Direct Imaging of Orbitals using Inelastic X-Ray Scattering

*L. H. Tjeng (1), H. Yavaş (1,2), M. Sundermann (1,3), B. Leedahl (1), K. Chen (3), A. Amorese (1,3), A. Severing (1,3), H. Gretarsson (1,2), and M. W. Haverkort (4)
(1) Max Planck Institute for Chemical Physics of Solids, Dresden, Germany, (2) Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany, (3) Institute of Physics II, University of Cologne, Cologne, Germany, (4) Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany

It is generally accepted that the correlated motion of electrons is at the origin of many interesting physical properties including unconventional superconductivity, colossal magnetoresistance, and multiferroicity, just to name a few. These spectacular properties emerge through intricate interplay of charge-spin-orbital degrees of freedom of valence electrons, so their characterization is an essential ingredient for modeling these curious behaviors and revealing the underlying mechanisms. This is a very challenging and delicate undertaking, which often requires the knowledge of the active valence wave function.

We developed a new experimental method that directly images the active orbital in solids, without advanced calculation or spectroscopic analysis [1]. The method, s-core-level non-resonant inelastic X-ray scattering (s-NIXS), relies on high momentum transfer in the inelastic scattering process, which is necessary for dipole-forbidden terms to gain spectral weight. To demonstrate the strength of the technique, we imaged the text-book example, x2-y2/3x2-r2 hole orbital of the Ni2+ ion in NiO single crystal. We will present the basic principles of s-NIXS and its experimental implementation. We will also show how we can apply this technique to unveil the active orbitals in complex oxides as well as to determine the orbital character in highly metallic systems such as elemental Cr, Fe, and Ni.

[1] H. Yavaş, M. Sundermann, K. Chen, A. Amorese, A. Severing, H. Gretarsson, M. W. Haverkort, L. H. Tjeng, Nature Physics (2019);