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

Abstract

Using the usual mean-field theory approximation, the critical behaviour (i.e. the Curie temperature T c and the critical surface transverse field sc ) in a multiple-surface-layer ferroelectric thin film is studied on the basis of the spin-1 2 transverse Ising model. The dependence of the Curie temperature T c on the surface transverse field s and the surface layer number N s are discussed in detail. Meanwhile the dependence of the critical surface transverse field sc on the surface layer number N s is also examined. The numerical results indicate that the critical behaviour of ferroelectric thin films is obviously affected by modifications of the surface transverse field s and surface layer number N s .

Influence of surface and bulk layers on the crossover features for interaction parameters of a ferroelectric thin film

“…The phase diagram of the thin film can be obtained on condition that the coefficient determinant is equal to zero. Thus, the general equations for the phase diagram of an N -layer ferroelectric thin film with different surface layers N s can be obtained [5,11] (1) N s D 1…”

Critical Behaviors and Polarizations in A Transverse Ising Film

“…Within the framework of the usual MFA [3][4][5][6][7][8][9][10][11], the spin average value in the layer numbered i along the z…”

“…As a result, the higher-order terms of z i S tend to zero faster than the linear terms of z i S , we can only take into account those linear terms. Therefore, the spin average value z i S for an N -layer ferroelectric thin film with s N surface layers can be expanded and there are N linear equations [10][11]:…”

“…In recent years, various high quality ferroelectric thin films have been successfully fabricated by different kinds of physical or chemical techniques in experiment [1,2]. On the other hand, the ferroelectric thin film described by the transverse Ising model has also been studied by the usual mean-field approximation (MFA) [3][4][5][6][7][8][9][10][11]. Usually, the second-order phase transition in a transverse Ising thin film is calculated only by taking the nearest-neighbor twospin exchange interaction into account.…”

“…Effects of the surface exchange interaction and the thickness on the Curie temperature in a thin film with different numbers of surface layers have been discussed in detail. Recently, the effects of surface modification on the critical behavior in a multiple-surface-layer ferroelectric thin film have been inspected by using the usual MFA [10]. Very recently, the influence of surface and bulk layers on the crossover features for interaction parameters of a ferroelectric thin film has also been calculated under the usual MFA [11].…”