Domain Wall Orientations in Ferroelectric Superlattices Probed with Synchrotron X-Ray Diffraction

Ferroelectric domains in ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices are studied using synchrotron x-ray diffraction. Macroscopic measurements reveal a change in the preferential domain wall orientation from $\{100\}$ to $\{110\}$ crystallographic planes with increasing temperature. The temperature range of this reorientation depends on the ferroelectric layer thickness and domain period. Using a nanofocused beam, local changes in the domain wall orientation within the buried ferroelectric layers are imaged, both in structurally uniform regions of the sample and near defect sites and argon ion-etched patterns. Domain walls are found to exhibit a preferential alignment with the straight edges of the etched patterns as well as with structural features associated with defect sites. The distribution of out-of-plane lattice parameters is mapped around one such feature, showing that it is accompanied by inhomogeneous strain and large strain gradients.

Figure 1

In-plane RSMs around the 002 superlattice Bragg peak. The ring of intensity is due to diffuse scattering from periodic ferroelectric domains, with a period ${\mathrm{\Lambda }}_d\simeq 5\mathrm{nm}$. The domain structure evolves from walls lying predominantly in the $\{100\}$ planes at room temperature, to a more isotropic configuration at 375 K (uniform ring), to $\{110\}$ DWs at 450 K. No diffuse scattering is observed in the paraelectric phase at 675 K.

Figure 2

Average tetragonality ($c/a$) and domain satellite intensities for the two DW orientations normalized by the values at room temperature. Hollow markers correspond to intensities first normalized by the square of the polarization.

Figure 3

Spatial variation of domain satellite intensity for (010) (a) and (100) (b) DWs. Horizontal scale bars correspond to $1\mu \mathrm{m}$. The black boxes show two anticorrelated regions. (c) Normalized average autocorrelation functions for images in (a) (red circles) and (b) (black squares). Fitting parameters $\xi$ and $h$ are discussed in the main text. The bottom left inset is an expanded plot around the dashed box in the main figure, showing a minimum at 300 nm for one DW orientation. The top right inset shows the in-plane RSM around the 003 peak of the superlattice (unfocused beam). The dashed blue line indicates the approximate orientation of the detector in reciprocal space, whereas the red and blue boxes indicate the domain satellites used for mapping the intensity in (a) and (b), respectively.

Figure 4

(a) Domain satellite intensity around a defect in the superlattice, showing DW alignment parallel to the long features of the defect. The schematics show the probed DW orientation for each image, with the central RSM indicating the RS regions probed in each map. The bottom right image is a map of the Bragg peak intensity around the same region. The color bars show the intensity in arbitrary units. The central bottom figure shows an AFM scan of the topography at the center of the defect. (b) Map of the strain ${\epsilon }_{33}$ in the region marked by the box in the top right image of (a). (c) AFM image of the superlattice topography around the same region. (d) Map of the 2D strain gradient ${\nabla }_{x,y}{\epsilon }_{33}$ with arrows and colors representing its direction and magnitude, respectively. The arrows around the region with the largest strain gradient point to a direction perpendicular to the DWs. The horizontal scale bars in all images have a size of $2\mu \mathrm{m}$.