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.

Magnetic properties of a cylindrical Ising nanowire (or nanotube)

“…Also, the numerical results obtained from the EFT for the mixed spin Ising model have been compared with the numerical results obtained from the Monte Carlo method 24. Even at the present date, the formulation is still applied to a variety of Ising problems 12, 17, 25–28.…”

Polarization behaviors in a transverse Ising film with multi-surface layers

“…1 are the layer indices. The Hamiltonian of the transverse Ising system is [2][3][4][5][6][7][8][9][10] , 1 2…”

“…Theoretically, the transverse Ising model is considered as an excellent candidate to study phase transitions in the ferroelectric thin film with multi-surface layers [2][3][4][5][6][7][8][9][10]. Within the framework of the mean-field theory, Wang et al [2,3] and Sy [4] investigated the dependence of Curie temperature on the surface layer number and total layer number as well as interaction parameters.…”

“…Soon afterwards, within the framework of the effective-field theory with correlations, Arhchoui et al [8] studied the phase diagrams of the ferroelectric thin film with two surface layers and paid a special attention to the effect of surface transverse field on phase transitions. Furthermore, Lu et al [9] derived a general equation for the diagram of an N-layer ferroelectric thin film with two surface layers and analyzed the dependence of the phase diagrams on the exchange interactions and transverse fields as well as the number of layers N. At the same time, the crossover features for various interaction parameters of the N-layer ferroelectric thin film are also obtained. In most of above mention, however, only the rare works have been carried out on the polarization behaviors of a transverse Ising film.…”

Effects of surface modification on the critical behaviour in multiple-surface-layer ferroelectric thin films

“…Wang et al [8,9] and Sy [10] studied the Curie temperature T c as a function of the thickness of ferroelectric thin film, the surface exchange interaction and the surface layer number with the treatment of the MFA. Because the surface layer number has a significant effect on the phase diagram of a thin film, the influence of the surface layer number on phase transition properties of ferroelectric thin films have been calculated using the MFA [11,12] and the EFT with correlations [13][14][15]. However, the effects of the surface layer number on the critical behaviour of the Curie temperature T c and the surface transverse field sc have not been reported.…”