The search for new quantum materials with novel properties is often focused on materials containing transition-metal, rare-earth and/or actinide elements. The presence of the atomic-like d or f orbitals provides a fruitful playground to generate novel phenomena. The intricate interplay of band formation with the local electron correlation and atomic multiplet effects leads to phases that are nearly iso-energetic, making materials’ properties highly tunable by doping, temperature, pressure or magnetic field. Understanding the behavior of the d and f electrons is essential for designing and controlling novel quantum materials. Therefore, identifying the d or f orbitals that actively participate in the formation of the ground state is crucial. So far, these orbitals have mostly been deduced from optical, X- ray and neutron spectroscopies in which spectra must be analyzed using theory or modelling. This, however, is also a challenge in and of itself, since ab-initio calculations hit their limits due to the many-body nature of the problem.

Here we developed a new experimental method that circumvents the need for involved analysis and instead provides the information as measured. With this technique, we can make a direct image of the active orbital and determine what the atomic-like object looks like in a real solid. The method, X-Ray Raman spectroscopy or non-resonant inelastic X-ray scattering using an s-core level (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,ground-state x2-y2/3x2-r2 hole orbital of the Ni2+ ion in NiO single crystal (see Figure). We will present the basic principles of s-NIXS and details of its experimental implementation. We will show how we can apply this technique to unveil the active orbitals in a wide range of single crystalline materials. We will also lay out what instrumental improvements are needed to advance this method further.

[1] H. Yava?, M. Sundermann, K. Chen, A. Amorese, A. Severing, H. Gretarsson, M.W. Haverkort, L.H. Tjeng, Nature Physics 15, 559 (2019)
[2] B. Leedahl, M. Sundermann, A. Amorese, A. Severing, H. Gretarsson, L. Zhang, A.C. Komarek, A. Maignan, M.W. Haverkort, and L.H. Tjeng, Nature Commun. 10, 5447 (2019).
[3] A. Amorese, B. Leedahl, M. Sundermann, H. Gretarsson, Z. Hu, H.-J. Lin, C.T. Chen, M. Schmidt, H. Borrmann, Yu. Grin, A. Severing, M.W. Haverkort, and L.H. Tjeng, Phys. Rev. X 11, 011002 (2021).