Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers

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.

Momentum-resolved spin-conserving two-triplon bound state and continuum in a cuprate ladder

Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate Sr 14 Cu 24 O 41 with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.

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.

A compact extreme ultraviolet high-throughput spectrometer based on the multilayer varied-line-spacing grating

In this paper, we propose a compact extreme ultraviolet high-throughput spectrometer covering the 50-70 eV energy band. The key element in this spectrometer is a multilayer varied-line-spacing grating that operates in near-normal incidence geometry. The spectrometer can obtain one order of magnitude higher throughput compared to the traditional grazing incidence grating spectrometer in this energy band. The spectrum collection time and sample radiation damage can be largely reduced using the presented design.

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.

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.

Conception of diffractive wavefront correction for XUV and soft x-ray spectroscopy

We present a simple and precise method to minimize aberrations of mirror-based, wavelength-dispersive spectrometers for the extreme ultraviolet (XUV) and soft x-ray domain. The concept enables an enhanced resolving power $ E/\Delta E $E/ΔE, in particular, close to the diffraction limit over a spectral band of a few percent around the design energy of the instrument. Our optical element, the "diffractive wavefront corrector" (DWC), is individually shaped to the form and figure error of the mirror profile and might be written directly with a laser on a plane and even strongly curved substrates. Theory and simulations of various configurations, like Hettrick-Underwood or compact, highly efficient all-in-one setups for $ {{\rm TiO}_2} $TiO₂ spectroscopy with $ E/\Delta E \mathbin{\lower.3ex\hbox{$\buildrel{\displaystyle{\lt}}\over{\smash{\displaystyle\sim}\vphantom{_x}}$}} 4.5 \times {10^4} $E/ΔE∼_x<4.5×10⁴, are addressed, as well as aspects of their experimental realization.

Soft X-ray varied-line-spacing gratings fabricated by near-field holography using an electron beam lithography-written phase mask

A fabrication method comprising near-field holography (NFH) with an electron beam lithography (EBL)-written phase mask was developed to fabricate soft X-ray varied-line-spacing gratings (VLSGs). An EBL-written phase mask with an area of 52 mm × 30 mm and a central line density greater than 3000 lines mm-1 was used. The introduction of the EBL-written phase mask substantially simplified the NFH optics for pattern transfer. The characterization of the groove density distribution and diffraction efficiency of the fabricated VLSGs indicates that the EBL-NFH method is feasible and promising for achieving high-accuracy groove density distributions with corresponding image properties. Vertical stray light is suppressed in the soft X-ray spectral range.

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.

Zone plates as imaging analyzers for resonant inelastic x-ray scattering

We have implemented and successfully tested an off-axis transmission Fresnel zone plate as a novel type of analyzer optics for resonant inelastic x-ray scattering (RIXS). We achieved a spectral resolution of 64 meV at the nitrogen K-edge (E/dE = 6200), closely matching theoretical predictions. The fundamental advantage of transmission optics is the fact that it can provide stigmatic imaging properties. This opens up a variety of advanced RIXS configurations, such as efficient scanning RIXS, parallel detection for varying incident energy and time-resolved measurements.

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.

Varied-line-spacing switchable holographic grating using polymer-dispersed liquid crystal

A varied-line-spacing switchable holographic grating is demonstrated through a changeable interference pattern recorded in polymer-dispersed liquid crystal. The pattern is generated by the interference between one plane wave and another cylindrical wave. The line spacing and the period of grating can be controlled by varying the distance between the cylindrical lens and the grating sample and by changing the exposure angle between the two beams. Experimental period measurements and calculations show good agreement with the theoretical results. High diffraction efficiency of more than 80% for the middle period of the grating has been achieved under appropriate exposure time of 120 s and intensity of 19.1  mW/cm². In addition, the diffraction can be switched on and off by virtue of the external driving voltage of approximately 120 V. The grating also possesses a fast response with a rise time of 300 μs and a fall time of 750 μs. This grating, which can change the period in the grating structure to allow switchable diffraction of transmitted light, shows great potential application for diffractive optics.

