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Tender X-rays

A tender X-ray momentum-resolved spectroscopy for probing elementary excitations in 4d quantum materials is reported and used to measure dispersive spin excitations in a ruthenate microcrystal.

Ruthenium oxides exhibit a plethora of quantum phases, such as unconventional superconductivity with spin-triplet Cooper pairs1, quantum criticality2 and electronic nematicity3, to name just a few. The increasing interest in these phenomena, which are cooperatively driven by strong spin–orbit interactions and electronic correlations4, has pushed ruthenates — or, more broadly, the 4d transition metal quantum materials — into the spotlight. To understand these phenomena, it is necessary to probe elementary excitations, such as spin excitations, which can reveal information on the underlying quantum states and fundamental interactions. Traditionally, inelastic neutron scattering has been the most powerful tool to probe magnetic excitations in solids. However, the intrinsically weak neutron–matter interaction only elicits measurable signals from large single-crystal samples and constructed single-crystal mosaics that have a total mass of a few grams. Unfortunately, this can be a severe limitation for the many quantum materials that are available as either small single crystals or thin films with nanometre thicknesses. These challenges call for an alternative momentum-resolved spectroscopy that can reveal spin and, ideally, other elementary excitations in these novel materials. Now, writing in Nature Materials, Hakuto Suzuki and colleagues5 have utilized a newly developed instrument to perform resonant inelastic X-ray scattering at the Ru L edge, revealing spin states and a branch of dispersive spin wave excitations in a microcrystal of SrRu2O6 (~50 μm), an antiferromagnet with an unusually high Néel temperature of 563 K.

Resonant inelastic X-ray scattering (RIXS) has become a powerful tool to probe elementary excitations in energy–momentum space6. RIXS can be described as a two-step resonant process (Fig. 1): an incident X-ray, with an energy tuned to coincide with an absorption edge of a constituent element of the material, photoexcites a core electron to the unoccupied lowest energy valence state, leaving behind a hole in the core level. Radiative decay of a valence shell electron then fills the core level, leading to the emission of an X-ray photon and leaving the system in an excited final state. Appropriately chosen absorption edges, involving transitions to valence states that determine the underlying quantum phases, allow the RIXS final state to carry important information on elementary charge, orbital, lattice and even spin excitations. One can map these elementary excitations in energy–momentum space by analysing the energy loss and momentum transfer between the incident and emitted X-ray photons. Importantly, this light–matter interaction is orders of magnitude stronger than the neutron–matter interaction, allowing RIXS to measure these excitations for sub-millimetre single crystals or thin films of nanometre thickness.

Fig. 1: Schematics of the coherent two-step RIXS process.

Figure adapted from ref. 9, SNL.

The photon energy of the incident X-ray (i, blue arrow) is tuned to the Ru L edge. Upon absorption, a core electron in the Ru 2p orbital transitions to the unoccupied 4d valence band near the Fermi energy EF, bringing the system to an intermediate state |m〉. Then, the emission process occurs: the 2p core hole is filled with a valence electron, a photon is emitted (f, red arrow) and the system is left in an excited final state |f〉 that couples to a variety of elementary excitations including spin, lattice and charge excitations. The energy–momentum information of these elementary excitations can be deduced by tracking the peak and spectral weight in RIXS spectra as a function of the momentum transfer Q and the energy loss E of the scattering photons. qi and qf represent the momentum of the incident and scattered photons, respectively.

While the RIXS technique has been in use for decades, it is only recently that the energy resolution has improved to a point that is sufficient to resolve important low-energy elementary excitations such as phonons, magnetic and low-energy charge excitations (in other words, better than 100 meV). The first breakthrough for this technique came in the soft X-ray regime, suitable for RIXS at the L edge of 3d transition metal compounds, leading to observations of single- and multi-magnon excitations in nickelates, cuprates and iron-based superconductors7. Then, hard X-ray instruments, designed for RIXS at the L edge of 5d compounds, led to the discovery of magnons in the iridates8. However, a high-resolution RIXS instrument for the L edge of 4d compounds has been unavailable until now, due to the photon energy of 4d L edges lying in a grey area between the soft and hard X-ray regimes, where neither crystal analysers nor gratings are able to provide optimal high-resolution X-ray optics.

As reported by Suzuki et al., such an RIXS instrument has now debuted with an energy resolution of 140 meV at the Ru L edge. Using this instrument, Suzuki and colleagues demonstrate the ability of RIXS to map magnon excitations in an antiferromagnetically ordered ruthenate. By analysing the spectrum and determining both the spin state and spin Hamiltonian, new light has been shed on the mechanism underlying the high Néel temperature of SrRu2O6. From a technical perspective, a stimulating aspect of this work is that it opens the door for investigating magnetic excitations in other ruthenium oxides and possibly other 4d transition metal compounds, for example those containing palladium or rhodium. As demonstrated by RIXS studies on cuprate superconductors9,10, both electron–phonon coupling and, most importantly, charge dynamics in 4d compounds could be within the grasp of RIXS; if so, such information could help further the understanding of this rich quantum phenomenon in 4d compounds.

Overall, the work by Suzuki et al. ushers in a new era for RIXS studies on quantum materials containing transition metal elements. However, even with the identified potential, significant groundwork still needs to be done. Due to the nature of the resonant process, the interpretation of the RIXS cross-section may not be as straightforward as other two-particle correlation functions and linear response probes. Fortunately, one may manage the task by combining theoretical calculations and experimental mapping of the dispersion in reciprocal space, as demonstrated for the case of magnetic excitations5,8,11. Importantly, implementing full polarization analysis for RIXS measurements will provide a powerful tool to identify the nature of RIXS excitations, in analogy to the polarization analysis commonplace in Raman spectroscopy. In fact, many synchrotron light sources worldwide have been geared up to develop next-generation RIXS instruments with higher resolution and full polarization analysis. Notably, RIXS instruments planned at X-ray free-electron laser (XFEL) facilities, such as the European XFEL and Linac Coherent Light Source II (LCLS-II), will enable measurements of elementary excitations in materials driven out of equilibrium, creating a new frontier for quantum materials research and exploration.


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Correspondence to Wei-Sheng Lee.

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Lee, WS., Moritz, B. Tender X-rays. Nat. Mater. 18, 537–538 (2019).

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