Statistical theory of hysteresis in ferroelectric materials

A theory is developed based on the model of random interactions between a large number of lattice defects and domain walls in ferroelectric materials. The theory gives the characteristic parameters of the hysteresis loop such as initial dielectric constant εi, Rayleigh constant ν, and coercive field Ec in terms of the microstructure of the domain walls and the number and interaction strength of the lattice defects. Results from large amplitude measurements on BaTiO3 doped with Fe show that a linear relationship exists between the dielectric constant and the ac field as required by Rayleigh’s law. In addition, the Rayleigh constant itself is inversely proportional to the Fe concentration as predicted by the model. Therefore, it is concluded that Fe as a dopant in BaTiO3 can act as obstacles to domain wall motion and control the characteristics of the hysteresis loop.