A general analytical equation for phase diagrams of an N-layer ferroelectric thin film with two surface layers

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.