Origin of interfacial polar order in incipient ferroelectrics

There are ample experimental evidences indicating that the ferroelastic domain walls of incipient ferroelectrics, such as $\mathrm{SrTi}{\mathrm{O}}_3$ and $\mathrm{CaTi}{\mathrm{O}}_3$, are polar. The emergence of such interfacial polar order at a domain wall is exciting and believed to arise from the coupling between a primary order parameter, such as a strain or an antiferrodistortive (AFD) order parameter, and polarization. There have been several mechanisms proposed to explain the emergence of interfacial polar order, including biquadratic coupling, AFD-antiferroelectric coupling, and flexoelectric coupling. Using $\mathrm{CaTi}{\mathrm{O}}_3$ as an example, we demonstrate, using both asymptotic analytics and numerical calculation, that the flexoelectric coupling is likely the dominant mechanism leading to the interfacial polar order.

Figure 1

The schematic of the simulation system. There are three domains, I, II, and III with two twin walls. The corresponding order parameters are shown for each domain. The coordinate system is chosen along crystallographic directions of the pseudocubic lattice.

Figure 2

The schematics of the domain wall profiles for the biquadratic coupling. The profile can be either kinklike or breatherlike.

Figure 3

The calculated domain wall profiles from phase-field simulation with flexoelectric contribution. (a) and (b) correspond to the left and right wall, respectively, in Fig. 1. The $P_1$ component shows an AFE-like profile that is identical in two walls, while the $P_2$ component changes sign. The profiles of the oxygen octahedra tilt are identical to the phase-field simulation results without including the flexoelectric effect.