Resonant inelastic x-ray scattering studies of elementary excitations

High-resolution resonant inelastic X-ray scattering with soft X-rays at the ADRESS beamline of the Swiss light source: Instrumental developments and scientific highlights

ABSTRACTHard X-ray resonant inelastic X-ray scattering (RIXS) is a promising X-ray spectroscopic tool for measuring low-energy excitation spectra from complex materials under high pressure. In the past, these measurements have been stymied by technical difficulties inherent in measuring a tiny sample, held at high pressure, inside a diamond anvil cell. Now, due to substantial advances in X-ray instrumentation, high-resolution ( meV) RIXS spectrometers at third-generation synchrotron radiation sources have started to successfully address these samples in their extreme environment. However, compared to elastic X-ray scattering and X-ray emission spectroscopy, RIXS is a very photon hungry technique and high-resolution RIXS for samples under high pressure is in its infancy. In this review, the fundamentals of the high-resolution RIXS and associated instrumentation are presented, as well as technical details of diamond anvil cells, sample preparation, and the measurement geometry. Experimental data from measurements of 3d- and 5d-transition metal oxides are shown and future improvements of the RIXS technique in the context of high pressure are discussed.

The study of elementary bosonic excitations is essential toward a complete description of quantum electronic solids. In this context, resonant inelastic X-ray scattering (RIXS) has recently risen to becoming a versatile probe of electronic excitations in strongly correlated electron systems. The nature of the radiation-matter interaction endows RIXS with the ability to resolve the charge, spin and orbital nature of individual excitations. However, this capability has been only marginally explored to date. Here, we demonstrate a systematic method for the extraction of the character of excitations as imprinted in the azimuthal dependence of the RIXS signal. Using this novel approach, we resolve the charge, spin, and orbital nature of elastic scattering, (para-)magnon/bimagnon modes, and higher energy dd excitations in magnetically-ordered and superconducting copper-oxide perovskites (Nd2CuO4 and YBa2Cu3O6.75). Our method derives from a direct application of scattering theory, enabling us to deconstruct the complex scattering tensor as a function of energy loss. In particular, we use the characteristic tensorial nature of each excitation to precisely and reliably disentangle the charge and spin contributions to the low energy RIXS spectrum. This procedure enables to separately track the evolution of spin and charge spectral distributions in cuprates with doping. Our results demonstrate a new capability that can be integrated into the RIXS toolset, and that promises to be widely applicable to materials with intertwined spin, orbital, and charge excitations.

The essence of quantum materials lies in the intricate coupling among charge, spin, orbital and lattice degrees of freedom. Although X-ray photoemission spectroscopy and inelastic neutron scattering have advantages in detecting fermionic single-particle spectral function and bosonic spin excitations in quantum materials, respectively, probing other bosonic collective excitations especially their coupling is not possible until the establishment of the advanced resonant inelastic X-ray scattering (RIXS). In the past decades, RIXS has flourished with continuously improved energy resolution which made a paradigm shift from measuring crystal-field splitting and the charge-transfer excitation, to probing collective excitations and the order parameters of all degrees of freedom. This review paper summarises the latest research progress of quantum materials studied by the soft X-ray RIXS. For instance, three-dimensional collective charge excitations, plasmons, were discovered experimentally by RIXS in both electron and hole doped cuprate superconductors. The collective orbital excitations and excitons were found in copper and nickel based quantum materials. For the newly discovered nickelate superconductors, RIXS has made substantial contributions to characterising their electronic and magnetic excitations and the related ordering phenomena critical for an in-depth understanding of the underlying superconducting mechanicsm. The RIXS is a unique tool in probing the higher-order spin excitations in quantum materials due to the strong spin-orbit coupling and the core-valence exchange interaction. The RIXS is also found to be superior in probing the Stoner magnetic excitations in magnetic metals and topological magnetic materials. Finally, the development of RIXS technology in Chinese large-scale research facilities is briefly prospected.

Resonant inelastic X-ray scattering (RIXS) is a powerful probe of elementary\nexcitations in solids. It is now widely applied to study magnetic excitations.\nHowever, its complex cross-section means that RIXS has been more difficult to\ninterpret than inelastic neutron scattering (INS). Here we report\nhigh-resolution RIXS measurements of magnetic excitations of La2CuO4, the\nantiferromagnetic parent of one system of high-temperature superconductors. At\nhigh energies (~2 eV), the RIXS spectra show angular-dependent dd orbital\nexcitations which are found to be in good agreement with single-site multiplet\ncalculations. At lower energies (<0.3 eV), we show that the\nwavevector-dependent RIXS intensities are proportional to the product of the\nsingle-ion spin-flip cross section and the dynamical susceptibility of the\nspin-wave excitations. When the spin-flip crosssection is dividing out, the\nRIXS magnon intensities show a remarkable resemblance to INS data. Our results\nshow that RIXS is a quantitative probe the dynamical spin susceptibility in\ncuprate and therefore should be used for quantitative investigation of other\ncorrelated electron materials.\n

