Extended Data Figure 4: X-ray spectroscopy and resonant X-ray diffraction measurements of epitaxial NdNiO₃/LaAlO₃ (111) and (001) films.

a, X-ray absorption spectroscopy (XAS) at the Ni K edge shows a clear pre-edge intensity, when the incident X-ray polarization (E) is along [111] of a NdNiO₃ (111) film. The near-edge X-ray absorption fine structure (NEXAFS) indicates the Ni displacement is more pronounced along [111]_pc of the NdNiO₃ (111) film, while weaker along the other two in-plane directions. The response from a NdNiO₃ (001) film is similar to the in-plane results from the NdNiO₃ (111) film. The weak pre-edge intensity is due to transitions from the 1s to 3d levels. At the K edge, s–d electric dipole transition is forbidden for this octahedral case and weak quadrupole transition is allowed. However, as the central Ni atom is displaced from its cubic symmetric site, the displacement breaks the inversion symmetry, mixing p-state symmetry with unfilled d-states and allowing the dipole transition. The strength of the dipole transition is proportional to the square of the displacement along the incident X-ray polarization. b, Resonant X-ray diffraction (XRD) intensity at a film peak in pseudo-cubic notation (that is, equivalent to a (011) Bragg peak in orthorhombic notation) across the Ni K edge is shown. The Ni response at the arises from a combination of the finite size effect of the film (thickness fringes) and monoclinic distortion related to the Ni displacement. The error bars for both the XAS and resonant XRD results are calculated as the square root of the measured intensity.