Polarization properties of ferroelectric thin films on transverse Ising model

By taking into account surface transition layers (STL), an improved transverse Ising model (TIM) with a depolarization field effect also considered is used to describe the polarization properties of ferroelectric thin films in the framework of the mean-field approximation. Functions representing the intralayer and interlayer couplings are introduced to characterize STL, which makes the model more realistic compared to previous treatment of surface layers using uniform surface exchange interactions and a transverse field. By comparison with the results obtained from the traditional treatments for the thin films using only the single surface layer (SSL), some new results are derived by adding the STL in the model. The results also show that the effect of the transverse field is notable when tunneling is essential. The influence of the depolarization field is to flatten the spontaneous polarization profile and make the polarization distribution of films more homogeneous, which is consistent with the results obtained from the Ginzburg -Landau-Devonshire (OLD) theory.