Simulations of domain pattern in lead-titanate by molecular dynamics simulations aided q-state Potts model

Manipulation or detection of domain patterns in ferroelectrics is of great interest due to wide applications for such materials. Among all the simulation methods, q-state Potts model is a common method used to simulate the domain pattern of ferroelectrics. The method, however, expresses the effect of temperature and coupling energy between interacting cells in an implicit way. In this study, we developed a new scheme that can explicitly study the temperature and coupling energy effect on the domain pattern of ferroelectrics. The method combined molecular dynamics (MD) simulations with a modified q-state Potts model. In the traditional q-state Potts model, each state is represented by a constant. Here we propose that the states are a function of temperature. We tested our method with a standard J_p in various temperatures. The results are consistent with those by phase-field method. The effect of J_p was also studied. By adjusting the J_p, effect of external stress/strain or the buffer layer on the domain pattern of PbTiO₃ may be simulated. The correlation between the hysteresis loop and changing of domain pattern was also investigated. This new method provides insights in evolution of domain patterns in terms of temperature, the coupling energy and external electric voltage.