Highly efficient beamline and spectrometer for inelastic soft X-ray scattering at high resolution

Analyzing the Local Electronic Structure of Co3O4 Using 2p3d Resonant Inelastic X-ray Scattering

We present the cobalt 2p3d resonant inelastic X-ray scattering (RIXS) spectra of Co₃O₄. Guided by multiplet simulation, the excited states at 0.5 and 1.3 eV can be identified as the ⁴ T ₂ excited state of the tetrahedral Co²⁺ and the ³ T _2g excited state of the octahedral Co³⁺, respectively. The ground states of Co²⁺ and Co³⁺ sites are determined to be high-spin ⁴ A ₂(T _d ) and low-spin ¹ A _1g (O_h ), respectively. It indicates that the high-spin Co²⁺ is the magnetically active site in Co₃O₄. Additionally, the ligand-to-metal charge transfer analysis shows strong orbital hybridization between the cobalt and oxygen ions at the Co³⁺ site, while the hybridization is weak at the Co²⁺ site.

I21: an advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source

The I21 beamline at Diamond Light Source is dedicated to advanced resonant inelastic X-ray scattering (RIXS) for probing charge, orbital, spin and lattice excitations in materials across condensed matter physics, applied sciences and chemistry. Both the beamline and the RIXS spectrometer employ divergent variable-line-spacing gratings covering a broad energy range of 280-3000 eV. A combined energy resolution of ∼35 meV (16 meV) is readily achieved at 930 eV (530 eV) owing to the optimized optics and the mechanics. Considerable efforts have been paid to the design of the entire beamline, particularly the implementation of the collection mirrors, to maximize the X-ray photon throughput. The continuous rotation of the spectrometer over 150° under ultra high vacuum and a cryogenic manipulator with six degrees of freedom allow accurate mappings of low-energy excitations from solid state materials in momentum space. Most importantly, the facility features a unique combination of the high energy resolution and the high photon throughput vital for advanced RIXS applications. Together with its stability and user friendliness, I21 has become one of the most sought after RIXS beamlines in the world.

Development of the Soft X-ray AGM-AGS RIXS beamline at the Taiwan Photon Source

We report on the development of a high-resolution and highly efficient beamline for soft X-ray resonant inelastic X-ray scattering (RIXS) located at the Taiwan Photon Source. This beamline adopts an optical design that uses an active grating monochromator (AGM) and an active grating spectrometer (AGS) to implement the energy compensation principle of grating dispersion. Active gratings are utilized to diminish defocus, coma and higher-order aberrations, as well as to decrease the slope errors caused by thermal deformation and optical polishing. The AGS is mounted on a rotatable granite platform to enable momentum-resolved RIXS measurements with scattering angles over a wide range. Several high-precision instruments developed in-house for this beamline are described briefly. The best energy resolution obtained from this AGM-AGS beamline was 12.4 meV at 530 eV, achieving a resolving power of 4.2 × 104, while the bandwidth of the incident soft X-rays was kept at 0.5 eV. To demonstrate the scientific impact of high-resolution RIXS, we present an example of momentum-resolved RIXS measurements on a high-temperature superconducting cuprate, i.e. La2-xSrxCuO4. The measurements reveal the A1g buckling phonons in superconducting cuprates, opening a new opportunity to investigate the coupling between these phonons and charge-density waves.

hv2-concept breaks the photon-count limit of RIXS instrumentation

Upon progressive refinement of energy resolution, the conventional resonant inelastic X-ray scattering (RIXS) instrumentation reaches the limit where the bandwidth of incident photons becomes insufficient to deliver an acceptable photon-count rate. Here it is shown that RIXS spectra as a function of energy loss are essentially invariant to their integration over incident energies within the core-hole lifetime. This fact permits RIXS instrumentation based on the hv2-concept to utilize incident synchrotron radiation over the whole core-hole lifetime window without any compromise on the much finer energy-loss resolution, thereby breaking the photon-count limit.

Diffraction gratings with two-orders-of-magnitude-enhanced dispersion rates for sub-meV resolution soft X-ray spectroscopy

Diffraction gratings with large angular dispersion rates are central to obtaining high spectral resolution in grating spectrometers operating over a broad spectral range from infrared to soft X-ray domains. The greatest challenge is of course to achieve large dispersion rates in the short-wavelength X-ray domain. Here it is shown that crystals in non-coplanar asymmetric X-ray Bragg diffraction can function as high-reflectance broadband soft X-ray diffraction gratings with dispersion rates that are at least two orders of magnitude larger than those that are possible with state-of-the-art man-made gratings. This opens new opportunities to design and implement soft X-ray resonant inelastic scattering (RIXS) spectrometers with spectral resolutions that are up to two orders of magnitude higher than what is currently possible, to further advance a very dynamic field of RIXS spectroscopy, and to make it competitive with inelastic neutron scattering. Examples of large-dispersion-rate crystal diffraction gratings operating near the 930 eV L₃ absorption edge in Cu and of the 2.838 keV L₃-edge in Ru are presented.

