Polarization switching of the incommensurate phases induced by flexoelectric coupling in ferroelectric thin films

The polarization switching of the incommensurate (INC) phases induced by flexocoupling in perovskite ferroelectric thin films is investigated with a multi-field coupling theoretical framework combining the flexoelectric effect. The dominant factors of the formation of INC phases that show antiferroelectric-like double hysteresis loops are examined. The simulations show that mechanical boundary conditions have little influence on the polarization responses of INC phases. The polarization switching behaviors of INC phases are governed by the flexocoupling types described by different flexocoupling coefficients. Only the transverse flexocoupling coefficient related INC phases show antiferroelectric-like double hysteresis loop. The longitudinal flexocoupling coefficient related and shear flexocoupling coefficient related INC phases show imprint-like hysteresis loops and hysteresis loops similar to those of the ferroelectric phase, respectively. The observed different polarization switching behaviors are rationalized by free energy density curves of the INC phases.