Magnetic excitations and phase separation in the underdoped La2-xSrxCuO4 superconductor measured by resonant inelastic X-ray scattering

Magnon interactions in a moderately correlated Mott insulator

Quantum fluctuations in low-dimensional systems and near quantum phase transitions have significant influences on material properties. Yet, it is difficult to experimentally gauge the strength and importance of quantum fluctuations. Here we provide a resonant inelastic x-ray scattering study of magnon excitations in Mott insulating cuprates. From the thin film of SrCuO2, single- and bi-magnon dispersions are derived. Using an effective Heisenberg Hamiltonian generated from the Hubbard model, we show that the single-magnon dispersion is only described satisfactorily when including significant quantum corrections stemming from magnon-magnon interactions. Comparative results on La2CuO4 indicate that quantum fluctuations are much stronger in SrCuO2 suggesting closer proximity to a magnetic quantum critical point. Monte Carlo calculations reveal that other magnetic orders may compete with the antiferromagnetic Néel order as the ground state. Our results indicate that SrCuO2-due to strong quantum fluctuations-is a unique starting point for the exploration of novel magnetic ground states.

Composite antiferromagnetic and orbital order with altermagnetic properties at a cuprate/manganite interface

Heterostructures from complex oxides allow one to combine various electronic and magnetic orders as to induce new quantum states. A prominent example is the coupling between superconducting and magnetic orders in multilayers from high-T c cuprates and manganites. A key role is played here by the interfacial CuO2 layer whose distinct properties remain to be fully understood. Here, we study with resonant inelastic X-ray scattering the magnon excitations of this interfacial CuO2 layer. In particular, we show that the underlying antiferromagnetic exchange interaction at the interface is strongly suppressed to J ≈ 70 meV, when compared with J ≈ 130 meV for the CuO2 layers away from the interface. Moreover, we observe an anomalous momentum dependence of the intensity of the interfacial magnon mode and show that it suggests that the antiferromagnetic order is accompanied by a particular kind of orbital order that yields a so-called altermagnetic state. Such a 2D altermagnet has recently been predicted to enable new spintronic applications and superconducting proximity effects.

Evolution of the Magnetic Excitations in Electron-Doped La_{2-x}Ce_{x}CuO_{4}

We investigated the high energy spin excitations in electron-doped La_{2-x}Ce_{x}CuO_{4}, a cuprate superconductor, by resonant inelastic x-ray scattering (RIXS) measurements. Efforts were paid to disentangle the paramagnon signal from non-spin-flip spectral weight mixing in the RIXS spectrum at Q_{∥}=(0.6π,0) and (0.9π,0) along the (1 0) direction. Our results show that, for doping level x from 0.07 to 0.185, the variation of the paramagnon excitation energy is marginal. We discuss the implication of our results in connection with the evolution of the electron correlation strength in this system.

Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering

Characterizing and controlling entanglement in quantum materials is crucial for the development of next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in macroscopic solids is theoretically and experimentally challenging. At equilibrium the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopic observables and a nonequilibrium extension of this method could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials with time-resolved resonant inelastic x-ray scattering. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced many-body entanglement due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via ultrafast spectroscopic measurements.

Quantifying vibronic coupling with resonant inelastic X-ray scattering

Electron–phonon interactions are fundamental to the behavior of chemical and physical systems.

