Nonlinear dielectric response of relaxor ferroelectrics

The behavior of the third-order nonlinear dynamic dielectric susceptibility χ₃(ω) in relaxor ferroelectrics is investigated in the framework of the spherical random-bond--random-field model. It is shown that there are two distinct contributions to χ₃(ω): The first one χ₃(ω)I, which has been studied earlier, is due to the intrinsic nonlinearity of the rigid spherical model; the second contribution χ₃(ω)II arises from the field modulation of the average coupling between polar clusters. The frequency and temperature dependence of χ₃(ω)II is calculated and compared with χ₃(ω)I. In the static limit, the results for χ₃(ω)II are in qualitative agreement with the measured field-cooled static nonlinear dielectric permittivity in Pb_1-xLaₓ(ZryTi_1-y)_1-x/4O₃ ceramics.