Fig. 1: Structure characterizations and domain distribution of HfO₂-based films.

a XRD θ−2θ patterns of the films. b XAS and XLD at O-K edge of La³⁺ doped and LT co-doped samples. The shaded background regions with different colors represent different crystal fields, and the inset shows a schematic of the experimental configuration for the spectroscopy studies. c The pole figure of {002} planes observed along [111] direction of the LT:HfO₂ film. The colored cycles in the pole figure represent 4 domain variants marked as A, B, C and D types, where the A type domain includes a (002), a’ (020) and a” (200) planes (Likewise, B type: b (002), b’ (020) and b” (200) planes; C type: c (002), c’ (020) and c” (200) planes; D type: d (002), d’ (020) and d” (200) planes). d 2θ scans of 12 diffraction points in the{002}-plane pole figure. The displayed θ−2θ data were processed with Lorentz fitting. e An example of HfO₂ (111) domain distribution on the (001) plane of 4 × 4 STO supercells. STEM images observed along φ = 15° (zone axis STO [001] defined as φ = 0°) of (f) the La:HfO₂ film and (g) the LT:HfO₂ film. The rhombohedrons inset indicate the domains within HfO₂ films with different in-plane rotation angles. The white solid lines enclosed with green and yellow dotted lines in f describe the dislocations.