Evidence of Sharp and Diffuse Domain Walls in ${\mathrm{BiFeO}}_3$ by Means of Unit-Cell-Wise Strain and Polarization Maps Obtained with High Resolution Scanning Transmission Electron Microscopy

Domain walls (DWs) substantially influence a large number of applications involving ferroelectric materials due to their limited mobility when shifted during polarization switching. The discovery of greatly enhanced conduction at ${\mathrm{BiFeO}}_3$ DWs has highlighted yet another role of DWs as a local material state with unique properties. However, the lack of precise information on the local atomic structure is still hampering microscopical understanding of DW properties. Here, we examine the atomic structure of ${\mathrm{BiFeO}}_3$ 109° DWs with pm precision by a combination of high-angle annular dark-field scanning transmission electron microscopy and a dedicated structural analysis. By measuring simultaneously local polarization and strain, we provide direct experimental proof for the straight DW structure predicted by ab initio calculations as well as the recently proposed theory of diffuse DWs, thus resolving a long-standing discrepancy between experimentally measured and theoretically predicted DW mobilities.

Figure 1

Schematic of (a) Miller-Weinreich and (b) diffuse DW adapted from Shin et al. [5] to the case of ${\mathrm{BiFeO}}_3$ 109° DW (see below). The black and gray arrows indicate the projected unit-cell-wise electric polarization $\mathbf{P}$. A vertical shift of the steps into $y$ ($-y$) direction denoted by small red (blue) arrows leads to a horizontal shift of the whole DW to the right (left) denoted by big red (blue) arrows.

Figure 2

Lattice analysis principle and 109° DW structure. (a) Overview of ${\mathrm{BiFeO}}_3$ layer grown on ${\mathrm{DyScO}}_3$. (b) Original HAADF image. (c) Enlarged rectangle (upper part) and simulated STEM image of DFT DW structure (lower part). (d) Fitted column positions and types (upper part) and the according DFT DW structure (lower part). (d) Unit cell wise shear (color) and electric polarization (arrows) obtained from the experimental (upper part) and simulated STEM image (lower part).

Figure 3

(a) Lattice and (b) polarization rotation field at ${\mathrm{BiFeO}}_3$ 109° DW containing steps. The comparatively large scatter in polarization angle is caused by the Fe-position error. In contrast to the lattice strain, the polarization vector field at the steps (enlarged squares) shows, on the length scale of the diagonal boundary, a diffuse rotation and attenuation.