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Abstract The unconventional superconductor Sr2RuO4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L 3-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr2RuO4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr2RuO4 and provide key information for the understanding of its unconventional superconductivity.

RuCl3 has stood out as a prime candidate in the search for quantum spin liquids; however, its antiferromagnetic ordering at low temperature suggests deviations from typical QSL models. Here, using resonant inelastic x-ray scattering, the authors provide a comprehensive determination of the low energy effective Hamiltonian.

Herein we show that nonresonant inelastic x-ray scattering involving an s core level is a powerful spectroscopic method to characterize the excited states of transition metal compounds. The spherical charge distribution of the s core hole allows the orientational dependence of the intensities of the various spectral features to produce a spatial charge image of the associated multiplet states in a straightforward manner, thereby facilitating the identification of their orbital character. In addition, the s core hole does not add an extra orbital angular momentum component to the multiplet structure so that the well-established Sugano-Tanabe-Kamimura diagrams can be used for the analysis of the spectra. For α-MnS we observe the spherical charge density corresponding to its high-spin 3d^{5} (^{6}A_{1}) ground state configuration and we were able to selectively image its excited states and identify them as t_{2g} (^{5}T_{2}) and e_{g} (^{5}E) with an energy splitting 10Dq of 0.78 eV.

Magnetic materials are composed of the simple building blocks of magnetic moments on a crystal lattice that interact via magnetic exchange. Yet from this simplicity emerges a remarkable diversity of magnetic states. Some reveal the deep quantum mechanical origins of magnetism, for example, quantum spin liquid (QSL) states in which magnetic moments remain disordered at low temperatures despite being strongly correlated through quantum entanglement. A promising theoretical model of a QSL is the Kitaev model, composed of unusual bond-dependent exchange interactions, but experimentally, this model is challenging to realise. Here we show that the material requirements for the Kitaev QSL survive an extended pseudo-edge-sharing superexchange pathway of Ru 3+ octahedra within the honeycomb layers of the inorganic framework solid, RuP 3 SiO 11 . We confirm the requisite j eff = 1 2 state of Ru 3+ in RuP 3 SiO 11 and resolve the hierarchy of exchange interactions that provide experimental access to an unexplored region of the Kitaev model., Competing Interests: Competing interests The authors declare no competing interests., (© 2024. The Author(s).)

The interplay of spin-orbit coupling with other relevant parameters gives rise to the rich phase competition in complex ruthenates featuring octahedrally coordinated Ru 4+ . While locally, spin-orbit coupling stabilizes a nonmagnetic J eff = 0 state, intersite interactions resolve one of two distinct phases at low temperatures: an excitonic magnet stabilized by the magnetic exchange of upper-lying J eff = 1 states or Ru 2 molecular orbital dimers driven by direct orbital overlap. Pyrochlore ruthenates A 2 Ru 2 O 7 ( A = rare earth, Y) are candidate excitonic magnets with geometrical frustration. We synthesized In 2 Ru 2 O 7 with covalent In─O bonds. This pyrochlore ruthenate hosts a local J eff = 0 state at high temperatures; however, at low temperatures, it forms a unique nonmagnetic ground state with nearly linear Ru─O─Ru molecules, in stark contrast to other A 2 Ru 2 O 7 compounds. The disproportionation of covalent In─O bonds drives Ru 2 O molecule formation, quenching not only the local spin-orbit singlet but also geometrical frustration.

Solid-state sodium ion conductors are crucial for the next generation of all-solid-state sodium batteries with high capacity, low cost, and improved safety. Sodium closo-carbadodecaborate (NaCB 11 H 12 ) is an attractive Na-ion conductor owing to its high thermal, electrochemical, and interfacial stability. Mechanical milling has recently been shown to increase conductivity by five orders of magnitude at room temperature, making it appealing for application in all-solid-state sodium batteries. Intriguingly, milling longer than 2 h led to a significant decrease in conductivity. In this study, X-ray Raman scattering (XRS) spectroscopy is used to probe the origin of the anomalous impact of mechanical treatment on the ionic conductivity of NaCB 11 H 12 . The B, C, and Na K-edge XRS spectra are successfully measured for the first time, and ab initio calculations are employed to interpret the results. The experimental and computational results reveal that the decrease in ionic conductivity upon prolonged milling is due to the increased proximity of Na to the CB 11 H 12 cage, caused by severe distortion of the long-range structure. Overall, this work demonstrates how the XRS technique, allowing investigation of low Z elements such as C and B in the bulk, can be used to acquire valuable information on the electronic structure of solid electrolytes and battery materials in general., (© 2023 The Authors. Small Methods published by Wiley-VCH GmbH.)

