Nonresonant Inelastic X-ray Scattering Research Articles

Non-resonant inelastic X-ray scattering for discrimination of pigments.

Inelastic X-ray scattering (IXS) spectroscopy has been used in many fields of solid-state physics and theoretical chemistry as an accurate and quantitative probe of elementary excitations. We show that non-resonant IXS spectra in the energy loss range below 100 eV exhibit a strong contrast across a wide range of commercially available pigments, opening new routes for their discrimination. These signatures combine plasmonic transitions, collective excitations and low energy absorption edges. We have performed IXS to discriminate different artists' pigments within complex mixtures and to quantitatively determine rutile and anatase polymorphs of TiO2. The integration of experimental data on pigment powders with suitable ab initio simulations shows a precise fit of the spectroscopic data both in the position of the resonances and in their relative intensity.

Non-resonant inelastic X-ray scattering spectroscopy: A momentum probe to detect the electronic structures of atoms and molecules

Non-resonant inelastic X-ray scattering (NRIXS) is a new technique for atomic and molecular physics that allows one to measure the electronic structures and dynamic parameters of the ground and excited states of atoms and molecules in momentum space. There is a clearly understood physical picture of NRIXS, which reveals its remarkable advantages of satisfying the first Born approximation and being able to excite dipole-forbidden transitions. Various physical properties of atoms and molecules, such as their elastic and inelastic squared form factors, optical oscillator strengths, and Compton profiles, can be explored using NRIXS under different experimental conditions. In this paper, we review newly developed experimental methods for NRIXS, together with its characteristics and various applications, with emphasis on the new insights into excitation mechanism and other new information revealed by this technique. The intrinsic connections and differences between NRIXS and fast electron impact spectroscopy are elucidated. Future applications of this method to atomic and molecular physics are also described.

Transuranium compounds probed by nonresonant inelastic x-ray scattering

While x-ray absorption spectroscopy is mainly governed by electric-dipole transitions, the technique of nonresonant inelastic x-ray scattering (NIXS) offers the possibility to explore higher-order multipole transitions. These transitions obey different selection rules that can reach final states of higher angular momenta, opening complementary spectroscopic perspectives. Here, we investigate the suitability of NIXS to study transuranium compounds. We show that the $K$ edge of the Be encapsulation can be practically fully excluded by using the imaging capabilities of the technique arising from the position of the signals on the multidetector. Experimental results for the multipole transitions at the actinide ${O}_{4,5}$ edges (90--120 eV) in ${\mathrm{UO}}_{2}$, ${\mathrm{NpO}}_{2}$, ${\mathrm{PuO}}_{2}$, and ${\mathrm{Pu}}_{2}{\mathrm{O}}_{3}$ are compared with multielectronic calculations. The spectral features are shown to be very sensitive to the ratio of the triakontadipole and octupole transitions, which could potentially be used to assess the radial expansion of the $5f$ wave function, which is expected to occur in covalent mixing with the O $2p$ states.

Orientation of the ground-state orbital inCeCoIn5andCeRhIn5

We present core level non-resonant inelastic x-ray scattering (NIXS) data of the heavy fermion compounds CeCoIn$_5$ and CeRhIn$_5$ measured at the Ce $N_{4,5}$-edges. The higher than dipole transitions in NIXS allow determining the orientation of the $\Gamma_7$ crystal-field ground-state orbital within the unit cell. The crystal-field parameters of the Ce$M$In$_5$ compounds and related substitution phase diagrams have been investigated in great detail in the past; however, whether the ground-state wavefunction is the $\Gamma_7^+$ ($x^2\,-\,y^2$) or $\Gamma_7^-$ ($xy$ orientation) remained undetermined. We show that the $\Gamma_7^-$ doublet with lobes along the (110) direction forms the ground state in CeCoIn$_5$ and CeRhIn$_5$. For CeCoIn$_5$, however, we find also some contribution of the first excited state crystal-field state in the ground state due to the stronger hybridization of 4$f$ and conduction electrons, suggesting a smaller $\alpha^2$ value than originally anticipated from x-ray absorption. A comparison is made to the results of existing density functional theory plus dynamical mean-field theory calculations.

