Origin of interfacial polar order in incipient ferroelectrics

There are ample experimental evidences indicating that the ferroelastic domain walls of incipient ferroelectrics, such as SrTiO3 and CaTiO3, 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 CaTiO3 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.