The unconventional superconductor Sr 2 RuO 4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L 3 -edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr 2 RuO 4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr 2 RuO 4 and provide key information for the understanding of its unconventional superconductivity., (© 2023. The Author(s).)

X-ray Raman spectroscopy (XRS) is an emerging spectroscopic technique that utilizes inelastic scattering of hard X-rays to study X-ray absorption edges of low Z elements in bulk material. It was used to identify and quantify the amount of carbonyl bonds in a cathode sample, in order to track the redox reaction inside metal-organic batteries during the charge/discharge cycle. XRS was used to record the oxygen K-edge absorption spectra of organic polymer cathodes from different multivalent metal-organic batteries. The amount of carbonyl bond in each sample was determined by modeling the oxygen K-edge XRS spectra with the linear combination of two reference compounds that mimicked the fully charged and the fully discharged phases of the battery. To interpret experimental XRS spectra, theoretical calculations of oxygen K-edge absorption spectra based on density functional theory were performed. Overall, a good agreement between the amount of carbonyl bond present during different stages of battery cycle, calculated from linear combination of standards, and the amount obtained from electrochemical characterization based on measured capacity was achieved. The electrochemical mechanism in all studied batteries was confirmed to be a reduction of double carbonyl bond and the intermediate anion was identified with the help of theoretical calculations. X-ray Raman spectroscopy of the oxygen K-edge was shown to be a viable characterization technique for accurate tracking of the redox reaction inside metal-organic batteries., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

Spin-orbit Mott insulators composed of t_{2g}^{4} transition metal ions may host excitonic magnetism due to the condensation of spin-orbital J=1 triplons. Prior experiments suggest that the 4d antiferromagnet Ca_{2}RuO_{4} embodies this notion, but a J=0 nonmagnetic state as a basis of the excitonic picture remains to be confirmed. We use Ru L_{3}-edge resonant inelastic x-ray scattering to reveal archetypal J multiplets with a J=0 ground state in the cubic compound K_{2}RuCl_{6}, which are well described within the LS-coupling scheme. This result highlights the critical role of unquenched orbital moments in 4d-electron compounds and calls for investigations of quantum criticality and excitonic magnetism on various crystal lattices.

α-RuCl 3 is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-RuCl 3 by a resonant inelastic x-ray scattering study at the Ru L 3 absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism - along with the Kitaev spin liquid - as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-RuCl 3 in magnetic fields., (© 2021. The Author(s).)

Knowledge of the microscopic structure of fluids and changes thereof with pressure and temperature is important for the understanding of chemistry and geochemical processes. In this work we investigate the influence of sodium chloride on the hydrogen-bond network in aqueous solution up to supercritical conditions. A combination of in situ X-ray Raman scattering and ab initio molecular dynamics simulations is used to probe the oxygen K-edge of the alkali halide aqueous solution in order to obtain unique information about the oxygen's local coordination around the ions, e.g. solvation-shell structure and the influence of ion pairing. The measured spectra exhibit systematic temperature dependent changes, which are entirely reproduced by calculations on the basis of structural snapshots obtained via ab initio molecular dynamics simulations. Analysis of the simulated trajectories allowed us to extract detailed structural information. This combined analysis reveals a net destabilizing effect of the dissolved ions which is reduced with rising temperature. The observed increased formation of contact ion pairs and occurrence of larger polyatomic clusters at higher temperatures can be identified as a driving force behind the increasing structural similarity between the salt solution and pure water at elevated temperatures and pressures with drawback on the role of hydrogen bonding in the hot fluid. We discuss our findings in view of recent results on hot NaOH and HCl aqueous fluids and emphasize the importance of ion pairing in the interpretation of the microscopic structure of water.