Unconventional exciton evolution from the pseudogap to superconducting phases in cuprates

Electron quasiparticles play a crucial role in simplifying the description of many-body physics in solids with surprising success. Conventional Landau's Fermi-liquid and quasiparticle theories for high-temperature superconducting cuprates have, however, received skepticism from various angles. A path-breaking framework of electron fractionalization has been established to replace the Fermi-liquid theory for systems that show the fractional quantum Hall effect and the Mott insulating phenomena; whether it captures the essential physics of the pseudogap and superconducting phases of cuprates is still an open issue. Here, we show that excitonic excitation of optimally doped Bi₂Sr₂CaCu₂O_8+δ with energy far above the superconducting-gap energy scale, about 1 eV or even higher, is unusually enhanced by the onset of superconductivity. Our finding proves the involvement of such high-energy excitons in superconductivity. Therefore, the observed enhancement in the spectral weight of excitons imposes a crucial constraint on theories for the pseudogap and superconducting mechanisms. A simple two-component fermion model which embodies electron fractionalization in the pseudogap state provides a possible mechanism of this enhancement, pointing toward a novel route for understanding the electronic structure of superconducting cuprates.

X-ray synchrotron radiation studies of actinide materials

By reviewing a selection of X-ray diffraction (XRD), resonant X-ray scattering (RXS), X-ray magnetic circular dichroism (XMCD), resonant and non-resonant inelastic scattering (RIXS, NIXS), and dispersive inelastic scattering (IXS) experiments, the potential of synchrotron radiation techniques in studying lattice and electronic structure, hybridization effects, multipolar order and lattice dynamics in actinide materials is demonstrated.

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.

Unraveling the Orbital Physics in a Canonical Orbital System KCuF_{3}

We explore the existence of the collective orbital excitations, orbitons, in the canonical orbital system KCuF_{3} using the Cu L_{3}-edge resonant inelastic x-ray scattering. We show that the nondispersive high-energy peaks result from the Cu^{2+}  dd orbital excitations. These high-energy modes display good agreement with the ab initio quantum chemistry calculation, indicating that the dd excitations are highly localized. At the same time, the low-energy excitations present clear dispersion. They match extremely well with the two-spinon continuum following the comparison with Müller ansatz calculations. The localized dd excitations and the observation of the strongly dispersive magnetic excitations suggest that the orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong local Jahn-Teller effect in KCuF_{3}, which predominantly drives orbital ordering.

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.

Doping evolution of the magnetic excitations in the monolayer CuO2

In this paper, we study theoretically the doping evolution behaviors of the magnetic excitations (MEs) in the monolayer CuO2grown on Bi2Sr2CaCu2O8+δsubstrate. For the undoped system, the MEs exhibit the low energy commensurate behavior around (π,π). They turn to be incommensurate when the system is slightly hole-doped. In the intermediate doping regime, the low energy MEs diminish gradually. They turn to be dominated by the high energy modes. With further doping, an exotic structure transition of the MEs occurs in the heavily hole-doped regime which is directly related to the Lifshitz transition. Distinct MEs are separated by the transition point around which the low energy MEs exhibit the ring-like structure around (0, 0). Before the transition, the MEs are dominated by the broad particle-hole continuum at very high energies. In contrast, across the transition point, two new low energy modes develop around (0, 0) and (π,π) attributing to the intrapocket and interpocket particle-hole scatterings, respectively.

Montel mirror based collimating analyzer system for high-pressure resonant inelastic X-ray scattering experiments

Resonant inelastic X-ray scattering (RIXS) is increasingly playing a significant role in studying highly correlated systems, especially since it was proven capable of measuring low-energy magnetic excitations. However, despite high expectations for experimental evidence of novel magnetic phases at high pressure, unequivocal low-energy spectral signatures remain obscured by extrinsic scattering from material surrounding the sample in a diamond anvil cell (DAC): pressure media, Be gasket and the diamond anvils themselves. A scattered X-ray collimation based medium-energy resolution (∼100 meV) analyzer system for a RIXS spectrometer at the Ir L₃-absorption edge has been designed and built to remediate these difficulties. Due to the confocal nature of the analyzer system, the majority of extrinsic scattering is rejected, yielding a clean low-energy excitation spectrum of an iridate Sr₂IrO₄ sample in a DAC cell. Furthermore, the energy resolution of different configurations of the collimating and analyzing optics are discussed.