Saturation and self-absorption effects in the angle-dependent 2p3d resonant inelastic X-ray scattering spectra of Co3

Angle-dependent 2p3d resonant inelastic X-ray scattering spectra of a LaCoO3 single crystal and a 55 nm LaCoO3 film on a SrTiO3 substrate are presented. Theoretical calculation shows that, with ∼20 meV resolved Co 2p3d resonant inelastic X-ray scattering (RIXS), the excited states of the isotropic 1A1g(Oh) ground state are split by 3d spin-orbit coupling, which can be distinguished via their angular dependence. However, strong self-absorption and saturation effects distort the spectra of the LaCoO3 single crystal and limit the observation of small angular dependence. In contrast, the RIXS on 55 nm LaCoO3 shows less self-absorption effects and preserves the angular dependence of the excited states.

A design of resonant inelastic X-ray scattering (RIXS) spectrometer for spatial- and time-resolved spectroscopy

The optical design of a Hettrick-Underwood-style soft X-ray spectrometer with Wolter type 1 mirrors is presented. The spectrometer with a nominal length of 3.1 m can achieve a high resolving power (resolving power higher than 10000) in the soft X-ray regime when a small source beam (<3 µm in the grating dispersion direction) and small pixel detector (5 µm effective pixel size) are used. Adding Wolter mirrors to the spectrometer before its dispersive elements can realize the spatial imaging capability, which finds applications in the spectroscopic studies of spatially dependent electronic structures in tandem catalysts, heterostructures, etc. In the pump-probe experiments where the pump beam perturbs the materials followed by the time-delayed probe beam to reveal the transient evolution of electronic structures, the imaging capability of the Wolter mirrors can offer the pixel-equivalent femtosecond time delay between the pump and probe beams when their wavefronts are not collinear. In combination with some special sample handing systems, such as liquid jets and droplets, the imaging capability can also be used to study the time-dependent electronic structure of chemical transformation spanning multiple time domains from microseconds to nanoseconds. The proposed Wolter mirrors can also be adopted to the existing soft X-ray spectrometers that use the Hettrick-Underwood optical scheme, expanding their capabilities in materials research.

Resonant inelastic x-ray scattering study of [Formula: see text]-RuCl3: a progress report

Ru M₃-edge resonant inelastic x-ray scattering (RIXS) measurements of [Formula: see text] with 27 meV resolution reveals a spin-orbit exciton without noticeable splitting. We extract values for the spin-orbit coupling constant ([Formula: see text] meV) and trigonal distortion field energy ([Formula: see text] meV) which support the [Formula: see text] nature of [Formula: see text]. We demonstrate the feasibility of M-edge RIXS for 4d systems, which allows ultra high-resolution RIXS of 4d systems until instrumentation for L-edge RIXS improves.

Resonant inelastic X-ray scattering of magnetic excitations under pressure

Resonant inelastic X-ray scattering (RIXS) is an extremely valuable tool for the study of elementary, including magnetic, excitations in matter. The latest developments of this technique have mostly been aimed at improving the energy resolution and performing polarization analysis of the scattered radiation, with a great impact on the interpretation and applicability of RIXS. Instead, this article focuses on the sample environment and presents a setup for high-pressure low-temperature RIXS measurements of low-energy excitations. The feasibility of these experiments is proved by probing the magnetic excitations of the bilayer iridate Sr₃Ir₂O₇ at pressures up to 12 GPa.

Giant thermal hysteresis in Verwey transition of single domain Fe3O4 nanoparticles

Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe₃O₄ is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe₃O₄ nanoparticles exhibits size-dependent thermal hysteresis in magnetization, ⁵⁷Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience.

Cobalt-to-vanadium charge transfer in polyoxometalate water oxidation catalysts revealed by 2p3d resonant inelastic X-ray scattering

2p3d RIXS spectra reveal electronic structures ofCo4V2WOC, which offers insights into its enhanced catalytic activity thanCo4P2WOC.

