Phase field study on the flexoelectric response of dielectric–ferroelectric multilayers

We report a theoretical modeling of the flexoelectric response of dielectric–ferroelectric (DE–FE) multilayers based on phase field simulations in the framework of the Landau–Ginzburg–Devonshire (LGD) theory. The correlation between negative capacitance and flexoelectric response is revealed, and the single-domain and multi-domain models are compared. It shows that the dielectric layers drive the ferroelectric layer into a negative capacitance regime, and the flexoelectric response of the multilayer is maximal when the negative capacitance of the ferroelectric layer has a minimal absolute value. Moreover, the flexoelectric response peak will be shifted to a lower temperature by increasing the thickness of dielectric layer, indicating a possibility of achieving a stronger flexoelectric response at room temperature compared with that of pure ferroelectric. However, while the single-domain model shows that the flexoelectric response peak is simply shifted to a lower temperature with near constant peak value and width, the multi-domain model reveals a significant suppressing of the flexoelectric peak by the dielectric layer. This is attributed to the formation of the vortex domain state, which eases the depolarization effect and leads to large absolute value of negative capacitance of the ferroelectric layer. Our work provides new insights into flexoelectricity in ferroelectric heterostructures.