On the ferroelectric dc nonlinear dielectric permittivity and its relation with the macroscopic polarization

The relation between the nonlinear dielectric permittivity \(\varepsilon '(E)\) and the macroscopic polarization P(E) is obtained for ferroelectrics considering a weak alternating electric field \(E_1\cos (\omega t)\) superimposed to a dc bias field \(E_0\). Two different empirical models are reviewed. The first model uses the hyperbolic tangent function to represent the hysteretic behavior of the macroscopic polarization. In the second model is assumed that the dielectric permittivity is proportional to the reciprocal of a quadratic function of the local field, i.e., \(\varepsilon ' \propto {\{\alpha +\beta {\left[ E+\kappa P(E)\right] }^2 \}}^{-1}\). A combination of both models is used to fit the experimental curve \(\varepsilon '(E)\) and to reproduce P(E). The parameters obtained from the fitting with this model can be used to get a better understanding of the correlation between the macroscopic response and the domain structure.