Thermodynamics of polarization dynamics in ferroelectrics implemented by the phase field model

Abstract

Polarization dynamical response is a fundamental issue for both physics and functional device applications for ferroelectrics. The phase field model has been proved as an efficient and indispensable method to capture the polarization evolution behaviors. With the size of polar element reducing to be atomic scale, the underlying physics in the phase field model should be well clarified. Starting from the generalized many-body stochastic dynamics, we discuss the thermodynamics of the polarization dynamics simulated based on the phase field scheme. It is found that the presence of random force guarantees the thermodynamics of polarization system. The numerical simulations indicate that the thermal fluctuations induced by random force give rise to a different heat dissipation mechanism during the process of polarization dynamical responses, which is not taken into account in the conventional phase field simulations. In addition, the thermal fluctuations of random force are found to lead to the unexpected phase instability when considering the atomic-scale polarization dynamical behaviors, which is considered to be originated from the incompatibility between the free-energy functional and random force used in the current phase field model. If simply revising the free-energy functional to get rid of such contradiction, the possible phase instability can be eliminated, but it results in the underestimation of thermal fluctuations and the associated polarization dynamical behaviors. In our opinion, the viable solution is to reconstruct the potential field, making it be compatible with the thermal fluctuation induced by random force. Our discussion could help to provide hints for the development of multiscale modeling scheme in polarization dynamics based on a phase field model.