Ferroelectric domain periodicities in nanocolumns of single crystal barium titanate

A focused ion beam microscope has been used to mill rectangular “picture-frame” shapes from single crystal barium titanate. The lengths of the sides of the picture frames were of the order of $3–5μm$⁠, while the side width and thickness dimensions were of the order of $100–500nm$⁠. Such aspect ratios meant that each of the frame sides approximates to a column with rectangular cross section. Scanning transmission electron microsopy was used to characterize the ferroelectric domain configurations associated with these nanocolumns. It was found that conventional stripe domain patterns occurred in all cases, down to columnar cross-section sizes of the order of $∼100×100nm2$⁠. Despite the geometry of the columns rendering the ferroelectric as shape constrained in two dimensions, the domain periodicity was only noticeably sensitive to variations in the magnitude of one of those dimensions. Such observations were rationalized using arguments based on those used by Kittel [Phys. Rev. 70, 965 (1946)] and Mitsui and Furuichi [Phys. Rev. 90, 193 (1953)] for predicting the equilibrium domain periodicities in macroscopic slabs of ferroic material.