Abstract

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, x2 − y2/3z2 − r2 orbital of the Ni2+ ion in NiO single crystal.

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The data that support the findings of this study are available from the corresponding authors upon request.

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Acknowledgements

M.S., K.C. and A.S. acknowledge support from the German funding agency DFG under grant no. SE1441-4-1.

Author information

Author notes

    • Hasan Yavaş

    Present address: SLAC National Accelerator Lab, Menlo Park, CA, USA

    • Kai Chen

    Present address: Helmholtz-Zentrum Berlin, BESSY II, Berlin, Germany

Affiliations

  1. Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

    • Hasan Yavaş
    • , Martin Sundermann
    • , Andrea Amorese
    • , Andrea Severing
    • , Hlynur Gretarsson
    •  & Liu Hao Tjeng
  2. PETRA III, Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

    • Hasan Yavaş
    •  & Hlynur Gretarsson
  3. Institute of Physics II, University of Cologne, Cologne, Germany

    • Martin Sundermann
    • , Kai Chen
    • , Andrea Amorese
    •  & Andrea Severing
  4. Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany

    • Maurits W. Haverkort

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Contributions

L.H.T. and M.W.H. initiated the project. H.Y., M.S., K.C., A.A. and H.G. performed the experiment and analysed the data. H.Y., A.S., M.W.H. and L.H.T. wrote the manuscript with input from all authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Liu Hao Tjeng.

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DOI

https://doi.org/10.1038/s41567-019-0471-2