Structural, Electronic and Magnetic Properties of a Few Nanometer-Thick Superconducting NdBa2Cu3O7 Films

Epitaxial films of high critical temperature (Tc) cuprate superconductors preserve their transport properties even when their thickness is reduced to a few nanometers. However, when approaching the single crystalline unit cell (u.c.) of thickness, Tc decreases and eventually, superconductivity is lost. Strain originating from the mismatch with the substrate, electronic reconstruction at the interface and alteration of the chemical composition and of doping can be the cause of such changes. Here, we use resonant inelastic x-ray scattering at the Cu L3 edge to study the crystal field and spin excitations of NdBa2Cu3O7−x ultrathin films grown on SrTiO3, comparing 1, 2 and 80 u.c.-thick samples. We find that even at extremely low thicknesses, the strength of the in-plane superexchange interaction is mostly preserved, with just a slight decrease in the 1 u.c. with respect to the 80 u.c.-thick sample. We also observe spectroscopic signatures for a decrease of the hole-doping at low thickness, consistent with the expansion of the c-axis lattice parameter and oxygen deficiency in the chains of the first unit cell, determined by high-resolution transmission microscopy and x-ray diffraction.

IRIXS: a resonant inelastic X-ray scattering instrument dedicated to X-rays in the intermediate energy range

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 L2,3 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 L3-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 (SiO2). A total resolution of 100 meV (full width at half-maximum) has been achieved at the Ru L3-edge, a number that is in excellent agreement with ray-tracing simulations.

Many-Body Physics of Single and Double Spin-Flip Excitations in NiO

Understanding many-body physics of elementary excitations has advanced our control over material properties. Here, we study spin-flip excitations in NiO using Ni L_{3}-edge resonant inelastic x-ray scattering (RIXS) and present a strikingly different resonant energy behavior between single and double spin-flip excitations. Comparing our results with single-site full-multiplet ligand field theory calculations we find that the spectral weight of the double-magnon excitations originates primarily from the double spin-flip transition of the quadrupolar RIXS process within a single magnetic site. Quadrupolar spin-flip processes are among the least studied excitations, despite being important for multiferroic or spin-nematic materials due to their difficult detection. We identify intermediate state multiplets and intra-atomic core-valence exchange interactions as the key many-body factors determining the fate of such excitations. RIXS resonant energy dependence can act as a convincing proof of existence of nondipolar higher-ranked magnetic orders in systems for which, only theoretical predictions are available.

Magnetic Contrast at Spin-Flip Excitations: An Advanced X-Ray Spectroscopy Tool to Study Magnetic-Ordering

The determination of the local orientation and magnitude of the magnetization in spin textures plays a pivotal role in understanding and harnessing magnetic properties for technological applications. Here, we show that by employing the polarization dependence of resonant inelastic X-ray scattering (RIXS), we can directly probe the spin ordering with chemical and site selectivity. Applied on the prototypical ferrimagnetic mixed-valence system, magnetite ([Fe³⁺]_A[Fe³⁺,Fe²⁺]_BO₄), we can distinguish spin-flip excitations at the A and B antiferromagnetically coupled Fe³⁺ sublattices and quantify the exchange field. Furthermore, it is possible to determine the orbital contribution to the magnetic moment from detailed angular dependence measurements. RIXS dichroism measurements performed at spin-flip excitations with nanometer spatial resolution will offer a powerful mapping contrast suitable for the characterization of magnetic ordering at interfaces and engineered spin textures.

