.092103

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 $T_{tr}$.

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