No abstract

Within the framework of effective-field theory with correlations, the phase diagrams of an N-layer ferroelectric thin film with two surface layers are studied by the differential operator technique based on the spin-1/2 transverse Ising model. A general analytical equation for the phase diagram of a ferroelectric thin film with arbitrary layer number as well as exchange interactions and transverse fields is derived, and then the effects of exchange interactions and transverse fields on phase diagrams are discussed for an arbitrary layer number N. Meanwhile, the crossover features, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for various parameters of an N-layer ferroelectric thin film with two surface layers are investigated. As a result, an N-independent common intersection point equation is obtained, and the three-dimensional curved surfaces for the crossover values are constructed. In comparison with the usual mean-field approximation, the differential operator technique with correlations reduces to some extent the ferroelectric features of a ferroelectric thin film.

Utilizing the higher order decoupling approximation to the Fermi-type Green’s function, crossover properties of interaction parameters of an n-layer ferroelectric thin film from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD) are investigated on the basis of the transverse Ising model. The curved surfaces for crossover values of interaction parameters of a thin film with certain layers are constructed in the three-dimensional parameter space. Because both the z-component <Sz> (the polarization) and the transverse component <Sx> of the spin are further included in the eigenfrequency, the results are in agreement with that of the effective-field theory with correlations to some extent. It shows that the higher order decoupling approximation diminishes the ferroelectric feature of a ferroelectric thin film compared with the usual mean-field approximation.