Ferroelectric phase transition and soft-mode behavior in Ba_xSr_1−xTiO₃: a refined treatment of a quasi-harmonic model

Abstract

The composition and temperature dependences of the soft-mode and ferroelectric phase transition in BaxSr1−xTiO3 (BST) are presented and analyzed within the framework of a refined treatment of a quasi-harmonic model (QHM) for quantum particles. The QHM involves generalized simple microscopic quantum particles with anharmonic on-site double-Morse-type potential and harmonic interactions. The theory uses the variational principle scheme at finite temperature in the mean-field approximation while taking into account the predominant mass effect, the cell volume effect as well as ferroelectric distortion. The soft-mode frequency and the Ba concentration (x) dependence of the ferroelectric phase transition temperature are analyzed and show good agreement with experimental results throughout the full x range (0 ⩽ x ⩽ 1). It is found that BST is paraelectric below the critical impurity concentration xc = 0.01 with a softening of the soft mode. It becomes ferroelectric above this critical concentration (x ⩾ xc), and as the impurity concentration increases the predominant displacive soft-mode behavior stiffens in the ferroelectric phase with much less softening in crystals indicating a possible phase change at high x. Around x′c = 0.5, Tc deviates gradually from linear behavior with a rather slight round stagnation which might characterize an equilibrium ‘region’ where several ferroelectric phases coexist. The proposed x dependence of the soft-mode behavior indicates that the ferroelectric phase transition is of first order in BST with x > x′c, and of second order for low Ba concentrations (xc ⩽ x < x′c), throughout the tricritical point at x = x′c. Finally, the quantum dynamics of the ferroelectric phase transition and the mode softening are also addressed and discussed, suggesting a net increase of quantum effects with a decrease of x for x ⩽ 0.1, and a dominant Curie–Weiss law for x > 0.1.

Indirect measurements of electrocaloric effect in ferroelectric thin films by positive-up-negative-down method

“…8) This method allows us to separately evaluate the leakage current and the polarization; therefore, "true" polarization values can be determined. We measured the polarization of (001)-epitaxial Ba 0.3 Sr 0.7 O 3 (BST30/70) thin film, as a typical ferroelectric showing second order phase transition, 9) to testify the validity of our method. The temperature change was then estimated from the set of polarization values at various electric fields and temperatures and was compared with the temperature change estimated by the conventional PE hysteresis loop measurement.…”