Direct Imaging of Orbitals in Quantum Materials

The search for new quantum materials with novel properties is often focused on materials containing transition-metal or rare-earth elements. The presence of the atomic-like d or f orbitals provides a fruitful playground to generate novel phenomena and understanding the behavior of those d and f electrons is essential for designing and tuning new 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 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, 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 [1]. 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. Yavas, M. Sundermann, K. Chen, A. Amorese, A. Severing, H. Gretarsson, M.W. Haverkort, L.H. Tjeng,
Nature Physics (2019) ; https://doi.org/10.1038/s41567-019-0471-2.