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

Magnetically propagating Hund's exciton in van der Waals antiferromagnet NiPS3

Magnetic van der Waals (vdW) materials have opened new frontiers for realizing novel many-body phenomena. Recently NiPS3 has received intense interest since it hosts an excitonic quasiparticle whose properties appear to be intimately linked to the magnetic state of the lattice. Despite extensive studies, the electronic character, mobility, and magnetic interactions of the exciton remain unresolved. Here we address these issues by measuring NiPS3 with ultra-high energy resolution resonant inelastic x-ray scattering (RIXS). We find that Hund's exchange interactions are primarily responsible for the energy of formation of the exciton. Measuring the dispersion of the Hund's exciton reveals that it propagates in a way that is analogous to a double-magnon. We trace this unique behavior to fundamental similarities between the NiPS3 exciton hopping and spin exchange processes, underlining the unique magnetic characteristics of this novel quasiparticle.

Elementary excitations of single-photon emitters in hexagonal boron nitride

Single-photon emitters serve as building blocks for many emerging concepts in quantum photonics. The recent identification of bright, tunable and stable emitters in hexagonal boron nitride (hBN) has opened the door to quantum platforms operating across the infrared to ultraviolet spectrum. Although it is widely acknowledged that defects are responsible for single-photon emitters in hBN, crucial details regarding their origin, electronic levels and orbital involvement remain unknown. Here we employ a combination of resonant inelastic X-ray scattering and photoluminescence spectroscopy in defective hBN, unveiling an elementary excitation at 285 meV that gives rise to a plethora of harmonics correlated with single-photon emitters. We discuss the importance of N π* anti-bonding orbitals in shaping the electronic states of the emitters. The discovery of elementary excitations in hBN provides fundamental insights into quantum emission in low-dimensional materials, paving the way for future investigations in other platforms.

Angle-resolved X-ray emission spectroscopy facility realized by an innovative spectrometer rotation mechanism at SPring-8 BL07LSU

The X-ray emission spectrometer at SPring-8 BL07LSU has recently been upgraded with advanced modifications that enable the rotation of the spectrometer with respect to the scattering angle. This major upgrade allows the scattering angle to be flexibly changed within the range of 45-135°, which considerably simplifies the measurement of angle-resolved X-ray emission spectroscopy. To accomplish the rotation system, a sophisticated sample chamber and a highly precise spectrometer rotation mechanism have been developed. The sample chamber has a specially designed combination of three rotary stages that can smoothly move the connection flange along the wide scattering angle without breaking the vacuum. In addition, the spectrometer is rotated by sliding on a flat metal surface, ensuring exceptionally high accuracy in rotation and eliminating the need for any further adjustments during rotation. A control system that integrates the sample chamber and rotation mechanism to automate the measurement of angle-resolved X-ray emission spectroscopy has also been developed. This automation substantially streamlines the process of measuring angle-resolved spectra, making it far easier than ever before. Furthermore, the upgraded X-ray emission spectrometer can now also be utilized in diffraction experiments, providing even greater versatility to our research capabilities.

Spatiotemporal response of concave VLS grating to ultra-short X-ray pulses

In soft X-ray free-electron laser (FEL) beamlines, variable-line-spacing (VLS) gratings are often used as dispersive components of monochromators and spectrometers due to their combined dispersion and focusing properties. X-ray FEL pulses passing through the VLS grating can result in not only transverse focusing but also spatiotemporal coupling effects, such as pulse front tilt, pulse front rotation, and pulse stretching. In this paper, we present a theoretical study of the spatiotemporal response of concave VLS gratings to ultra-short X-ray pulses. The theoretical analysis indicates that the tilt angle of the non-zero diffraction orders varies with the propagation distance, and disappears at the focus, where the focal lengths and pulse stretching differ for different diffraction orders. The model demonstrates the pulse duration after the concave VLS grating is the convolution of the initial pulse duration and the stretching term induced by dispersion, while the beam size at the focus in x dimension is the convolution of the geometric scaling beam size and the dispersion term. This work provides a mathematical explanation for the spatiotemporal response of concave VLS grating to ultra-short X-ray pulses and offers valuable insights into the design of FEL grating monochromators, spectrometers, pulse compressors, and pulse stretchers.