Strong localization of oxidized Co3+ state in cobalt-hexacyanoferrate

Secondary batteries are important energy storage devices for a mobile equipment, an electric car, and a large-scale energy storage. Nevertheless, variation of the local electronic state of the battery materials in the charge (or oxidization) process are still unclear. Here, we investigated the local electronic state of cobalt-hexacyanoferrate (Na _x Co[Fe(CN)₆]_0.9), by means of resonant inelastic X-ray scattering (RIXS) with high energy resolution (~100 meV). The L-edge RIXS is one of the most powerful spectroscopic technique with element- and valence-selectivity. We found that the local electronic state around Co²⁺ in the partially-charged Na_1.1Co²⁺_0.5Co³⁺_0.5[Fe²⁺(CN)₆]_0.9 film (x = 1.1) is the same as that of the discharged Na_1.6Co²⁺[Fe²⁺(CN)₆]_0.9 film (x = 1.6) within the energy resolution, indicating that the local electronic state around Co²⁺ is invariant against the partial oxidization. In addition, the local electronic state around the oxidized Co³⁺ is essentially the same as that of the fully-charged film Co³⁺[Fe²⁺(CN)₆]_0.3[Fe³⁺(CN)₆]_0.6 (x = 0.0) film. Such a strong localization of the oxidized Co³⁺ state is advantageous for the reversibility of the redox process, since the localization reduces extra reaction within the materials and resultant deterioration.

Coulomb Correlations Intertwined with Spin and Orbital Excitations in LaCoO_{3}

We carried out temperature-dependent (20-550 K) measurements of resonant inelastic x-ray scattering on LaCoO_{3} to investigate the evolution of its electronic structure across the spin-state crossover. In combination with charge-transfer multiplet calculations, we accurately quantified the renomalized crystal-field excitation energies and spin-state populations. We show that the screening of the effective on-site Coulomb interaction of 3d electrons is orbital selective and coupled to the spin-state crossover in LaCoO_{3}. The results establish that the gradual spin-state crossover is associated with a relative change of Coulomb energy versus bandwidth, leading to a Mott-type insulator-to-metal transition.

Jahn-Teller distortion driven magnetic polarons in magnetite

The first known magnetic mineral, magnetite, has unusual properties, which have fascinated mankind for centuries; it undergoes the Verwey transition around 120 K with an abrupt change in structure and electrical conductivity. The mechanism of the Verwey transition, however, remains contentious. Here we use resonant inelastic X-ray scattering over a wide temperature range across the Verwey transition to identify and separate out the magnetic excitations derived from nominal Fe²⁺ and Fe³⁺ states. Comparison of the experimental results with crystal-field multiplet calculations shows that the spin–orbital dd excitons of the Fe²⁺ sites arise from a tetragonal Jahn-Teller active polaronic distortion of the Fe²⁺O₆ octahedra. These low-energy excitations, which get weakened for temperatures above 350 K but persist at least up to 550 K, are distinct from optical excitations and are best explained as magnetic polarons.

The Verwey transition of magnetite is complex due to the coexistence of strong correlations and electron-phonon coupling. Here, the authors use resonant inelastic X-ray scattering to show evidence for magnetic polarons in magnetite and provide insight into the nature of the transition.

Highly efficient soft X-ray spectrometer based on a reflection zone plate for resonant inelastic X-ray scattering measurements

We present a newly designed compact and flexible soft X-ray spectrometer for resonant inelastic X-ray scattering (RIXS) studies within an energy range from 380 eV to 410 eV, which would include the K alpha emission lines of vital elements like nitrogen. We utilized an off-axis reflection zone plate (RZP) as the wavelength selective element with a maximum line density of 10000 l/mm. A higher energy resolution over a broader range of ± 15 eV around the designed energy was achieved by displacing the RZP. Additionally, for the first time, an actual optical side effect, the so-called comatic aberration was exploited to increase the energy resolution. First results show a resolving power in the order of 1300 for photon energy of 395 eV, which is comparable to a commercial varied line spacing grating (VLS).

Doping Dependence of Collective Spin and Orbital Excitations in the Spin-1 Quantum Antiferromagnet La_{2-x}Sr_{x}NiO_{4} Observed by X Rays

We report the first empirical demonstration that resonant inelastic x-ray scattering (RIXS) is sensitive to collective magnetic excitations in S=1 systems by probing the Ni L_{3} edge of La_{2-x}Sr_{x}NiO_{4} (x=0, 0.33, 0.45). The magnetic excitation peak is asymmetric, indicating the presence of single and multi-spin-flip excitations. As the hole doping level is increased, the zone boundary magnon energy is suppressed at a much larger rate than that in hole doped cuprates. Based on the analysis of the orbital and charge excitations observed by RIXS, we argue that this difference is related to the orbital character of the doped holes in these two families. This work establishes RIXS as a probe of fundamental magnetic interactions in nickelates opening the way towards studies of heterostructures and ultrafast pump-probe experiments.

