Beyond conventional chemical mapping: prospects and challenges of orbital mapping

Abstract text (incl. figure legends and references)

It is well-known that core-loss EELS data contains not only information about the chemical elements present in the sample, but also about the scattering atoms" chemical environment, which manifests itself in the near-edge fine structure (ELNES). This enables some more advanced characterization techniques such as the fingerprinting of chemical compounds and the mapping of oxidation states. In this work, we explore the possibilities of fine structure mapping at "sub-atomic" spatial resolution, i.e., the real-space mapping of transitions to individual orbitals such as p_z or d_xy inside the sample.

Arguably, an electron is more likely to trigger a transition from, say, a 1s core-electron to an unoccupied p_x state if it passes close to the region where the 1s-p_x-overlap is large than it is when passing "far away". Therefore, it is conceivable that by mapping the inelastic scattering probability (i.e., an EEL spectrum) with very high spatial resolution allows to map the orientation and shape of the p_x orbital. Indeed, this is corroborated by detailed theoretical calculations [1] as well as proof-of-principle experiments [2,3]. Fig. 1 shows an example from the mapping of Ti-e_g-like states in Rutile oriented along the [0 0 1] zone axis at 80 kV. Despite the noise, the 90° rotation between adjacent Ti atoms is clearly visible.

In this work, we discuss the fundamental requirements for successfully performing orbital mapping, include conditions on the sample (such as geometry, symmetry and stability), the experimental setup (such as spatial resolution, energy resolution and high-tension), and the detection process (such as the signal to noise levels). In particular, it is shown that a low symmetry in the chosen orientation is required to clearly separate the ELNES peaks of different orbitals, that narrow energy ranges are generally necessary, and that high incident doses are required, even with direct electron detectors.

Despite the technical challenges, the prospect of mapping the electronic transitions between individual orbitals is exciting not only from a fundamental quantum mechanical point of view, but also for its possibilities for the design and characterization of novel materials in many fields, including electronics, energy storage, and catalysis. [4]

[1] Löffler et al., Ultramicroscopy 131 (2013) 39
[2] Löffler et al., Ultramicroscopy 177 (2017) 26
[3] Bugnet et al., PRL 128 (2022) 116401
[4] The authors acknowledge financial support by the Austrian Science Fund (FWF) under grant nr. I4309-N36.

Fig. 1: Example of mapping transitions to Ti-e_g-like orbitals in Rutile. a) EELS spectrum with selected energy range (yellow). b) charge density calculated with WIEN2k. c) Experimental imaging after averaging over several unit cells. d) Same as c after Gaussian filtering. e) Simulated image at infinite dose. f) Simulated image at realistic dose. g) Same as f after Gaussian filtering. All scalebars indicate 5 Å. Adapted from [2].