Development of ferroelectric correlations in the quantum paraelectric and antiferrodistortive regimes in BaxSr1-xTiO3 (x ≤ 0.10)

The dielectric response ε(T)  of BaxSr1-xTiO3 (x ≤ 0.1) for compositions at and below the critical composition for the ferroelectric transition has been studied. With progressive Ba substitution, the growth of ferroelectric correlations and the weakening of the Antiferrodistortive (AFD) and the quantum paraelectric (QPE) effects have been studied by monitoring the changes in both the in and out of phase parts of the dielectric response. For the compositions close to pure SrTiO3 (x = 0 and x = 0.02), the temperature dependence exhibits a continuous rise in the in-phase part and no ferroelectric peak, consistent with the QPE behavior. With increasing Ba substitution, the low temperature behavior of the in phase part ε′ progressively changes from a continuous rise to exhibit a weak maximum and finally to a well developed cusp. For higher Ba concentrations, the low temperature peak (T ∼ 50K), which corresponds to ferroelectric correlations, becomes increasingly sharper until at the critical composition, x = 0.10, the system shows a single well defined ferroelectric peak. However, the out of phase response of the x = 0.1 composition exhibited a succession of three BaTiO3 type ferroelectric transitions. For x≤0.04, the out of phase part shows evidence of an ordering around T ∼ 100K, which is the expected AFD ordering temperature. The deviations of the ε′(T) data from the Curie-Weiss law have been analyzed within the frame work of two different theoretical models. It was determined that the dielectric behavior for lower concentrations of Ba (up to x ≤ 0.08) was explainable in terms of a model of non-interacting regions which are themselves homogeneously polarized and undergo a second order phase transition. For the phase boundary composition, i.e., x = 0.1, on the other hand, the data are explainable in terms of the Sherrington and Kirkpatrick model which includes the effects of weak correlations between the polar regions characterized by a glassy order parameter.