Resonant inelastic X-ray scattering (RIXS) is a momentum-resolved spectroscopic method used to study vibrational and electronic excitations, combining inelastic scattering and spectroscopy to examine the electronic structure of materials.1
Image Credit: Digital abstract Art/Shutterstock.com
XS operates through the interaction of X-rays with matter, introducing dependencies on polarization, energy, and momentum. The RIXS spectra are typically represented as a combination of X-ray emission and absorption, creating a two-dimensional (2D) RIXS plane based on emission and excitation energies.2
This technique is useful for investigating collective excitations such as orbitons, plasmons, phonons, and magnons in quantum materials like iridates, nickelates, and cuprates, which exhibit complex low-energy physics.2
Additionally, RIXS can be applied in operando experiments using hard X-rays to achieve high-resolution X-ray absorption spectra by minimizing spectral broadening caused by the short core hole lifetime.2
Fundamental Principles of RIXS
RIXS is an element- and orbital-selective X-ray spectroscopy technique that operates through a two-step, two-photon resonant process.1 It combines X-ray emission and absorption spectroscopy by measuring coherent X-ray emission at an incident photon energy near the edge of the X-ray absorption spectrum.2
In the first step (X-ray absorption), an incoming photon, characterized by its wave vector, polarization state, and energy, excites an electron from a core level to an unoccupied state, creating an intermediate state with a short-lived core hole lasting only a few femtoseconds.2
In the second step (X-ray emission), the system decays radiatively into a final state as a core or valence electron fills the core hole, emitting a photon characterized by its polarization state, energy, and wave vector. The final state differs from the initial ground state in RIXS, indicating that it is an excited state.2
Although the final state energy is higher than the ground state energy, anti-Stokes lines may also be observed. RIXS probes dispersive excitations and functions as a scattering technique, involving both momentum and energy transfer to the system under study. The process depends on the resonant energy and the polarization of both incoming and outgoing light, making RIXS a combined scattering and spectroscopy technique.2
Synchrotron radiation sources or free electron lasers are essential for conducting RIXS due to its high photon requirements. RIXS typically measures final states in the soft X-ray energy range, capturing de-excitations and excitations between transition metal 2p electrons or oxygen 1s electrons and the strongly hybridized valence states of 3d transition metal oxides, a technique known as valence RIXS.2
Valence RIXS probes the ordering states and collective excitations like charge density waves and phonons in quantum materials. Over the past decade, soft X-ray RIXS has advanced significantly with the establishment of dedicated high-resolution facilities at various light sources, achieving energy resolutions as high as 20 meV at the copper L edge.2
These next-generation, high-resolution RIXS facilities allow for detailed studies of collective excitations and their interaction with polarization. In hard X-ray RIXS, a crystal analyzer is used to measure X-ray emission following the excitation of a 2p electron in 4f, 5d, or 5f systems or a 1s core electron in 3d systems.2
While many 1s3p and 1s2p RIXS experiments typically operate at a resolution of 0.5–1.0 eV, certain specialized stations can achieve narrower bandwidths, down to 20 meV. These core RIXS experiments are particularly effective for studying systems under extreme conditions.2
Similarly, valence RIXS is used for the 2p → 5d → 2p de-excitation and excitation process in the hard X-ray energy range. High-resolution studies are essential for exploring elementary excitations in 4d and 5d transition metal compounds at the L edges of these metals.2
RIXS Applications in Research
RIXS is used to investigate the optical properties of materials, such as energy band structures, optical transitions, and electronic excitations. For instance, the 2p3d RIXS spectra primarily exhibit dd transitions, some of which can also be observed in the optical spectrum.2
The RIXS cross-section depends on the polarization (ε), direction (k), and energy (ω), as described by the Kramers–Heisenberg equation. Both the X-ray emission and X-ray absorption operators are dependent on k, ε, and ω. The final state is a function of Δk, Δε, and Δω, from which three critical parameters are defined in an RIXS experiment.2
For instance, Δω-RIXS is used to explore energy effects, including core and valence magnetic, vibrational, and electronic excitations in the final state. Similarly, momentum-dependent effects, such as the dispersion of collective and electronic excitations in solids, are investigated using Δk-RIXS.2
For molecules, momentum transfer is less significant, and RIXS primarily measures electronic excitations and vibrations. Polarization or dichroism effects related to the system’s symmetry properties are studied using Δε-RIXS. These effects can be measured using a circularly or linearly polarized photon-in with polarization analysis of the photon-out.2
Innovations in RIXS Technology
Recent advancements in RIXS instrumentation have significantly improved precision and resolution.
For example, the Sydor Spectro CCD is an effective detector for X-ray spectroscopy applications like RIXS, featuring an ultra-fine pixel structure ideal for photon-starved experiments that require low noise and high quantum efficiency.3 The integration of tilted mechanics with ultra-fine pixels allows for resolution below 2 microns, which is essential for high-precision spectroscopy.3
Similarly, the development of the intermediate X-ray energy RIXS (IRIXS) instrument at beamline P01 of the PETRA III synchrotron has enabled investigations in the intermediate energy range.4
This instrument targets the L2,3 absorption edges of various 4d elements, such as molybdenum, ruthenium, rhodium, palladium, and silver, facilitating the study of low-energy magnetic and charge excitations. While currently optimized for the ruthenium L3 edge, the IRIXS instrument can be adapted to other 4d elements using the same conceptual framework.4
RIXS: Future Trends and Insights
RIXS is a versatile technique for examining electronic excitations in materials, with applications across various fields, including optics. Recent advancements in RIXS instrumentation have significantly enhanced its capabilities, allowing for detailed studies of a broad range of materials and phenomena.
Improvements in momentum and energy resolution, along with increased count rates, will enable more comprehensive scattering function mapping. Achieving a soft X-ray RIXS resolution of 5 meV with good momentum resolution will facilitate electron-hole excitation band structure mapping, while in the hard X-ray range, this will allow for full Brillouin zone mapping.
More from AZoOptics: Exploring Ultra-Lightweight Space Cameras for Space Missions
References and Further Reading
- Yang, Z., et al. (2023). Resonant inelastic x-ray scattering from electronic excitations in α-RuCl 3 nanolayers. Physical Review B. 10.1103/PhysRevB.108.L041406, https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.L041406
- De Groot, FM., Haverkort, MW., Elnaggar, H., Juhin, A., Zhou, K., Glatzel, P. (2024). Resonant inelastic X-ray scattering. Nature Reviews Methods Primers, 4(1), 1-21. DOI: 10.1038/s43586-024-00322-6, https://www.nature.com/articles/s43586-024-00322-6
- Syndor Technologies. (n.d.) Spectroscopy CCD. [Online] Syndor Technologies. Available at https://sydortechnologies.com/direct-detectors/sydor-spectro-ccd/
- Gretarsson, H. et al. (2020). IRIXS: a resonant inelastic X-ray scattering instrument dedicated to X-rays in the intermediate energy range. Journal of Synchrotron Radiation. DOI: 10.1107/S1600577519017119, https://journals.iucr.org/s/issues/2020/02/00/yi5085/index.html
Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.