Fig. 5: Frequency-evolution of the electric, mechanical, and electromechanical phases.
a The sign change of the electrostrictive coefficient corresponds to a sudden change of the electrostrictive phase when it reaches φx = π/2 (from purple shaded region to red shaded region). This change is not correlated to a change of either the dielectric φelec or mechanical φmec phases. The sample remains elastic (mechanical loss angle φmec remains close to 0), whereas the dielectric loss angle φelec decreases slightly as the frequency increases. The electrostrictive phase φx is minimum at 10 Hz, leading to a non-hysteretic electrostrictive response after the sign change of M. On the contrary, the strain switches from extension to compression when the electrostrictive phase reaches π/4 (at 2 Hz, from dark purple shaded region to light purple shaded region). b Viscous damping coefficient c as a function of excitation frequency derived from the measured frequency-dependence of φx (Fig. 5a) and the modeled dependence of φx on the damping coefficient c (Fig. S7b). The linear dependence of the damping coefficient on frequency supports the velocity-squared damping assumption (see Supplementary information S7).
