Electromechanics of Domain Walls in Uniaxial Ferroelectrics

Piezoresponse force microscopy (PFM) is used for investigation of the electromechanical behavior of the head-to-head (H-H) and tail-to-tail (T-T) domain walls on the non-polar surfaces of three uniaxial ferroelectric materials with different crystal structures: LiNbO₃, Pb₅Ge₃O₁₁, and ErMnO₃. It is shown that, contrary to the common expectation that the domain walls should not exhibit any PFM response on the non-polar surface, an out-of-plane deformation of the crystal at the H-H and T-T domain walls occurs even in the absence of the out-of-plane polarization component due to a specific form of the piezoelectric tensor. In spite of their different symmetry, in all studied materials, the dominant contribution comes from the counteracting shear strains on both sides of the H-H and T-T domain walls. The finite element analysis approach that takes into account a contribution of all elements in the piezoelectric tensor, is applicable to any ferroelectric material and can be instrumental for getting a new insight into the coupling between the electromechanical and electronic properties of the charged ferroelectric domain walls.