Non-linear dielectric behaviour and glass phase in Sr1-xCaxTiO3 (x = 0.002 and x = 0.003)

This work reports a study of the temperature and electric field dependence of the dielectric constant of strontium calcium titanate. The first part of the paper is focused on the analysis of a mean-field model for the polar clusters generated by the random impurities of calcium. It is shown that the dipolar moments within each cluster can be represented by an equivalent quantum two-level system. General expressions for the temperature and field dependence of the Edward-Anderson order parameter and of the electrical polarization are given. Analytical solutions are also obtained in the limit of high temperatures and in the limit of high tunnelling frequencies. The second part of the work reports experimental results on the temperature and electric field dependence of the dielectric constant of strontium calcium titanate (SCT: Sr1-xCaxTiO3), measured along the [100] pseudo-cubic direction, in samples with nominal Ca content of x = 0.002 and x = 0.003. The analysis of the data suggests that for these low Ca concentrations quantum fluctuations prevent the onset of either a ferroelectric or a glass phase.