Modular soft x-ray spectrometer for applications in energy sciences and quantum materials

Over the past decade, the advances in grating-based soft X-ray spectrometers have revolutionized the soft X-ray spectroscopies in materials research. However, these novel spectrometers are mostly dedicated designs, which cannot be easily adopted for applications with diverging demands. Here we present a versatile spectrometer design concept based on the Hettrick-Underwood optical scheme that uses modular mechanical components. The spectrometer's optics chamber can be used with gratings operated in either inside or outside orders, and the detector assembly can be reconfigured accordingly. The spectrometer can be designed to have high spectral resolution, exceeding 10 000 resolving power when using small source (∼1μm) and detector pixels (∼5μm) with high line density gratings (∼3000 lines/mm), or high throughput at moderate resolution. We report two such spectrometers with slightly different design goals and optical parameters in this paper. We show that the spectrometer with high throughput and large energy window is particularly useful for studying the sustainable energy materials. We demonstrate that the extensive resonant inelastic X-ray scattering (RIXS) map of battery cathode material LiNi_1/3Co_1/3Mn_1/3O₂ can be produced in few hours using such a spectrometer. Unlike analyzing only a handful of RIXS spectra taken at selected excitation photon energies across the elemental absorption edges to determine various spectral features like the localized dd excitations and non-resonant fluorescence emissions, these features can be easily identified in the RIXS maps. Studying such RIXS maps could reveal novel transition metal redox in battery compounds that are sometimes hard to be unambiguously identified in X-ray absorption and emission spectra. We propose that this modular spectrometer design can serve as the platform for further customization to meet specific scientific demands.

Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer

We present the optical design of the Centurion soft X-ray resonant inelastic X-ray scattering (RIXS) spectrometer to be located on the SIX beamline at NSLS-II. The spectrometer is designed to reach a resolving power of 100 000 at 1000 eV at its best resolution. It is also designed to have continuously variable 2θ motion over a range of 112° using a custom triple rotating flange. We have analyzed several possible spectrometer designs capable of reaching the target resolution. After careful analysis, we have adopted a Hettrick-Underwood spectrometer design, with an additional plane mirror to maintain a fixed direction for the outgoing beam. The spectrometer can cancel defocus and coma aberrations at all energies, has an erect focal plane, and minimizes mechanical motions of the detector. When the beamline resolution is accounted for, the net spectral resolution will be 14 meV at 1000 eV. This will open up many low energy excitations to study and will expand greatly the power of soft X-ray RIXS.

Orbital Engineering in Nickelate Heterostructures Driven by Anisotropic Oxygen Hybridization rather than Orbital Energy Levels

Resonant inelastic x-ray scattering is used to investigate the electronic origin of orbital polarization in nickelate heterostructures taking LaTiO_{3}-LaNiO_{3}-3×(LaAlO_{3}), a system with exceptionally large polarization, as a model system. We find that heterostructuring generates only minor changes in the Ni 3d orbital energy levels, contradicting the often-invoked picture in which changes in orbital energy levels generate orbital polarization. Instead, O K-edge x-ray absorption spectroscopy demonstrates that orbital polarization is caused by an anisotropic reconstruction of the oxygen ligand hole states. This provides an explanation for the limited success of theoretical predictions based on tuning orbital energy levels and implies that future theories should focus on anisotropic hybridization as the most effective means to drive large changes in electronic structure and realize novel emergent phenomena.

X-ray Echo Spectroscopy

X-ray echo spectroscopy, a counterpart of neutron spin echo, is being introduced here to overcome limitations in spectral resolution and weak signals of the traditional inelastic x-ray scattering (IXS) probes. An image of a pointlike x-ray source is defocused by a dispersing system comprised of asymmetrically cut specially arranged Bragg diffracting crystals. The defocused image is refocused into a point (echo) in a time-reversal dispersing system. If the defocused beam is inelastically scattered from a sample, the echo signal acquires a spatial distribution, which is a map of the inelastic scattering spectrum. The spectral resolution of the echo spectroscopy does not rely on the monochromaticity of the x rays, ensuring strong signals along with a very high spectral resolution. Particular schemes of x-ray echo spectrometers for 0.1-0.02 meV ultrahigh-resolution IXS applications (resolving power >10^{8}) with broadband ≃5-13  meV dispersing systems are introduced featuring more than 10^{3} signal enhancement. The technique is general, applicable in different photon frequency domains.

Raman and fluorescence characteristics of resonant inelastic X-ray scattering from doped superconducting cuprates

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi_1.5Pb_0.6Sr_1.54CaCu₂O_8+δ. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast, the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-T_c cuprate superconductors.