The ferroelectric properties of films with defect layers

Using the transverse Ising model and the effective field theory based on the probability distribution technique, which accounts for the single-site spin correlations, the phase transition temperature, polarization, susceptibility and hysteresis loops for a ferroelectric (FE) film with defect layers are studied. It is shown that the defect layers in the FE film can induce a strong increase or decrease of the critical temperature of the phase transition due to different exchange interactions in the defect layers, which is connected with the values of the exchange interactions that depend on the distance between the spins. Considering the fact that the interactions can be different in defect layers compared to layers without defects, we have shown that the coercive field decreases in the case of different numbers of defect layers. The results obtained are in qualitative agreement with experimental data on ferroelectric films with different thicknesses