Spectroscopic mapping of local structural distortions in ferroelectric PbTiO${}_3$/SrTiO${}_3$ superlattices at the unit-cell scale

The local structural distortions in polydomain ferroelectric PbTiO${}_3$/SrTiO${}_3$ superlattices are investigated by means of high spatial and energy resolution electron-energy-loss spectroscopy combined with high-angle annular dark field imaging. Local structural variations across the interfaces have been identified with unit-cell resolution through the analysis of the energy-loss near-edge structure of the Ti $L_{2,3}$ and O $K$ edges. Ab initio and multiplet calculations of the Ti $L_{2,3}$ edges provide unambiguous evidence for an inhomogeneous polarization profile associated with the observed structural distortions across the superlattice.

Figure 1

(a) HAADF-STEM image of the [010] projection of a (6$|$6) PTO/STO superlattice. (b) X-ray reciprocal space scans around the (002) superlattice reflection show broad satellite peaks due to 180${}^{\circ }$ ferroelectric domains.

Figure 2

(a) Ti $L_{2,3}$ and (b) O $K$ edges for the STO substrate (black upper curve) and the 12-nm-thick PTO layer (red/gray lower curve). (c) Schematic projection along the [010] zone axis of the STO and PTO unit cells. The displacement of the atomic position is displayed as $\delta$ (Ti), $\delta$ (O1), and $\delta$ (O2).

Figure 3

(a) HAADF-STEM image and ELNES of Ti $L_{2,3}$ and O $K$ edges across the (6$|$6) superlattice. (b) Simultaneous dark field profile recorded along the line scan (black line) and concentration profiles of Sr (green line) and Pb (red line). Horizontal lines mark the interfaces. (c) Energy splitting values in PTO and STO layers across the superlattice. Dashed lines indicate the values for STO substrate and 12-nm-thick PTO. (d) High-resolution Ti $L_{2,3}$ and (e) O $K$ spectra across the PTO-STO interface after background substraction. (f) Ti $L_3$ edges obtained after ten R-L iterations.

Figure 4

Relaxed atomic displacements as a function of the $c/a$ ratio for (a) PTO and (b) STO structural models. CFS values for (c) PTO and (d) STO structural models as a function of the $c/a$ ratio. (e) Simulated $L_3$ spectra for PTO (red) and STO (black). (f) Simulated $L_3$ spectra for a paraelectric (blue) and polar (red) tetragonally distorted PTO unit cell ($c/a=1.063$).