Dielectric nonlinearity of relaxor ferroelectric ceramics at low ac   drives
  Dielectric nonlinear response of (PbMg$_{1/3}$Nb$_{2/3}$O$_3$)$_{0.9}$(PbTiO$_3$)$_{0.1}$ (0.9PMN-0.1PT) relaxor ceramics was investigated under different ac drive voltages. It was observed that: (i) the dielectric permittivity is independent on ac field amplitude at high temperatures; (ii) with increasing ac drive, the permittivity maximum increases, and the temperature of the maximum shifts to lower temperature; (iii) the nonlinear effect is weakened when the measurement frequency increases. The influences of increasing ac drive were found to be similar to that of decreasing frequency. It is believed that the dielectric nonlinearities of relaxors at low drives can be explained by the phase transition theory of ergodic space shrinking in succession. A Monte Carlo simulation was performed on the flips of micro polarizations at low ac drives to verify the theory. 
Xiao-Wen Zhang, Xi Liu, Zhi-Rong Liu, and Bing-Lin Gu