Bilinear Flexo-Antiferrodistortive Coupling in Ferroelastics: Polar Twins, Antiphase Boundaries and Fingerprints of Alterelectricity

Abstract

Using the Landau-Ginsburg-Devonshire approach we show that the linear gradient-type coupling between the electric polarization vector and antiferrodistortive long-range order parameter pseudovector, that has the form of Lifshitz invariant and named "bilinear flexo-antiferrodistortive coupling", can emerge in all antiferrodistortive ferroelastics, since it is symmetry-allowed. Using the four sublattices model we reveal that the bilinear flexo-antiferrodistortive coupling can induce the sublattice-sensitive polarization at the twin walls and antiphase boundaries in antiferrodistortive ferroelastics without any ferroelectric or antiferroelectric ordering. Since the induced polarization is perpendicular to the antiferrodistortive long-range order parameter and counter-directed in neighboring sublattices with checkerboard-type direction of antiferrodistortive long-range order parameter, such structure of polarization may correspond to the alterelectric-type quadrupolar electric order. However, physical manifestations of the bilinear flexo-antiferrodistortive coupling are invisible in most nanostructured antiferrodistortive ferroelectrics and antiferroelectrics due to the domination of piezoelectric and/or linear flexoelectric couplings. Since a common flexoelectric coupling cannot induce the alterelectric-type polarization at domain boundaries in antiferrodistortive ferroelastics, we believe that the bilinear flexo-antiferrodistortive coupling can be a fingerprint of recently discovered alterelectric long-range order in antiferrodistortive ferroelastics.