The IRIXS Spectrograph represents a new design of an ultra-high-resolution resonant inelastic X-ray scattering (RIXS) spectrometer that operates at the Ru L 3 -edge (2840 eV). First proposed in the field of hard X-rays by Shvyd'ko [(2015), Phys. Rev. A, 91, 053817], the X-ray spectrograph uses a combination of laterally graded multilayer mirrors and collimating/dispersing Ge(111) crystals optics in a novel spectral imaging approach to overcome the energy resolution limitation of a traditional Rowland-type spectrometer [Gretarsson et al. (2020), J. Synchrotron Rad. 27, 538-544]. In combination with a dispersionless nested four-bounce high-resolution monochromator design that utilizes Si(111) and Al 2 O 3 (110) crystals, an overall energy resolution better than 35 meV full width at half-maximum has been achieved at the Ru L 3 -edge, in excellent agreement with ray-tracing simulations., (open access.)

Using inelastic X-ray scattering beyond the dipole limit and hard X-ray photoelectron spectroscopy we establish the dual nature of the U [Formula: see text] electrons in U[Formula: see text] (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U [Formula: see text] configuration with the [Formula: see text] and [Formula: see text] quasi-doublet symmetry. The amount of the U 5[Formula: see text] configuration, however, varies considerably across the U[Formula: see text] series, indicating an increase of U 5f itineracy in going from M = Pd to Ni to Ru and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in [Formula: see text] and [Formula: see text], the availability of orbital degrees of freedom needed for the hidden order in [Formula: see text] to occur, as well as the appearance of Pauli paramagnetism in [Formula: see text] A unified and systematic picture of the U[Formula: see text] compounds may now be drawn, thereby providing suggestions for additional experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered [Formula: see text] structure., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)

A new resonant inelastic X-ray scattering (RIXS) instrument has been constructed at beamline P01 of the PETRA III synchrotron. This instrument has been named IRIXS (intermediate X-ray energy RIXS) and is dedicated to X-rays in the tender-energy regime (2.5-3.5 keV). The range covers the L 2,3 absorption edges of many of the 4d elements (Mo, Tc, Ru, Rh, Pd and Ag), offering a unique opportunity to study their low-energy magnetic and charge excitations. The IRIXS instrument is currently operating at the Ru L 3 -edge (2840 eV) but can be extended to the other 4d elements using the existing concept. The incoming photons are monochromated with a four-bounce Si(111) monochromator, while the energy analysis of the outgoing photons is performed by a diced spherical crystal analyzer featuring (102) lattice planes of quartz (SiO 2 ). A total resolution of 100 meV (full width at half-maximum) has been achieved at the Ru L 3 -edge, a number that is in excellent agreement with ray-tracing simulations., (open access.)

The one-dimensional cobaltate Ca[Formula: see text]Co[Formula: see text]O[Formula: see text] is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, [Formula: see text]-core-level non-resonant inelastic x-ray scattering ([Formula: see text]-NIXS), we were able to image the atomic Co [Formula: see text] orbital that is responsible for the Ising magnetism in this system. We can directly observe that corrections to the commonly accepted ideal prismatic trigonal crystal field scheme occur in Ca[Formula: see text]Co[Formula: see text]O[Formula: see text], and it is the complex [Formula: see text] orbital occupied by the sixth electron at the high-spin Co[Formula: see text] ([Formula: see text]) sites that generates the Ising-like behavior. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

Ruthenium compounds serve as a platform for fundamental concepts such as spin-triplet superconductivity 1 , Kitaev spin liquids 2-5 and solid-state analogues of the Higgs mode in particle physics 6,7 . However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including Hund's coupling, spin-orbit coupling and exchange interactions) are comparable in magnitude and their interplay is poorly understood, partly due to difficulties in synthesizing large single crystals for spectroscopic experiments. Here we introduce a resonant inelastic X-ray scattering (RIXS) 8,9 technique capable of probing collective modes in microcrystals of 4d electron materials. We observe spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu 2 O 6 (ref. 10 ) and use the extracted exchange interactions and measured magnon gap to explain its high Néel temperature 11-16 . We expect that the RIXS method presented here will enable momentum-resolved spectroscopy of a large class of 4d transition-metal compounds.