Crystal-field states ofUO2probed by directional dependence of nonresonant inelastic x-ray scattering

Nonresonant inelastic x-ray scattering (NIXS) has been performed on single crystals of UO$_2$ to study the direction dependence of higher-order-multipole scattering from the uranium $O_{4,5}$ edges (90--110 eV). By comparing the experimental results with theoretical calculations the symmetry of the ground state is confirmed directly as the crystal-field (CF) $\Gamma_5$ triplet state within the $J$ = 4 manifold. The results also demonstrate that the directional dichroism of the NIXS spectra is sensitive to the CF strength and establish NIXS as a tool for probing CF interactions quantitatively.

4f Crystal Field Ground State of the Strongly Correlated Topological Insulator SmB_{6}.

We investigated the crystal-electric field ground state of the 4f manifold in the strongly correlated topological insulator SmB_{6} using core-level nonresonant inelastic x-ray scattering. The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the Γ_{8} quartet state of the Sm f^{5} J=5/2 configuration governs the ground-state symmetry and, hence, the topological properties of SmB_{6}. Our findings contradict the results of density functional calculations reported so far.

Lithium borate crystals and glasses: How similar are they? A non-resonant inelastic X-ray scattering study around the B and O K-edges

The local environment of lithium borate glasses and their crystalline counterparts is investigated using non-resonant inelastic X-ray scattering (NRIXS) at energy losses corresponding to the B and O K-edges. Thanks to an extended series of lithium borate glasses and crystals, we have been able to finely interpret the local environments around boron and oxygen atoms in terms of coordination number, degree of polymerization of the borate network, superstructural units, and formation of non-bridging oxygens (NBOs). Even if a good local structural agreement between the glass and the crystal is found, an important structural discrepancy is found around the metaborate composition (50mol% of Li2O) rendering useless the use of the crystalline phase to describe the glassy state. In low alkali glasses, two subnetworks corresponding to a ‘Li-rich’ domain and a pure B2O3 domain containing boroxol rings have been evidenced. A spectral signature of the NBOs has also been evidenced in the π* peak of the B K-edge, making NRIXS a useful method offering a series of spectral signatures which can be used as structural probes for up-coming high-temperature or high-pressure in-situ experiments.

The quartet ground state in CeB6: An inelastic x-ray scattering study

We investigated the ground-state symmetry of the cubic hidden order compound CeB6 by means of core level non-resonant inelastic x-ray scattering (NIXS). The information is obtained from the directional dependence of the scattering function that arises from higher than dipole transitions. Our new method confirms that the ground state is well described using a localized crystal-field model assuming a Γ8 quartet ground state.

Direct bulk-sensitive probe of 5f symmetry in URu2Si2

The second-order phase transition into a hidden order phase in URu2Si2 goes along with an order parameter that is still a mystery, despite 30 years of research. However, it is understood that the symmetry of the order parameter must be related to the symmetry of the low-lying local electronic [Formula: see text]-states. Here, we present results of a spectroscopic technique, namely core-level nonresonant inelastic X-ray scattering (NIXS). This method allows for the measurement of local high-multipole excitations and is bulk-sensitive. The observed anisotropy of the scattering function unambiguously shows that the 5[Formula: see text] ground-state wave function is composed mainly of the [Formula: see text] with majority [Formula: see text] = [Formula: see text] + [Formula: see text] and/or [Formula: see text] singlet states. The incomplete dichroism indicates the possibility that quantum states of other irreducible representation are mixed into the ground state.

Orbital-selective electronic excitations in iron arsenides revealed by simulated nonresonant inelastic x-ray scattering

Nonresonant inelastic x-ray scattering (NIXS) is a possible tool to detect charge excitations in electron systems. In addition, multipole transitions at high-momentum-transfer region open a new possibility to determine orbital-selective electronic excitations in multi-orbital itinerant 3d electron systems. As a theoretical example, we chose the antiferromagnetic state of iron arsenides and demonstrate that the orbital-selective excitations are detectable by choosing appropriate momentum transfer in NIXS. We propose that both NIXS and resonant inelastic x-ray scattering are complementary to each other for fully understanding the nature of orbital excitations in multi-orbital itinerant electron systems.