Theory of angle-dependent marginal Fermi liquid self-energy and its existence at all dopings in cuprates

Various angle-dependent measurements in hole-doped cuprates suggested that non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main results is that the computed self-energy exhibits a marginal-FL (MFL)-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere at all dopings. The MFL self-energy stems from the fluctuations between the itinerant and localized densities-a result that appears when self-energy is calculated self-consistently and features an intermediate coupling behavior of cuprates. We also calculate the DC conductivity by including the full momentum dependent self-energy. We find that the resistivity-temperature exponent n becomes 1 near the optimal doping, while the MFL self-energy occupies largest momentum-space volume. Surprisingly, even in the NFL state near the optimal doping, the nodal region contains FL-like self-energies; while in the under- and over-dopings ([Formula: see text]), the antinodal region remains NFL-like. These results highlight the non-local correlation physics in cuprates and in other similar intermediately correlated materials, where a direct link between the microscopic single-particle spectral properties and the macroscopic transport behavior can not be well established.

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.

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'.

A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end-station for resonant inelastic X-ray scattering and (resonant) X-ray emission spectroscopy at beamline ID20 of ESRF - The European Synchrotron is presented. The spectrometer hosts five crystal analysers in Rowland geometry for large solid angle collection and is mounted on a rotatable arm for scattering in both the horizontal and vertical planes. The spectrometer is optimized for high-energy-resolution applications, including partial fluorescence yield or high-energy-resolution fluorescence detected X-ray absorption spectroscopy and the study of elementary electronic excitations in solids. In addition, it can be used for non-resonant inelastic X-ray scattering measurements of valence electron excitations.

Indirect K-edge bimagnon resonant inelastic x-ray scattering spectrum of α-FeTe

We calculate the K-edge indirect bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectra of the bicollinear antiferromagnetic order known to occur in the α-FeTe chalcogenide system. Utilizing linear spin wave theory for this large-S spin system we find that the bimagnon spectrum contains four scattering channels (two intraband and two interband). We find from our calculations that for suitable energy-momentum combination the RIXS spectra can exhibit a one-, two- or three- peak structure. The number of peaks provides a clue on the various bimagnon excitation processes that can be supported both in and within the acoustic and optical magnon branches of the bicollinear antiferromagnet. Unlike the RIXS response of the antiferromagnetic or the collinear antiferromagnetic spin ordering, the RIXS intensity spectrum of the bicollinear antiferromagnet does not vanish at the magnetic ordering wave vector [Formula: see text]. It is also sensitive to next-next nearest neighbor and biquadratic coupling interactions. Our predicted RIXS spectrum can be utilized to understand the role of multi-channel bimagnon spin excitations present in the α-FeTe chalcogenide.

Probing the OH Stretch in Different Local Environments in Liquid Water

We use resonant inelastic X-ray scattering (RIXS) to resolve vibrational losses corresponding to the OH stretch where the X-ray absorption process allows us to selectively probe different structural subensembles in liquid water. The results point to a unified interpretation of X-ray and vibrational spectroscopic data in line with a picture of two classes of structural environments in the liquid at ambient conditions with predominantly close-packed high-density liquid (HDL) and occasional local fluctuations into strongly tetrahedral low-density liquid (LDL).

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.

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.

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.

Quenched Magnon excitations by oxygen sublattice reconstruction in (SrCuO2)n/(SrTiO3)2 superlattices

The recently discovered structural reconstruction in the cuprate superlattice (SrCuO2)n/(SrTiO3)2 has been investigated across the critical value of n = 5 using resonant inelastic x-ray scattering (RIXS). We find that at the critical value of n, the cuprate layer remains largely in the bulk-like two-dimensional structure with a minority of Cu plaquettes being reconstructed. The partial reconstruction leads to quenching of the magnons starting at the Γ-point due to the minority plaquettes acting as scattering points. Although comparable in relative abundance, the doped charge impurities in electron-doped cuprate superconductors do not show this quenching of magnetic excitations.

Toroidal silicon polarization analyzer for resonant inelastic x-ray scattering

Resonant Inelastic X-ray Scattering (RIXS) is a powerful probe for studying electronic excitations in materials. Standard high energy RIXS measurements do not measure the polarization of the scattered x-rays, which is unfortunate since it carries information about the nature and symmetry of the excitations involved in the scattering process. Here we report the fabrication of thin Si-based polarization analyzers with a double-concave toroidal surface, useful for L-edge RIXS studies in heavier atoms such as the 5-d transition metals.

Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe

By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

Observation of momentum-resolved charge fluctuations proximate to the charge-order phase using resonant inelastic x-ray scattering

In strongly correlated electron systems, enhanced fluctuations in the proximity of the ordered states of electronic degrees of freedom often induce anomalous electronic properties such as unconventional superconductivity. While spin fluctuations in the energy-momentum space have been studied widely using inelastic neutron scattering, other degrees of freedom, i.e., charge and orbital, have hardly been explored thus far. Here, we use resonant inelastic x-ray scattering to observe charge fluctuations proximate to the charge-order phase in transition metal oxides. In the two-leg ladder of Sr_14−xCa_xCu₂₄O₄₁, charge fluctuations are enhanced at the propagation vector of the charge order (q_CO) when the order is melted by raising temperature or by doping holes. In contrast, charge fluctuations are observed not only at q_CO but also at other momenta in a geometrically frustrated triangular bilayer lattice of LuFe₂O₄. The observed charge fluctuations have a high energy (~1 eV), suggesting that the Coulomb repulsion between electrons plays an important role in the formation of the charge order.

Glue function of optimally and overdoped cuprates from inversion of the Raman spectra

We address the issue of identifying the mediators of effective interactions in cuprates superconductors. Specifically, we use inversion theory to analyze Raman spectra of optimally and over-doped La2-x Sr x CuO4 samples. This allows us to extract the so-called glue function without making any a priori assumption based on any specific model. We use instead two different techniques, namely the singular value decomposition and a multi-rectangle decomposition. With both techniques we find consistent results showing that: (i) two distinct excitations are responsible for the glue function, which have completely different doping dependence. One excitation becomes weak above optimal doping, where on the contrary the other keeps (or even slightly increases) its strength; (ii) there is a marked temperature dependence on the weight and spectral distribution of these excitations, which therefore must have a somewhat critical character. It is quite natural to identify and characterize these two distinct excitations as damped antiferromagnetic spin waves and damped charge density waves, respectively. This sets the stage for a scenario in which superconductivity is concomitant and competing with a charge ordering instability.

Ground state potential energy surfaces around selected atoms from resonant inelastic x-ray scattering

Thermally driven chemistry as well as materials’ functionality are determined by the potential energy surface of a systems electronic ground state. This makes the potential energy surface a central and powerful concept in physics, chemistry and materials science. However, direct experimental access to the potential energy surface locally around atomic centers and to its long-range structure are lacking. Here we demonstrate how sub-natural linewidth resonant inelastic soft x-ray scattering at vibrational resolution is utilized to determine ground state potential energy surfaces locally and detect long-range changes of the potentials that are driven by local modifications. We show how the general concept is applicable not only to small isolated molecules such as O₂ but also to strongly interacting systems such as the hydrogen bond network in liquid water. The weak perturbation to the potential energy surface through hydrogen bonding is observed as a trend towards softening of the ground state potential around the coordinating atom. The instrumental developments in high resolution resonant inelastic soft x-ray scattering are currently accelerating and will enable broad application of the presented approach. With this multidimensional potential energy surfaces that characterize collective phenomena such as (bio)molecular function or high-temperature superconductivity will become accessible in near future.

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.

Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic X-ray scattering

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.

Probing single magnon excitations in Sr₂IrO₄ using O K-edge resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) at the L-edge of transition metal elements is now commonly used to probe single magnon excitations. Here we show that single magnon excitations can also be measured with RIXS at the K-edge of the surrounding ligand atoms when the center heavy metal elements have strong spin-orbit coupling. This is demonstrated with oxygen K-edge RIXS experiments on the perovskite Sr2IrO4, where low energy peaks from single magnon excitations were observed. This new application of RIXS has excellent potential to be applied to a wide range of magnetic systems based on heavy elements, for which the L-edge RIXS energy resolution in the hard x-ray region is usually poor.

