Orbital Reflectometry and the Electronic Structure of Oxide Interfaces

The occupation of $d$-orbitals has a key influence on the physical properties of transition-metal (TM) oxides.\footnote{Tokura, Y. $\&$ Nagaosa, N. Science {\bf 288}, 462-468 (2000).} Due to the strong hybridization with neighboring oxygen ions, the electronic structure is very sensitive to changes in the TM-oxygen bond distances induced by strain and/or by the chemical bonding to other ions with different electronic configuration. Both effects might be important in oxide heterostructures,\footnote{Han, M. J., Marianetti, C. A. $\&$ Millis, A. J. Phys.\ Rev.\ B {\bf 82}, 134408 (2010).} but thus far it has been difficult to probe atomic-scale modulations of the orbital occupation in a quantitative manner.\footnote{Chakhalian, J. \textit{et al.} Science {\bf 318}, 1114-1117 (2007).} We present results from polarized soft x-ray resonant reflectivity, which demonstrate that it is possible to derive quantitative, spatially resolved orbital polarization profiles. We show that this method is sensitive enough to resolve differences of $\sim 3\%$ in the occupation of Ni $e_g$ orbitals in adjacent atomic layers of a LaNiO$_3$-LaAlO$_3$ superlattice, and the experimental findings are in good agreement with electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up new perspectives for orbital physics in oxide heterostructures.