The negative dielectric permittivity of polycrystalline barium titanate nanofilms under high-strength kHz-AC fields

Unlike the conventional high-frequency dielectric behavior for which the amplitude of the applied field is too small to cause polarization switching, the dynamically-driven polarization reorientation brings remarkable frequency dependence to the nonlinear electromechanical behaviors of ferroelectric nanofilms. In this study, we developed a thermodynamically consistent phase-field model with an introduced second-order kinetic equation to investigate the dynamics of polarization switching in polycrystalline barium titanate nanofilms under high-strength AC fields. The newly introduced kinetic equation consists of an additional dynamic inertial term that brings about collective resonance of polarization within a certain frequency range. Negative dielectric permittivity is observed in a certain frequency band as the applied frequency varies from 30 to 80 kHz, and the maximum absolute value is reached around 40 kHz. It was demonstrated through microstructure-based analysis that such negative dielectric behavior is inherited from the frequency-dependent polarization switching in the nanograins. It also serves as the mechanism for other observed frequency-dependent physical properties, e.g., the remnant polarization, the piezoelectric coefficient at zero electric field and the coercive field. In addition, we further explored the influence of the damping coefficient in the kinetic equation and the influence of the in-plane strain to such frequency-dependent behaviors. It was found that a higher damping coefficient or applied in-plane strain tends to weaken the occurrence of negative permittivity.