Lattice-Rotation Vortex at the Charged Monoclinic Domain Boundary in a Relaxor Ferroelectric Crystal

We present evidence of lattice-rotation vortices having an average radius of $\sim 7\mathrm{nm}$ at the ferroelectric domain boundary of $(1\text{−}x)\mathrm{Pb}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3\text{−}{\mathrm{xPbTiO}}_3$ ($x=0.08$). Maps of crystal orientations and domain symmetry breaking are obtained using scanning convergent beam electron diffraction, which show fractional rotation vortices near the 50° monoclinic domain walls. The merging of 2D and 1D topological defects is consistent with inhomogeneous boundary charge and expected to have a large impact on the domain-switching mechanisms in relaxor ferroelectric crystals and ferroelectric devices.

Figure 1

Principles of using CBED for determining mirror symmetry and crystal rotation. Figure (a) shows an example for the mirror symmetry quantification, while crystal rotation along the $x$ and $y$ axes leads to a shift in the center of the CBED (000) pattern as shown in (b) and (c). The average of the cross-correlation coefficients of three pairs of discs labeled in orange in (a) is taken as ${\gamma }_{m,\text{average}}$, whose values are shown in (d) for a scan of $15\times 15$ points or 225 CBED patterns. Here, each color represents a different CBED pattern, whereas similar CBED patterns are shown in the same color.

Figure 2

Distribution of two nanodomains using SCBED. (a), (b), and (c) map out the ${\gamma }_{m,\text{average}}$ variations across two types of domains. The red dashed line indicates the domain boundary. The orange arrows indicate the projected polarization directions for each type of domain.

Figure 3

Maps of distribution of two nanodomains and lattice rotation vortices. Figures (a), (b), and (c) show the crystal rotation at each pixel, superimposed with the domain walls indicated by the blue dashed lines. Figures (d), (e), and (f) illustrates how the crystal rotates across the domain boundaries schematically.

Figure 4

Experimental and simulated CBED patterns along various zone axes. The mirror plane in the (a) type-1 and (b) type-2 domains is rotated by 45°. Figures (c) and (d) show simulated patterns of ${\mathrm{M}}_C$ ($Pm$) using the Bloch wave method and corresponding to the experimental (a) and (b) patterns, respectively. The indexing is based on simulated diffraction patterns.

Figure 5

Orientation relationship between two nanodomains with respect to the pseudocubic axes. Figures (a) and (b) correspond to type-1 and type-2 domains, respectively.

Figure 6

Schematic diagrams of various types of polarization vortices. The reported (a) flux-closure quadrants in a thin ferroelectric film embedded in a dielectric matrix, (b) dipole vortex-anti-vortex pairs in a very thin ferroelectric film, (c) 180° charged domain wall, and (d) our observation of 50° monoclinic charged domain wall. $E_1$ and $E_2$ represents the inhomogeneous electric field in type-1 and type-2 domains, respectively.