Low-energy quasi-circular electron correlations with charge order wavelength in Bi2Sr2CaCu2O8+δ

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the q_x-q_y scattering plane in underdoped Bi₂Sr₂CaCu₂O_8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the q_x-q_y scattering plane with radius equal to the magnitude of the charge order wave vector, q_CO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [q_x = ±q_CO, q_y = 0] and [q_x = 0, q_y = ±q_CO]) as the origin of the observed correlations.

Slope error correction on X-ray reflection gratings by a variation of the local line density

The patterning of x-ray grating surfaces by electron-beam lithography offers large flexibility to realize complex optical functionalities. Here, we report on a proof-of-principle experiment to demonstrate the correction of slope errors of the substrates by modulating the local density of the grating lines. A surface error map of a test substrate was determined by optical metrology and served as the basis for an aligned exposure of a corrected grating pattern made by electron-beam lithography. The correction is done by a variation of the local line density in order to compensate for the local surface error. Measurements with synchrotron radiation and simulations in the soft X-ray range confirm that the effects of slope errors were strongly reduced over an extended wavelength range.

Kondo quasiparticle dynamics observed by resonant inelastic x-ray scattering

Effective models focused on pertinent low-energy degrees of freedom have substantially contributed to our qualitative understanding of quantum materials. An iconic example, the Kondo model, was key to demonstrating that the rich phase diagrams of correlated metals originate from the interplay of localized and itinerant electrons. Modern electronic structure calculations suggest that to achieve quantitative material-specific models, accurate consideration of the crystal field and spin-orbit interactions is imperative. This poses the question of how local high-energy degrees of freedom become incorporated into a collective electronic state. Here, we use resonant inelastic x-ray scattering (RIXS) on CePd₃ to clarify the fate of all relevant energy scales. We find that even spin-orbit excited states acquire pronounced momentum-dependence at low temperature—the telltale sign of hybridization with the underlying metallic state. Our results demonstrate how localized electronic degrees of freedom endow correlated metals with new properties, which is critical for a microscopic understanding of superconducting, electronic nematic, and topological states.

The fate of high-energy degrees of freedom, such as spin-orbit interactions, in the coherent state of Kondo lattice materials remains unclear. Here, the authors use resonant inelastic x-ray scattering in CePd₃ to show how Kondo-quasiparticle excitations are renormalized and develop a pronounced momentum dependence, while maintaining a largely unchanged spin-orbit gap.

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.

Using photoelectron spectroscopy to measure resonant inelastic X-ray scattering: a computational investigation

Resonant inelastic X-ray scattering (RIXS) has become an important scientific tool. Nonetheless, conventional high-resolution (few hundred meV or less) RIXS measurements, especially in the soft X-ray range, require low-throughput grating spectrometers, which limits measurement accuracy. Here, the performance of a different method for measuring RIXS, i.e. photoelectron spectrometry for analysis of X-rays (PAX), is computationally investigated. This method transforms the X-ray measurement problem of RIXS to an electron measurement problem, enabling use of high-throughput, compact electron spectrometers. X-rays to be measured are incident on a converter material and the energy distribution of the resultant photoelectrons, the PAX spectrum, is measured with an electron spectrometer. A deconvolution algorithm for analysis of such PAX data is proposed. It is shown that the deconvolution algorithm works well on data recorded with ∼0.5 eV resolution. Additional simulations show the potential of PAX for estimation of RIXS features with smaller widths. For simulations using the 3d levels of Ag as a converter material, and with 105 simulated detected electrons, it is estimated that features with a few hundred meV width can be accurately estimated in a model RIXS spectrum. For simulations using a sharp Fermi edge to encode RIXS spectra, it is estimated that one can accurately distinguish 100 meV FWHM peaks separated by 45 meV with 105 simulated detected electrons that were photoemitted from within 0.4 eV of the Fermi level.