Transition metal compounds represent a unique class of solids characterized by a surprising richness of physical properties. They display many phenomena and represent the main area of interest for the research on strongly correlated materials. Many novel ideas such as spintronics, magnetoelectricity, multiferroicity and high-Tc superconductivity arose from transition metal compounds and form a fruitful field of research, promising and having already established important applications. This thesis focuses on two of these phenomena: ferroelectricity and high-Tc superconductivity. BaTiO3 is a well studied and technologically relevant ferroelectric material characterized by a high temperature for the paraelectric to ferroelectric transition. The temperature dependent RIXS investigation, reported in this thesis, provided a further clarification on the microscopic mechanism at the basis of its ferroelectric phase transition. Lowering the temperature, the RIXS spectra show a transfer of spectral weight from the elastic to the charge-transfer spectral features, indicative of increasing Ti 3d-O 2p hybridization. When the incident photon of the RIXS process is tuned to select transitions to the Ti 3d eg manifold, the quasielastic RIXS response exhibits a tail indicative of phonon excitations. A quantitative analysis of the line shape permitted the estimation of the electron-phonon coupling strength, placing BaTiO3 in the intermediate coupling regime. A vast area of research on high-Tc superconductivity concerns cuprate materials. In this work, the attention is focused on two different examples of this family: the benchmark La(2-x)SrxCuO4 compound and the alternative cuprate structure of Ba2Cu3O4Cl2. An excitation-energy dependent RIXS investigation on La(2-x)SrxCuO4 revealed a double peak structure located at a 2 eV. This feature shows fluorescent behaviour excluding the identification to purely dd excitations. Cluster calculations suggest significant contributions from the Zhang-Rice singlet (ZRS) state. A Cu L3 edge RIXS investigation on Ba2Cu3O4Cl2 provided the signature of the spin waves of this oxhychloride. These results compared with previous RIXS data on cuprates allowed to selectively determine the relevant parameters of the model Hamiltonian at the basis of the description of this class of materials.

Resonant inelastic x-ray scattering (RIXS) is a spectroscopic technique that has been widely used to study various elementary excitations in correlated and other condensed matter systems. For strongly correlated materials, besides boosting the overall signal the dependence of the resonant profile on incident photon energy is still not fully understood. Previous endeavors in connecting indirect RIXS, such as Cu K-edge where scattering takes place only via the core–hole created as an intermediate state, with the charge dynamical structure factor S(q,ω) neglected complicated dependence on the intermediate state configuration. To resolve this issue, we performed an exact diagonalization study of the RIXS cross-section using the single-band Hubbard model by fully addressing the intermediate state contribution. Our results are relevant to indirect RIXS in correlated materials, such as high-Tc cuprates. We demonstrate that RIXS spectra can be reduced to S(q,ω) when there is no screening channel for the core–hole potential in the intermediate state. We also show that two-magnon excitations are highlighted at the resonant photon energy when the core–hole potential in the corresponding intermediate state is poorly screened. Our results demonstrate that different elementary excitations can be emphasized at different intermediate states, such that selecting the exact incident energy is critical when trying to capture a particular elementary excitation.

We have performed neutron inelastic scattering and resonant inelastic X-ray scattering (RIXS) at the Cu-$L_3$ edge to study high-energy magnetic excitations at energy transfers of more than 100 meV for overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.25$ ($T_c=15$ K) and $x=0.30$ (non-superconducting) using identical single crystal samples for the two techniques. From constant-energy slices of neutron scattering cross-sections, we have identified magnetic excitations up to ~250 meV for $x=0.25$. Although the width in the momentum direction is large, the peak positions along the (pi, pi) direction agree with the dispersion relation of the spin-wave in the non-doped La$_{2}$CuO$_{4}$ (LCO), which is consistent with the previous RIXS results of cuprate superconductors. Using RIXS at the Cu-$L_3$ edge, we have measured the dispersion relations of the so-called paramagnon mode along both (pi, pi) and (pi, 0) directions. Although in both directions the neutron and RIXS data connect with each other and the paramagnon along (pi, 0) agrees well with the LCO spin-wave dispersion, the paramagnon in the (pi, pi) direction probed by RIXS appears to be less dispersive and the excitation energy is lower than the spin-wave of LCO near (pi/2, pi/2). Thus, our results indicate consistency between neutron inelastic scattering and RIXS, and elucidate the entire magnetic excitation in the (pi, pi) direction by the complementary use of two probes. The polarization dependence of the RIXS profiles indicates that appreciable charge excitations exist in the same energy range of magnetic excitations, reflecting the itinerant character of the overdoped sample. A possible anisotropy in the charge excitation intensity might explain the apparent differences in the paramagnon dispersion in the (pi, pi) direction as detected by the X-ray scattering.

