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Direct imaging of orbitals in quantum materials

Nature Physics volume 15, pages 559–562 (2019)Cite this article

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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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Fig. 1: Scattering geometry of the non-resonant inelastic X-ray scattering experiment.
Fig. 2: Experimental non-resonant inelastic X-ray scattering spectra of NiO containing the core level excitations on top of the Compton profile.
Fig. 3: Close-up view of the experimental Ni M1 (3s → 3d) edge spectra for different sample rotations and orientations. The spectra are background-corrected and normalized.
Fig. 4: Integrated intensities of M1 (3s → 3d) edge spectra plotted on the projections of the orbital shape of the 3A2 3d(x2 − y2)3d(3z2 − r2) hole density.
Fig. 5: Compton intensity as function of sample angle φ.

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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.

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Author notes

  1. Hasan Yavaş

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

  2. Kai Chen

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

Authors and 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.

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Correspondence to Liu Hao Tjeng.

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Yavaş, H., Sundermann, M., Chen, K. et al. Direct imaging of orbitals in quantum materials. Nat. Phys. 15, 559–562 (2019). https://doi.org/10.1038/s41567-019-0471-2

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