Scaling behavior of dynamic hysteresis in Bi3.25Pr0.75Ti3O12 thin films

The loop area ⟨A⟩ is related to the applied electric field E and frequency f by a power-law scaling relationship, which can be described as ⟨A⟩∝fa⋅Eb. Many experiments have confirmed that this relationship exists in most systems. Based on the scaling relationship, we can get information about domain nucleation and growth in ferroelectrics and predict their operating state at high frequencies. In this study, rare earth-doped Bi3.25Pr0.75Ti3O12 (BPT) thin films were selected as the research subject, an investigation into the scaling characteristics of its dynamic hysteresis was conducted. In the low electric field range, the relationship between the loop area of the film and the electric field E as well as the frequency f can be expressed as ⟨A⟩∝f−0.0997⋅E2.8946; in the high electric field range, this relationship is expressed as ⟨A⟩∝f−0.0997⋅E1.7152. Comparative analysis indicates that the BPT thin film exhibits weaker frequency dependence in its ferroelectric domain reversal, and demonstrates more stable polarization reversal characteristics. Meanwhile, the BPT film not only responds faster to voltage at low electric fields but also shows better stability at high electric fields.