Effect of broken symmetry on resonant inelastic x-ray scattering from undoped cuprates

We study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the L-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic terms is supported by numerical calculations on a two-dimensional spin cluster. We express the RIXS spectra in the form of spin-correlation functions with the coefficients evaluated on the cluster, and calculate the function in a two dimensional system within the 1/S expansion. Due to the anisotropic terms, the spectral intensities are considerably enhanced around momentum transfer q = 0 in both one-magnon and two-magnon excitation channels. This finding may be experimentally confirmed by examining carefully the q-dependence of the spectra.

Physical sciences at Diamond: past achievements and future opportunities

The start of user operation at the Diamond Light Source in January 2007 marks a major milestone for the physical sciences in the UK. The routine delivery to the UK community of ultra-bright X-ray beams from the third-generation source has provided us with capabilities that were available previously only at international sources, and indeed has created some that are unique. Here, a personal view is given of some of the achievements to date, and possible future opportunities outlined.

Fractional excitations in the square lattice quantum antiferromagnet

Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.

Valence to core X-ray emission spectroscopy

This Progress Report discusses the chemical sensitivity of Kβ valence to core X-ray emission spectroscopy (vtc-XES) and its applications for investigating 3d-transition-metal based materials. Vtc-XES can be used for ligand identification and for the characterization of the valence electronic levels. The technique provides information that is similar to valence band photoemission spectroscopy but the sample environment can be chosen freely and thus allows measurements in presence of gases and liquids and it can be applied for measurements under in situ/operando or extreme conditions. The theoretical basis of the technique is presented using a one-electron approach and the vtc-XES spectral features are interpreted using ground state density functional theory calculations. Some recent results obtained by vtc-XES in various scientific fields are discussed to demonstrate the potential and future applications of this technique. Resonant X-ray emission spectroscopy is briefly introduced with some applications for the study of 3d and 5d-transition-metal based systems.

The simultaneous measurement of energy and linear polarization of the scattered radiation in resonant inelastic soft x-ray scattering

Resonant Inelastic X-ray Scattering (RIXS) in the soft x-ray range is an element-specific energy-loss spectroscopy used to probe the electronic and magnetic excitations in strongly correlated solids. In the recent years, RIXS has been progressing very quickly in terms of energy resolution and understanding of the experimental results, but the interpretation of spectra could further improve, sometimes decisively, from a full knowledge of the polarization of incident and scattered photons. Here we present the first implementation, in a high resolution soft-RIXS spectrometer used to analyze the scattered radiation, of a device allowing the measurement of the degree of linear polarization. The system, based on a graded W/B4C multilayer mirror installed in proximity of the CCD detector, has been installed on the AXES spectrometer at the ESRF (European Synchrotron Radiation Facility); it has been fully characterized and it has been used for a demonstration experiment at the Cu L3 edge on a high-Tc superconducting cuprate. The loss in efficiency suffered by the spectrometer equipped with this test facility was a factor 17.5. We propose also a more advanced version, suitable for a routine use on the next generation of RIXS spectrometers and with an overall efficiency up to 10%.

Prospects of high-resolution resonant X-ray inelastic scattering studies on solid materials, liquids and gases at diffraction-limited storage rings

The spectroscopic technique of resonant inelastic X-ray scattering (RIXS) will particularly profit from immensely improved brilliance of diffraction-limited storage rings (DLSRs). In RIXS one measures the intensities of excitations as a function of energy and momentum transfer. DLSRs will allow for pushing the achievable energy resolution, signal intensity and the sampled spot size to new limits. With RIXS one nowadays probes a broad range of electronic systems reaching from simple molecules to complex materials displaying phenomena like peculiar magnetism, two-dimensional electron gases, superconductivity, photovoltaic energy conversion and heterogeneous catalysis. In this article the types of improved RIXS studies that will become possible with X-ray beams from DLSRs are envisioned.

