The Curie temperature of ultra-thin ferroelectric films

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Abstract
The Curie temperature of ferroelectric films described by the transverse Ising model was studied under the mean-field theory. The film layer number, the surface interaction and the surface layer number dependence of the Curie temperature were obtained. There is a critical surface interaction strength, which is JSC=1.25 J for single-surface-layer films, and JSC=1.078 J for multiple-surface-layer films. If the surface interaction strength exceeds the critical value, there exists an optimum film thickness which possesses the maximum Curie temperature; then the surface interaction strength is weaker than the critical value, the Curie temperature decreases monotonically with increasing film thickness, and there exist critical sizes or critical thicknesses at which the ferroelectricity will disappear if the surface interaction is weak enough.