Theory on the fringe patterns in the study of ferroelectric domain walls using electron holography

The realization of electron holography provides a new powerful tool to probe the subtle and local changes of electric and magnetic fields inside a crystal structure through the phase variation of electron wave function. For a ferroelectric system the interference fringe patterns across a domain wall are very strongly affected by the presence of surface charge compensations. If the compensation is incomplete, residue depolarization field will be present in the direction parallel to the electron beam, which can induce kink-like fringe bending. Earlier reported holographic images of ferroelectric domain walls revealed an asymmetry fringe bending. This behavior is explained through phase shifts induced by both the depolarization field and the strain field.