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

•Thermodynamic properties and the hysteresis behavior of the compositionally graded BST thin films are studied by the EFT.•The temperature and the number of slabs and layers in BST on the longitudinal polarization and the hysteresis loops are investigated.•The random bond model of related parameters is applied to mimic doping have been examined.

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−xSrxTiO3Ba1−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.