Bichiral structure of ferroelectric domain walls driven by flexoelectricity

The influence of flexoelectric coupling on the internal structure of neutral domain walls in the tetragonal phase of perovskite ferroelectrics is studied. The effect is shown to lower the symmetry of 180 degrees walls which are oblique with respect to the cubic crystallographic axes, while {100} and {110} walls stay "untouched." Being of the Ising type in the absence of the flexoelectric interaction, the oblique domain walls acquire a new polarization component with a structure qualitatively different from the classical Bloch-wall structure. In contrast to the Bloch-type walls, where the polarization vector draws a helix on passing from one domain to the other, in the flexoeffect-affected wall, the polarization rotates in opposite directions on the two sides of the wall and passes through zero in its center. Since the resulting polarization profile is invariant upon inversion with respect to the wall center, it does not break the wall symmetry, in contrast to the classical Bloch-type walls. The flexoelectric coupling lowers the domain wall energy and gives rise to its additional anisotropy, which is comparable to that conditioned by elastic anisotropy. The atomic order-of-magnitude estimates shows that the new polarization component P-2 may be comparable with spontaneous polarization P-s, thus suggesting that, in general, it is mandatory to include the flexoelectric coupling in domain wall simulations in ferroelectrics. Calculations performed for barium titanate yield the maximal value of P-2, which is much smaller than that of the spontaneous polarization. This smallness is attributed to an anomalously small value of a component of the "strain-polarization" electrostrictive tensor in this material.