Long-term correlations of the fluctuations in lattice displacements were studied within the framework of the mode-coupling theory of a dynamic transition from an ergodic to a non-ergodic state, as caused by defects. It was shown that the very hard local non symmetry-breaking defects which were formed by O vacancies could induce a dynamic transition at a critical temperature. The low-temperature non-ergodic state was characterized by long-term correlations of the local fluctuations in the polar displacements, which arose continuously below the critical temperature. Simultaneously, the local non symmetry-breaking defects led to the appearance of long-term correlations in the long-wavelength fluctuations of acoustic displacements via local random piezoelectric coupling below the critical temperature. The latter coupling was caused by the electrostrictive interaction, which was modified by the random electric fields of the frozen symmetry-breaking defects. It was shown that the unavoidable O vacancies in nominally pure samples of these materials were sufficient in number to produce the non-ergodic state.

The Long-Time Correlations Induced by Defects in the Quantum Paraelectrics SrTiO3 and KTaO3. I.M.Smolyaninov: Journal of Physics - Condensed Matter, 1998, 10[45], 10333-46