Concept of a multichannel spin-resolving electron analyzer based on Mott scattering

The concept of a multichannel electron spin detector based on optical imaging principles and Mott scattering (iMott) is presented. A multichannel electron image produced by a standard angle-resolving (photo) electron analyzer or microscope is re-imaged by an electrostatic lens at an accelerating voltage of 40 kV onto the Au target. Quasi-elastic electrons bearing spin asymmetry of the Mott scattering are imaged by magnetic lenses onto position-sensitive electron CCDs whose differential signals yield the multichannel spin asymmetry image. Fundamental advantages of this concept include acceptance of inherently divergent electron sources from the electron analyzer or microscope focal plane as well as small aberrations achieved by virtue of high accelerating voltages, as demonstrated by extensive ray-tracing analysis. The efficiency gain compared with the single-channel Mott detector can be a factor of more than 10(4) which opens new prospects of spin-resolved spectroscopies in application not only to standard bulk and surface systems (Rashba effect, topological insulators, etc.) but also to buried heterostructures. The simultaneous spin detection combined with fast CCD readout enables efficient use of the iMott detectors at X-ray free-electron laser facilities.

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

The design, construction and commissioning of a beamline and spectrometer for inelastic soft X-ray scattering at high resolution in a highly efficient system are presented. Based on the energy-compensation principle of grating dispersion, the design of the monochromator-spectrometer system greatly enhances the efficiency of measurement of inelastic soft X-rays scattering. Comprising two bendable gratings, the set-up effectively diminishes the defocus and coma aberrations. At commissioning, this system showed results of spin-flip, d-d and charge-transfer excitations of NiO. These results are consistent with published results but exhibit improved spectral resolution and increased efficiency of measurement. The best energy resolution of the set-up in terms of full width at half-maximum is 108 meV at an incident photon energy tuned about the Ni L3-edge.

New soft X-ray beamline BL07LSU at SPring-8

A new soft X-ray beamline, BL07LSU, has been constructed at SPring-8 to perform advanced soft X-ray spectroscopy for materials science. The beamline is designed to achieve high energy resolution (E/ΔE> 10000) and high photon flux [>10(12) photons s(-1) (0.01% bandwidth)(-1)] in the photon energy range 250-2000 eV with controllable polarization. To realise this state-of-the-art performance, a novel segmented cross undulator was developed and adopted as a light source. The details of the undulator light source and beamline monochromator design are described. The achieved performance of the beamline, such as the photon flux, energy resolution and the state of polarization, is reported.

Approaching ultimate resolution for soft x-ray spectrometers

We explore the potential performance of soft x-ray spectrometers based on the use of varied-line-spacing spherical diffraction gratings (VLS-SG). The quantitative assessment is based on an optimization procedure to obtain both negligible optical aberrations at full illumination of the grating and a quasi linear focal curve. It involves high-order optical aberration cancellation to calculate the focal curves. We also examine the validity of small divergence closed-form formulas describing the light path function. Optimizing the optical and geometric parameters gives an ultimate resolving power, at 930 eV, of between 10,800 for a 3 m long instrument and 34,000 for an 11 m spectrometer according to the Rayleigh criterion. Typical fabrication tolerances would scale these values down by about 10%. The findings are validated by ray-tracing simulations.

Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8

An extremely high resolution flat field type slit less soft x-ray emission spectrometer has been designed and constructed for the long undulator beamline BL07LSU in SPring-8. By optimizing the ruling parameters of two cylindrical gratings, a high energy resolution ΔE < 100 meV and/or an E∕ΔE ~ 10 000 are expected for the energy range of 350 eV - 750 eV taking into account the broadening by the spatial resolution (25 μm) of a CCD detector. A coma-free operation mode proposed by Strocov et al., is also applied to eliminate both defocus and coma aberrations. The spectrometer demonstrated experimentally that E/ΔE = 10 050 and 8046 for N 1s (402.1 eV) and Mn 2p (641.8 eV) edges, respectively.