Impact of critical point on piezoelectric and electrocaloric response in barium titanate

The prediction that the piezoelectric tensor is diverging at the critical point is verified for BaTiO${}_3$ (BTO), which is the oldest perovskite structured ferroelectric material with an extremely long and eventful research history. Here we investigate experimentally by dielectric and calorimetric measurements the existence and the position of the critical point in the electric-field-temperature ($E$-$T$) phase diagram of BTO in the vicinity of the paraelectric to ferroelectric phase transition. Measurements of the piezoelectric coefficient $d_{31}$ as a function of the temperature and the electric field applied along the [001] direction show a critical enhancement of the piezoelectric response in the vicinity of the critical point, in agreement with recent calculations by Porta et al. [J. Phys.: Condens. Matter 22, 345902 (2010)]. The electrocaloric responsivity is found to be enhanced due to the latent heat on the paraelectric to ferroelectric transition locus below the critical point.

Figure 1

Temperature dependence of the dielectric data of a BaTiO${}_3$ single crystal obtained in ZFC-FH experiment at various bias electric fields applied along the [001] direction.

Figure 2

Temperature evolution of the excess specific heat data obtained in the ac mode at various constant electric fields. The solid line is a guide to the eye, whereas open circles and crosses are the $c_p$ data obtained outside and inside the coexistence rang, respectively. In the first panel the anomalous response of $c_p$ in the coexistence range is so huge that it is out of the drawing limit.

Figure 3

Change of the sample temperature for the BaTiO${}_3$ single crystal due to the released latent heat at the field-induced cubic to tetragonal phase transition, measured at several constant bath temperatures.

Figure 4

(a) $E$-$T$ phase diagram for a BaTiO${}_3$ single crystal constructed from the calorimetric and dielectric data. Solid line represents the electric-field-induced first-order transition line between the paraelectric and ferroelectric phases, which ends in a critical point at $T_{\text{CP}}\sim$412 K and $E_{\text{CP}}\sim$10 kV/cm. The dashed line denotes the Widom line, and the solid arrows denote values of the electric field at which the piezoelectric response was measured. The two insets represent the temperature and electric field variation of the latent heat. (b) The temperature dependence of the piezoelectric coefficient $d_{31}$ obtained in a BaTiO${}_3$ single crystal poled along the [001] direction at four different values of the bias electric field below and above $E_{\text{CP}}$. The inset shows the electric field dependence of the piezoelectric coefficient $d_{31}$ at $T=T_{\text{CP}}$, which exhibits a maximum at the critical field $E_{\text{CP}}$ (arrow).

Figure 5

The electric-field dependence of the electrocaloric responsivity $\Delta T/E$ determined along the ferroelectric transition line shown in the $E$-$T$ phase diagram [Fig. 4a] for a BaTiO${}_3$ [001] single crystal. Solid line is obtained from the direct electrocaloric measurements (shown in the inset) at different temperatures and magnitudes of the electric field. Dashed line: Schematic field dependence of the electrocaloric responsivity for a system with vanishingly small latent heat; in such a case, the maximum of $\Delta T/E$ occurs near the critical field $E_{\text{CP}}$.[49]