Abstract

The displacement of the ferroelectric domain wall l is modeled by the equation of a particle in a force field. The forces that act in the domain walls are due to the external electric field E and the internal electric and elastic interactions, which arc represented by the effective potential U(l). The potential U(l) is chosen to describe a nonlinear dielectric response in a dc bias electric field. This model also correctly reproduces a real component of dielectric permittivity in a subswitching alternating electric field, but the predicted losses are lower than the experimental values. Subswitching dielectric losses are produced mostly by the interaction of domain walls with defects. Point defects can be modeled as a perturbation of the potential. Another way to model point defects is introducing a generalized damping function Gamma((l) over bar, (l))over bar>) so that the average displacement of domain walls I is determined by a single equation. The equivalence of both theoretical approaches is demonstrated. An analytical expression of the damping function is derived from the Rayleigh law. Simulations show that the method of the damping function correctly reproduces a nonlinear dielectric response and losses. The damping function method could be a useful theoretical framework to elucidate the friction force generated by the interaction of ferroelectric domain walls with defects, and it can be extended to study similar phenomena such as ferroelasticity and ferromagnetism.