Monte Carlo simulation of ferroelectric properties in bismuth titanate (Bi4Ti3O12) thin films

This work presents the modeling and simulation of bismuth titanate (Bi3Ti4O12) thin films ferroelectric properties. The sample dimensions are L × L × d (L = 15), where L × L indicates the dimensions in the x–y plane, considering periodic boundary conditions, and d is the film thickness (d = 10) in the z axis with free boundary conditions. The system was modeled using a Hamiltonian that contains two terms: the first one corresponds to the dipolar interaction and the second term includes the external electric field influence. Moreover, the polarization anisotropy was intrinsically included, having into account two preferential crystallographic directions a (x axis) and c (z axis), for the spontaneous polarization, taking values of Pa = 50 μC/cm2 and Pc = 4 μC/cm2 respectively. Simulations were carried out using the Monte Carlo method combined with the Metropolis algorithm, starting from a randomly oriented polarization state at a high temperature until the equilibrium state is reached. Therefore, the ferroelectric behavior such as polarization, hysteresis loops and dipoles state as a function of temperature and the applied electric field was obtaining. The results showed a transition temperature from paraelectric to ferroelectric phase close to 948 K, being in agreement with the reports. The electric domains formation was observed depending on the temperature and the electric field.