Piezoelectric nonlinearity due to motion of 180° domain walls in ferroelectric materials at subcoercive fields: A dynamic poling model

Abstract

A mechanism is described whereby 180° domain wall motion can contribute to the electrically induced strain in a ferroelectric material at subcoercive ac electric fields. The field-dependent, largely reversible motion of ferroelectric, 180° domain walls due to an applied ac electric field is considered. The Rayleigh law is modified to describe the piezoelectric response of the system. This results in both a linear dependence of the piezoelectric coefficient on the amplitude of the applied electric field and the creation of a second order harmonic of strain which adds to the electrostrictive response. The model was experimentally confirmed in $\mathrm{Pb}\left({\mathrm{Zr}}_{1-x}{\mathrm{Ti}}_x\right){\mathrm{O}}_3$ thin films.