Scaling of domain periodicity with thickness measured inBaTiO3single crystal lamellae and comparison with other ferroics

Abstract

The focused ion beam microscope has been used to cut parallel-sided {100}-oriented thin lamellae of single crystal barium titanate with controlled thicknesses, ranging from $530\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}70\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Scanning transmission electron microscopy has been used to examine domain configurations. In all cases, stripe domains were observed with {011}-type domain walls in perovskite unit-cell axes, suggesting 90\ifmmode^\circ\else\textdegree\fi{} domains with polarization in the plane of the lamellae. The domain widths were found to vary as the square root of the lamellar thickness, consistent with Kittel's law, and its later development by Mitsui and Furuichi and by Roytburd. An investigation into the manner in which domain period adapts to thickness gradient was undertaken on both wedge-shaped lamellae and lamellae with discrete terraces. It was found that when the thickness gradient was perpendicular to the domain walls, a continuous change in domain periodicity occurred, but if the thickness gradient was parallel to the domain walls, periodicity changes were accommodated through discrete domain bifurcation. Data were then compared with other work in literature, on both ferroelectric and ferromagnetic systems, from which conclusions on the widespread applicability of Kittel's law in ferroics were made.