Description of the nonlinear dielectric properties of ferroelectrics under a weak AC-field

Ferroelectric materials are interesting for their switching polarization and present a non linear variation of their permittivity which is due to domain wall motion. Currently, this variation of permittivity is described by the Rayleigh law for fields above a threshold field or by a power law in the case of soft ferroelectrics. In this study we propose a hyperbolic law based on domain wall motions and which includes these two classic approaches. The hyperbolic law allows to clearly define the threshold field by considering the reversible and irreversible components of the permittivity. All expressions are illustrated by the experimental data on hard ferroelectric thin films which present a linear variation of its permittivity at low field. Rayleigh law, dielectric permittivity, domain walls, low field.