Abstract
The frequency dependence of the electromechanical response of a barium titanate nano-thin film was studied through phase-field simulation. A two-dimensional phase-field model based on Landau–Devonshire energy density function was established in this work. The time-dependent Ginzburg–Landau equation was utilized to calculate the dynamics of the microstructure upon the application of an AC electric field. A segment of barium titanate thin film was modeled with 20 nm in thickness and 80 nm in width. Periodic boundary conditions were applied to both ends of the nano-thin film to represent an infinite length-to-thickness ratio. It was observed from the phase-field results that the loading frequency of the electric field can noticeably affect the hysteresis and butterfly loops of the nano-thin film through competition with the electric dipole evolution. A high-frequency electric field tends to yield a close-to-linear response of the thin film. Meanwhile, it was discovered that the existence of $$180^{\circ }$$ domain walls and their dynamics (oscillation) within the thin film have remarkable influence on the overall response.
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