Understanding doped perovskite ferroelectrics with defective dipole model

While doping is widely used for tuning physical properties of perovskites in experiments, it remains a challenge to exactly know how doping achieves the desired effects. Here, we propose an empirical and computationally tractable model to understand the effects of doping with Fe-doped BaTiO$_{3}$ as an example. This model assumes that the lattice sites occupied by Fe ion and its nearest six neighbors lose their ability to polarize, giving rise to a small cluster of defective dipoles. Employing this model in Monte-Carlo simulations, many important features like reduced polarization and the convergence of phase transition temperatures, which have been observed experimentally in acceptor doped systems, are successfully obtained. Based on microscopic information of dipole configurations, we provide insights into the driving forces behind doping effects and propose that active dipoles, which exist in proximity to the defective dipoles, can account for experimentally observed phenomena. Close attention to these dipoles are necessary to understand and predict doping effects.