In the context of a novel, high-resolution resonant inelastic X-ray scattering spectrometer, a flat-crystal-based quartz analyzer system has recently been demonstrated to provide an unprecedented intrinsic-energy resolution of 3.9 meV at the Ir L 3 absorption edge (11.215 keV) [Kim et al. (2018) Sci. Rep. 8, 1958]. However, the overall instrument resolution was limited to 9.7 meV because of an 8.9 meV incident band pass, generated by the available high-resolution four-bounce Si(844) monochromator. In order to better match the potent resolving power of the novel analyzer with the energy band pass of the incident beam, a quartz(309)-based double-bounce, high-resolution monochromator was designed and implemented, expected to yield an overall instrument resolution of 6.0 meV. The choice of lower-symmetry quartz is very attractive because of its wealth of suitable near-backscattering reflections. However, it was found that during room-temperature operation typical levels of incident power, barely affecting the Si monochromator, caused substantial thermal distortions in the first crystal of the quartz monochromator, rendering it practically unusable. Finite-element analyses and heat-flow analyses corroborate this finding. As a high-flux, lower resolution (15.8 meV) alternative, a two-bounce sapphire(078) version was also tested and found to be less affected than quartz, but notably more than silicon.

Spin excitations in the overdoped high temperature superconductors Tl_{2}Ba_{2}CuO_{6+δ} and (Bi,Pb)_{2}(Sr,La)_{2}CuO_{6+δ} were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-L_{3} absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle-hole excitations whose maximum shows a fluorescencelike shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping.

We have studied the magnetic excitations of electron-doped Sr_{2-x}La_{x}IrO_{4} (0≤x≤0.10) using resonant inelastic x-ray scattering at the Ir L_{3} edge. The long-range magnetic order is rapidly lost with increasing x, but two-dimensional short-range order (SRO) and dispersive magnon excitations with nearly undiminished spectral weight persist well into the metallic part of the phase diagram. The magnons in the SRO phase are heavily damped and exhibit anisotropic softening. Their dispersions are well described by a pseudospin-1/2 Heisenberg model with exchange interactions whose spatial range increases with doping. We also find a doping-independent high-energy magnetic continuum, which is not described by this model. The spin-orbit excitons arising from the pseudospin-3/2 manifold of the Ir ions broaden substantially in the SRO phase, but remain largely separated from the low-energy magnons. Pseudospin-1/2 models are therefore a good starting point for the theoretical description of the low-energy magnetic dynamics of doped iridates.

We have used Raman scattering to investigate the magnetic excitations and lattice dynamics in the prototypical spin-orbit Mott insulators Sr_{2}IrO_{4} and Sr_{3}Ir_{2}O_{7}. Both compounds exhibit pronounced two-magnon Raman scattering features with different energies, line shapes, and temperature dependencies, which in part reflect the different influence of long-range frustrating exchange interactions. Additionally, we find strong Fano asymmetries in the line shapes of low-energy phonon modes in both compounds, which disappear upon cooling below the antiferromagnetic ordering temperatures. These unusual phonon anomalies indicate that the spin-orbit coupling in Mott-insulating iridates is not sufficiently strong to quench the orbital dynamics in the paramagnetic state.

We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa_{2}Cu_{3}O_{6+x} over a wide range of doping levels (0.1≤x≤1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rather than from incoherent particle-hole excitations as recently suggested theoretically [Benjamin et al. Phys. Rev. Lett. 112, 247002 (2014)]. Implications for the theoretical description of the electron system in the cuprates are discussed.