The resonant X-ray scattering (RXS) and the resonant inelastic X-ray scattering (RIXS) in correlated electron systems with the orbital degree of freedom are reviewed from the theoretical view points. In the first part, the orbital order and RXS as an experimental tool to detect the orbital order are reviewed. We introduce characteristic interacting-orbital models and orbital orders, in which a unique orbital frustration effect emerges. As a case study, the theoretical and experimental studies in an impurity effect on the orbital order are presented. In the second part, the RIXS studies for observation of the orbital excitation are reviewed. In particular, we focus on the polarization dependence of RIXS which is crucial to identify the scattering from the orbital excitation. We introduce the recent progresses of the collective orbital excitations coupled with the lattice vibration. The non-resonant inelastic X-ray scattering as a tool to detect the orbital excitations is also reviewed.

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries, we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.

We performed a systematic study of the complexes of trivalent lanthanide cations with the hydridotris(1-pyrazolyl)borato (Tp) ligand (LnTp3; Ln = La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, and Lu) using both high-energy-resolution fluorescence-detected X-ray absorption near-edge structure (HERFD-XANES) and resonant inelastic X-ray scattering (RIXS) at the lanthanide L3 absorption edge. Here, we report the results obtained and we discuss them against calculations performed using density functional theory (DFT) and atomic multiplet theory. The spectral shape and the elemental trends observed in the experimental HERFD-XANES spectra are well reproduced by DFT calculations, while the pre-edge energy interval is better described by atomic multiplet theory. The RIXS data show a generally rather complex pattern that originates from the intra-atomic electron–electron interactions in the intermediate and final states, as demonstrated by the good agreement obtained with calculations using an atomic-only model of the absorber. Guided by theoretical predictions, we discuss the possible origins of the observed spectral features and the trends in energy splitting across the series. The insight into the electronic structure of trivalent lanthanide compounds demonstrated here and obtained with advanced X-ray spectroscopies coupled with theoretical calculations can be applied to any lanthanide-bearing compound and be of great interest for all research fields involving lanthanides.

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.

Resonant inelastic x-ray scattering (RIXS) has become a prominent technique to study quasiparticle excitations. With advances in polarization analysis capabilities at different facilities, RIXS offers exceptional potential for investigating symmetry-broken quasiparticles such as chiral phonons and magnons. At optical wavelengths, birefringence can severely affect polarization states in low-symmetry systems. Here we show its importance for soft x-ray resonances. Given the growing interest in circular dichroism (CD) in RIXS, it is important to evaluate how birefringence may affect the RIXS spectra of anisotropic systems. We investigate CuO, a well-known anisotropic material, using Cu L3-edge RIXS and detect significant CD in both magnetic and orbital excitations in the collinear antiferromagnetic phase. We demonstrate that the CD can be modeled by a proper treatment of RIXS scattering amplitudes derived from single-ion calculations with birefringence. Recognizing these effects is crucial for unambiguous identification of subtle dichroic effects induced by symmetry-broken quasiparticles. Furthermore, the combined sensitivity of RIXS and birefringence to local symmetry presents an opportunity to study microscopic changes driven by external perturbations.

Recent progress in the study of resonant inelastic X-ray scattering (RIXS) spectroscopy in d and f electron systems is described. The main space is devoted to the theoretical investigations, some typical experimental data and the comparison of calculated and experimental results, putting emphasis on the underlying physical mechanisms. We confine ourselves mainly to the studies performed since 2000, and discuss the following topics: (1) RIXS in high Tc cuprates, (2) f0 and d0 systems, (3) other transition metal compounds, (4) RIXS by electric quadrupole excitation, and (5) magnetic circular dichroism in RIXS of ferromagnetic systems. Some brief description is also given on the future prospect of the RIXS study.

Low-energy orbital excitations in spinel FeCr2S4 have been studied element specifically at both Fe and Cr 2p–3d resonances by resonant inelastic X-ray scattering (RIXS). As a first step X-ray absorption spectroscopy measurements confirmed that iron, located at the tetrahedral (Td) sites of the spinel structure, is in a Fe2+ (d6) state and chromium, located at the octahedral (Oh) sites, is in a Cr3+ (d3) state. We have identified RIXS spectral features with the help of crystal-field simulations that account consistently for on-site dd excitations and provide 10Dq = 0.30 ± 0.05 eV for Fe Td sites and 10Dq = 1.60 ± 0.05 eV for Cr Oh sites. The giant magneto-optical Kerr effect previously observed for photons with 0.3 eV can be unambiguously attributed to the lowest possible dd excitations on the iron site Fe(e3t23) → Fe(e2t24). A 1.6 eV energy-loss feature, measured in the Fe 2p–3d RIXS spectra, is found to be a two-site orbital excitation directly related to superexchange (SE) interaction between Fe and Cr cations. It opens new perspectives for applying RIXS to study SE in a broad range of 3d transition metal compounds.