Orientations of low-energy domain walls in perovskites with oxygen octahedral tilts

Many applications of ferroic materials, such as data storage and spintronics, are achieved through the control and manipulation of their domain wall (DW) orientations and configurations. Here we propose a rotational compatibility condition to identify low-energy DWs in perovskites with oxygen octahedral tilt instability. It is derived from the strong DW energy anisotropy arising from the rigidity and corner-sharing feature of the octahedral network. We analyze quantitatively the DWs in $\mathrm{SrTi}{\mathrm{O}}_{3}$ and explain successfully the unusual ferroelectric DW width and energy in $\mathrm{BiFe}{\mathrm{O}}_{3}$.