Study of Ba_xSr_1-xTiO₃ thin films using transverse-field Ising model

In this paper, the effects of doping on the thermodynamic properties of Ba_xSr_1-xTiO_3 (BST) thin film are investigated, based on the transverse-field Ising model (TIM) within the framework of mean field theory. We apply the double-peak distribution model of related parameters to mimic doping. The lattice expansion arising from doping with large Ba^2+ was also taken into account. We concentrate on the doping concentration dependence of peak temperature (T_\rm m), spontaneous polarization and dielectric susceptibility. It is found that the doping concentration has great influence on the dielectric properties and phase transition properties of BST thin films. We also discuss the quantum effect arising from doping.