Lattice model of resonant inelastic x-ray scattering in metals: relation of a strong core hole to the x-ray edge singularity

We show how the classic approach of Nozières and di Domenicis for treating the edge singularity in x-ray absorption and emission can be generalized to treat the more complex case of the resonant inelastic x-ray scattering (RIXS) process, including effects of the intermediate states involved therein in the presence of the core hole. We solve our lattice model essentially exactly (numerically) to obtain a novel form of edge singularity at the RIXS threshold energy. Our RIXS spectrum naturally includes both the well and poorly screened spectral components and their dispersions and allows its separation into pair and multiple-pair excitations.

High-energy spin and charge excitations in electron-doped copper oxide superconductors

The evolution of electronic (spin and charge) excitations upon carrier doping is an extremely important issue in superconducting layered cuprates and the knowledge of its asymmetry between electron- and hole-dopings is still fragmentary. Here we combine X-ray and neutron inelastic scattering measurements to track the doping dependence of both spin and charge excitations in electron-doped materials. Copper L3 resonant inelastic X-ray scattering spectra show that magnetic excitations shift to higher energy upon doping. Their dispersion becomes steeper near the magnetic zone centre and they deeply mix with charge excitations, indicating that electrons acquire a highly itinerant character in the doped metallic state. Moreover, above the magnetic excitations, an additional dispersing feature is observed near the Γ-point, and we ascribe it to particle-hole charge excitations. These properties are in stark contrast with the more localized spin excitations (paramagnons) recently observed in hole-doped compounds even at high doping levels.

Real-space visualization of remnant Mott gap and magnon excitations

We demonstrate the ability to visualize real-space dynamics of charge gap and magnon excitations in the Mott phase of the single-band Hubbard model and the remnants of these excitations with hole or electron doping. At short times, the character of magnetic and charge excitations is maintained even for large doping away from the Mott and antiferromagnetic phases. Doping influences both the real-space patterns and long timescales of these excitations with a clear carrier asymmetry attributable to particle-hole symmetry breaking in the underlying model. Further, a rapidly oscillating charge-density-wave-like pattern weakens, but persists as a visible demonstration of a subleading instability at half-filling which remains upon doping. The results offer an approach to analyzing the behavior of systems where momentum space is either inaccessible or poorly defined.

Femtosecond dynamics of momentum-dependent magnetic excitations from resonant inelastic X-ray scattering in CaCu2O3

Taking spinon excitations in the quantum antiferromagnet CaCu2O3 as an example, we demonstrate that femtosecond dynamics of magnetic electronic excitations can be probed by direct resonant inelastic x-ray scattering (RIXS). To this end, we isolate the contributions of single and double spin-flip excitations in experimental RIXS spectra, identify the physical mechanisms that cause them, and determine their respective time scales. By comparing theory and experiment, we find that double spin flips need a finite amount of time to be generated, rendering them sensitive to the core-hole lifetime, whereas single spin flips are, to a very good approximation, independent of it. This shows that RIXS can grant access to time-domain dynamics of excitations and illustrates how RIXS experiments can distinguish between excitations in correlated electron systems based on their different time dependence.

Photon polarization precession spectroscopy for high-resolution studies of spin waves

A new type of spectroscopy for high-resolution studies of spin waves that relies on resonant scattering of hard x rays is introduced. The energy transfer in the scattering process is encoded in the precession of the polarization vector of the scattered photons. Thus, the energy resolution of such a spectroscopy is independent of the bandwidth of the probing radiation. The measured quantity resembles the intermediate scattering function of the magnetic excitations in the sample. At pulsed x-ray sources, especially x-ray lasers, the proposed technique allows us to take single-shot spectra of the magnetic dynamics. The method opens new avenues to study low-energy nonequilibrium magnetic processes in a pump-probe setup.