Bichiral structure of feroelectric domain wall driven by   flexoelectricity
  The influence of flexoelectric coupling on the internal structure of neutral domain walls in tetragonal phase of perovskite ferroelectrics is studied. The effect is shown to lower the symmetry of 180-degree 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 brake the wall symmetry in contrast to the classical Bloch-type walls. The flexoelectric coupling lower the domain wall energy and gives rise to its additional anisotropy that is comparable to that conditioned by the elastic anisotropy. The atomic orderof- magnitude estimates shows that the new polarization component P2 may be comparable with spontaneous polarization Ps, thus suggesting that, in general, the flexoelectric coupling should be mandatory included in domain wall simulations in ferroelectrics. Calculations performed for barium titanate yields the maximal value of the P2, 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" elecrostictive tensor in this material. 
P. V. Yudin, A. K. Tagantsev, E. A. Eliseev, A. N. Morozovska and N.   Setter
cond-mat.mtrl-sci