Electric field induced critical points and polarization rotations in relaxor ferroelectrics

The giant electromechanical response in ferroelectric relaxors such as $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ (PMN-PT) is of great importance for a number of ultrasonic and medical applications as well as in telecommunications. On the basis of the dielectric, heat capacity, and piezoelectric investigations on PMN-PT crystals of various PT compositions and bias fields, we have recently shown the existence of a line of critical points for the paraelectric to ferroelectric transformations in the composition-temperature-electric field $(x\text{\ensuremath{-}}T\text{\ensuremath{-}}E)$ phase diagram. Here, we show the piezobehavior in more detail and present a theoretical evaluation of the Widom line and the critical line. This line effectively terminates a surface of first order transitions. Above this line, supercritical evolution has been observed. On approaching the critical point, both the enthalpy cost to induce the intermediate monoclinic states and thus the barrier for polarization rotations decrease significantly. The maximum of the piezoelectric response is not at $E=0$, but at the critical field values. It is shown that the critical fluctuations in the proximity of the critical points are directly responsible for the observed enhancement of the electromechanical response in the PMN-PT system. In view of the large electric field dependence of the dielectric constant near the critical point, these systems may also be important as electric field tunable elements.