Direct imaging of orbitals in quantum materials

The electronic states of quantum materials based on transition-metal, rare-earth and actinide elements are dominated by electrons in the d and f orbitals intertwined with the strong band formation of the solid. Until now, to estimate which specific orbitals contribute to the ground state and thereby determine their physical properties we have had to rely on theoretical calculations combined with spectroscopy. Here, we show that s-core-level non-resonant inelastic X-ray scattering can directly image the active orbital in real space, without the necessity for any modelling. The power and accuracy of this new technique is shown using the textbook example, $x^2 − y^2 / 3z^2 − r^2$ orbital of the Ni$^{2+}$ ion in NiO single crystal