We report a combination of Fe Kβ x-ray emission spectroscopy and density functional reduced Stoner theory calculations to investigate the correlation between structural and magnetic degrees of freedom in CaFe2(As1-xPx)2. The puzzling temperature behavior of the local moment found in rare earth-doped CaFe2As2 [H. Gretarsson et al., Phys. Rev. Lett. 110, 047003 (2013)] is also observed in CaFe2(As1-xPx)2. We explain this phenomenon based on first-principles calculations with scaled magnetic interaction. One scaling parameter is sufficient to describe quantitatively the magnetic moments in both CaFe2(As1-xPx)2 (x=0.055) and Ca0.78La0.22Fe2As2 at all temperatures. The anomalous growth of the local moments with increasing temperature can be understood from the observed large thermal expansion of the c-axis lattice parameter combined with strong magnetoelastic coupling. These effects originate from the strong tendency to form As-As dimers across the Ca layer in the CaFe2As2 family of materials. Our results emphasize the dual local-itinerant character of magnetism in Fe pnictides.

We report x-ray resonant magnetic scattering and resonant inelastic x-ray scattering studies of epitaxially strained Sr2IrO4 thin films. The films were grown on SrTiO3 and (LaAlO3)0.3(Sr2AlTaO6)0.7 substrates, under slight tensile and compressive strains, respectively. Although the films develop a magnetic structure reminiscent of bulk Sr2IrO4, the magnetic correlations are extremely anisotropic, with in-plane correlation lengths significantly longer than the out-of-plane correlation lengths. In addition, the compressive (tensile) strain serves to suppress (enhance) the magnetic ordering temperature TN, while raising (lowering) the energy of the zone-boundary magnon. Quantum chemical calculations show that the tuning of magnetic energy scales can be understood in terms of strain-induced changes in bond lengths.

We study the structural and magnetic orders in electron-doped BaFe(2-x)Ni(x)As2 by high-resolution synchrotron x-ray and neutron scatterings. Upon Ni doping x, the nearly simultaneous tetragonal-to-orthorhombic structural (T(s)) and antiferromagnetic (T(N)) phase transitions in BaFe2As2 are gradually suppressed and separated, resulting in T(s)>T(N) with increasing x, as was previously observed. However, the temperature separation between T(s) and T(N) decreases with increasing x for x≥0.065, tending toward a quantum bicritical point near optimal superconductivity at x≈0.1. The zero-temperature transition is preempted by the formation of a secondary incommensurate magnetic phase in the region 0.088≲x≲0.104, resulting in a finite value of T(N)≈T(c) + 10  K above the superconducting dome around x≈0.1. Our results imply an avoided quantum critical point, which is expected to strongly influence the properties of both the normal and superconducting states.

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

We report an Fe Kβ x-ray emission spectroscopy study of local magnetic moments in the rare-earth doped iron pnictide Ca(1-x)RE(x)Fe(2)As(2) (RE = La, Pr, and Nd). In all samples studied the size of the Fe local moment is found to decrease significantly with temperature and goes from ∼ 0.9 μ(B) at T = 300 K to ∼ 0.45 μ(B) at T = 70 K. In the collapsed tetragonal phase of Nd- and Pr-doped samples (T<70 K) the local moment is quenched, while the moment remains unchanged for the La-doped sample, which does not show lattice collapse. Our results show that Ca(1-x)RE(x)Fe(2)As(2) (RE = Pr and Nd) exhibits a spin-state transition and provide direct evidence for a nonmagnetic Fe(2+) ion in the collapsed tetragonal phase; spin state as predicted by Yildirim. We argue that the gradual change of the spin state over a wide temperature range reveals the importance of multiorbital physics, in particular the competition between the crystal field split Fe 3d orbitals and the Hund's rule coupling.

We report a comprehensive x-ray scattering study of the low-temperature orthorhombic (LTO)-high-temperature tetragonal (HTT) structural phase transition in 1% iron-doped La(2-x)Sr(x)CuO(4) (x = 0.2). The superlattice (032) peak intensity and the width are investigated in detail for a wide temperature range. We found that the structural phase transition is not sharp and the tilt ordering of the CuO(6) octahedra persists above the transition temperature T(S) (≈77 K). Even at room temperature, the superlattice peak is still observable. The structural phase transition is identified as an order-disorder type phase transition. We found that the tilt ordering in our iron-doped material is always short-ranged, and in the HTT phase the correlation between the tilts along the b axis is better preserved than that along the a axis. Moreover, we identify the role of the Fe as the nucleation centers of the LTO domains in the structural phase transition.