An ultra-high-stability four-axis ultra-high-vacuum sample manipulator

A report on a four-axis ultra-high-stability manipulator developed for use at the Veritas and Species RIXS beamlines at MAX IV Laboratory, Lund, Sweden, is presented. The manipulator consists of a compact, light-weight X-Y table with a stiffened Z tower carrying a platform with a rotary seal to which a manipulator rod holding the sample can be attached. Its design parameters have been optimized to achieve high eigen-frequencies via a light-weight yet stiff construction, to absorb forces without deformations, provide a low center of gravity, and have a compact footprint without compromising access to the manipulator rod. The manipulator system can house a multitude of different, easily exchangeable, manipulator rods that can be tailor-made for specific experimental requirements without having to rebuild the entire sample positioning system. It is shown that the manipulator has its lowest eigen-frequency at 48.5 Hz and that long-term stability is in the few tens of nanometres. Position accuracy is shown to be better than 100 nm. Angular accuracy is in the 500 nrad range with a long-term stability of a few hundred nanoradians.

Tuning spin excitations in magnetic films by confinement

Spin excitations of magnetic thin films are the founding element for magnetic devices in general. While spin dynamics have been extensively studied in bulk materials, the behaviour in mesoscopic films is less known due to experimental limitations. Here, we employ resonant inelastic X-ray scattering to investigate the spectrum of spin excitations in mesoscopic Fe films, from bulk-like films down to three unit cells. In bulk samples, we find isotropic, dispersive ferromagnons consistent with previous neutron scattering results for bulk single crystals. As the thickness is reduced, these ferromagnetic spin excitations renormalize to lower energies along the out-of-plane direction while retaining their dispersion in the in-plane direction. This thickness dependence is captured by simple Heisenberg model calculations accounting for the confinement in the out-of-plane direction through the loss of Fe bonds. Our findings highlight the effects of mesoscopic scaling on spin dynamics and identify thickness as a knob for fine tuning and controlling magnetic properties.

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.

Future trends in synchrotron science at NSLS-II

In this paper, we summarize briefly some of the future trends in synchrotron science as seen at the National Synchrotron Light Source II, a new, low emittance source recently commissioned at Brookhaven National Laboratory. We touch upon imaging techniques, the study of dynamics, the increasing use of multimodal approaches, the vital importance of data science, and other enabling technologies. Each are presently undergoing a time of rapid change, driving the field of synchrotron science forward at an ever increasing pace. It is truly an exciting time and one in which Roger Cowley, to whom this journal issue is dedicated, would surely be both invigorated by, and at the heart of.

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.

The chemical and physical properties of tetravalent lanthanides: Pr, Nd, Tb, and Dy

The thermochemistry, descriptive chemistry, spectroscopy, and physical properties of the tetravalent lanthanides (Pr, Nd, Tb and Dy) in extended phases, gas phase, solution, and as isolable molecular complexes are presented.

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.

Towards an extremely high resolution broad-band flat-field spectrometer in the `water window'

The optical design of a novel spectrometer is presented, combining a cylindrically convex pre-mirror with a cylindrically concave varied-line-spacing grating (both in the meridional) to deliver a resolving power of 100000-200000 in the `water window' (2-5 nm). Most remarkably, the extremely high spectral resolution is achieved for an effective meridional source size of 50 µm (r.m.s.); this property could potentially be applied to diagnose SASE-FEL and well resolve individual single spikes in its radiation spectrum. The overall optical aberrations of the system are well analysed and compensated, providing an excellent flat-field at the detector domain throughout the whole spectral range. Also, a machine-learning scheme - SVM - is introduced to explore and reconstruct the optimal system with high efficiency.

Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy

Gratings, one of the most important energy dispersive devices, are the fundamental building blocks for the majority of optical and optoelectronic systems. The grating period is the key parameter that limits the dispersion and resolution of the system. With the rapid development of large X-ray science facilities, gratings with periodicities below 50 nm are in urgent need for the development of ultrahigh-resolution X-ray spectroscopy. However, the wafer-scale fabrication of nanogratings through conventional patterning methods is difficult. Herein, we report a maskless and high-throughput method to generate wafer-scale, multilayer gratings with period in the sub-50 nm range. They are fabricated by a vacancy epitaxy process and coated with X-ray multilayers, which demonstrate extremely large angular dispersion at approximately 90 eV and 270 eV. The developed new method has great potential to produce ultrahigh line density multilayer gratings that can pave the way to cutting edge high-resolution spectroscopy and other X-ray applications.

Fabrication of wafer-scale nanogratings for X-ray spectroscopy is difficult especially for very high line densities. The authors use vacancy epitaxy to fabricate sub-50-nm-periodicity gratings, coated with multilayers for efficient operation, for use in ultra-high resolution x-ray spectroscopy.

Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective

Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitation of these materials holds great promise for understanding and controlling the properties of these states. Here, we introduce time-resolved resonant inelastic X-ray scattering (tr-RIXS) as a means of measuring the charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles and instrumentations of tr-RIXS, we review our first observations of transient antiferromagnetic correlations in quasi two dimensions in a photo-excited Mott insulator and present possible future routes of this fast-developing technique. The increasing number of X-ray free electron laser facilities not only enables tackling long-standing fundamental scientific problems, but also promises to unleash novel inelastic X-ray scattering spectroscopies. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Non-linear soft x-ray methods on solids with MUSIX-the multi-dimensional spectroscopy and inelastic x-ray scattering endstation

With the intense and coherent x-ray pulses available from free-electron lasers, the possibility to transfer non-linear spectroscopic methods from the laser lab to the x-ray world arises. Advantages especially regarding selectivity and thus information content as well as an improvement of signal levels are expected. The use of coherences is especially fruitful and the example of coherent x-ray/optical sum-frequency generation is discussed. However, many non-linear x-ray methods still await discovery, partially due to the necessity for extremely adaptable and versatile instrumentation that can be brought to free-electron lasers for the analysis of the spectral content emitted from the sample into a continuous range of emission angles. Such an instrument (called MUSIX) is being developed and employed at FLASH, the free-electron laser in Hamburg and is described in this contribution together with first results.

Ultra-low blaze angle gratings for synchrotron and free electron laser applications

We have developed a method for the manufacture of x-ray diffraction gratings with arbitrarily small blaze angles. These gratings are made by a process in which a high blaze angle grating made by anisotropic etching of Si (111) is subjected to planarization and reactive ion etching. Differential etching of the planarization medium and silicon ensures reduction of the blaze angle. Repeated application of this process leads to gratings of increasing perfection with an arbitrarily small blaze angle. This opens the way to highly efficient low line density gratings, to damage resistant gratings for ultra-high power applications such as free electron lasers, and for extension of the use of gratings into the hard x-ray energy range for dispersive spectroscopy.

A sagittally confined high-resolution spectrometer in the `water window'

The authors report a novel scheme for a grazing-incidence spectrometer forming an excellent meridional flat field in its detector domain to deliver the desired spectral resolution throughout the full designated spectral range, while reducing the sagittal astigmatism substantially to enhance the spectral intensity. The optical properties of the system are thoroughly investigated and optimized, and the detector plane is fitted well to the meridional or sagittal focal curves. The authors demonstrated that a resolving power of 6000-18000 could be achieved within the `water window' (2-5 nm) for an effective meridional source size of 200 µm (r.m.s.), and it would be further improved to 20000-40000 if the source size was confined to 50 µm (r.m.s.).

L-edge spectroscopy of dilute, radiation-sensitive systems using a transition-edge-sensor array

We present X-ray absorption spectroscopy and resonant inelastic X-ray scattering (RIXS) measurements on the iron L-edge of 0.5 mM aqueous ferricyanide. These measurements demonstrate the ability of high-throughput transition-edge-sensor (TES) spectrometers to access the rich soft X-ray (100-2000 eV) spectroscopy regime for dilute and radiation-sensitive samples. Our low-concentration data are in agreement with high-concentration measurements recorded by grating spectrometers. These results show that soft-X-ray RIXS spectroscopy acquired by high-throughput TES spectrometers can be used to study the local electronic structure of dilute metal-centered complexes relevant to biology, chemistry, and catalysis. In particular, TES spectrometers have a unique ability to characterize frozen solutions of radiation- and temperature-sensitive samples.

Large area nanoimprint enables ultra-precise x-ray diffraction gratings

A process for fabrication of ultra-precise diffraction gratings for high resolution x-ray spectroscopy was developed. A grating pattern with constant or variable line spacing (VLS) is recorded on a quartz plate by use of e-beam lithography with nanometer scale accuracy of the groove placement. The pattern is transferred to a massive grating blank by large area nanoimprint followed by dry or/and wet etching for groove shaping. High fidelity of the nanoimprint transfer step was confirmed by differential wavefront measurements. Successful implementation of the suggested fabrication approach was demonstrated by fabrication of a lamellar 900 lines/mm VLS grating for a soft x-ray fluorescence spectrometer.

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.