Hysteresis loops and dielectric properties of compositionally graded (Ba,Sr)TiO3 thin films described by the transverse Ising model

Using the effective field theory with a probability distribution technique that accounts for the self-spin correlations, we apply the transverse spin-1/2 Ising model to study the intrinsic hysteresis of compositionally graded Ba1-xSrxTiO3 (BST) thin films with x decreasing from 0.20 to 0.10 in successive slabs. The random bond model of related parameters is applied to mimic doping. The effects of the thickness, the concentration of Sr, the number of slabs and the temperature on the polarization and the hysteresis are discussed. (C) 2016 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.