The flexoelectric effect, which describes the induction of polarization from strain gradient, is negligible in bulk but not nanometer scale ferroelectrics. The influence of flexoelectric effects on magnetic field induced electric polarizations in multiferroic nanocomposite thin bilayer films has been investigated. It has been found that with flexoelectric effects taken into consideration, the polarization would not be reduced to zero even if the film was ultra-thin. Under an applied magnetic field, polarizations were induced from two effects, i.e., the conventional electrostrictive and flexoelectric effects. In the case where the film thickness was relatively large, the former factor was the main one influencing the magnetic field induced polarization. By decreasing the film thickness, the flexoelectric induced polarization became more and more dominant and it finally overcame the electrostrictive induced polarization and changed the value of magnetic field induced polarization from negative to positive.
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Chen et al. (2012) studied this question.
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