Absence of orbital rotation in superconductingCeCu2Ge2

We address the recently proposed orbital transition scenario in heavy fermion compounds exhibiting two superconducting domes. Our method of choice is nonresonant inelastic x-ray scattering (NIXS) which probes charge densities and can be modeled quantitatively. Our NIXS results of ${\mathrm{CeCu}}_{2}{\mathrm{Ge}}_{2}$, a model system of this class of materials, are well described by considering the same sequence of orbitals at all temperatures, thus putting into question whether orbital transitions are related to the formation of the second superconducting dome. The discrepancy between experimental findings and prediction could be due to the lack of accuracy in the theoretical description of the $4f$ states.

Detecting non-bridging oxygens: non-resonant inelastic X-ray scattering in crystalline lithium borates.

Probing the local environment of low-Z elements, such as oxygen, is of great interest for understanding the atomic-scale behavior in materials, but it requires experimental techniques allowing it to work with versatile sample environments. In this paper, the local environment of lithium borate crystals is investigated using non-resonant inelastic X-ray scattering (NRIXS) at energy losses corresponding to the oxygen K-edge. Large variations of the spectral features are observed close to the edge onset in the 535-540 eV energy range when varying the Li2O content. Calculations allow identification of contributions associated with bridging oxygen (BO) and non-bridging oxygen (NBO) atoms. The main result resides in the observed core-level shift of about 1.7 eV in the spectral signatures of the BO and NBO. The clear signature at 535 eV in the O K-edge NRXIS spectrum is thus an original way to probe the presence of NBOs in borates, with the great advantage of making possible the use of complex environments such as a high-pressure cell or high-temperature device for in situ measurements.

Effective orbital symmetry of CuO: Examination by nonresonant inelastic x-ray scattering

We report on measurements of nonresonant inelastic x-ray scattering (NIXS) to unravel the effective symmetry of Cu $3d$ orbitals in the ground state of CuO. A clear feature of energy loss at about 2 eV exists in the NIXS spectrum, arising from $dd$ excitations; the intensities of these excitations display a pronounced anisotropy. The comparison between the measured angular distributions of scattering and those from theoretical predictions by the tesseral harmonics indicates that, in terms of a hole picture, the lowest-energy $dd$ excitation is the orbital transition ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $xy$. In addition, the transition ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $3{z}^{2}\ensuremath{-}{r}^{2}$ has an energy higher than ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $yz/zx$, in contrast to a previous interpretation. Our results imply a large Jahn-Teller-like splitting between ${x}^{2}\ensuremath{-}{y}^{2}$ and $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. The theory assuming a ${C}_{4h}$ symmetry explains the angular dependence of the NIXS spectra fairly well, implying that this symmetry is a reasonable approximation. This demonstrates that NIXS can provide important information for modeling of the electronic structure of $d$ ions embedded in a complicated crystal field.

Interference between Resonant and Nonresonant Inelastic X-Ray Scattering

A detailed study of inelastic x-ray scattering from the ground state to the 3Σg(3σ(g)(-1)3s(g)1) state of the O2 molecule is presented. The observed angular anisotropy shows that the vibrational excitations within this final state are strongly dependent on the polarization of the incident radiation. The analysis demonstrates that this is a manifestation of interference between resonant and direct nonresonant inelastic x-ray scattering. This interference provides a new tool to monitor nuclear dynamics by relative rotation of the polarization vectors of the incident and scattered photons.

Inelastic X-ray Scattering Studies of Electronic Excitations

Inelastic x-ray scattering (IXS) has developed into one of the most powerful momentum-resolved spectroscopies. Especially in the last decade, it has achieved significant progress utilizing brilliant x-rays from third-generation synchrotron radiation facilities. Simultaneously, theoretical efforts have been made to predict or interpret the experimental spectra. One of the scientific fields studied intensively by IXS is strongly correlated electron systems, where the interplay of charge, spin, and orbital degrees of freedom determines their physical properties. IXS can provide a new insight into the electron dynamics of the systems through the observation of charge, spin, and orbital excitations. Focusing on the momentum-resolved electronic excitations in strongly correlated electron systems, we review IXS studies and the present capabilities of IXS for the study of the dynamics of materials. With nonresonant inelastic x-ray scattering (NIXS), one can directly obtain dynamical charge correlation and we disc...

Bulk-Sensitive Characterization of the Discharged Products in Li–O2Batteries by Nonresonant Inelastic X-ray Scattering

Understanding the nature of discharged products is critical to identifying suitable electrolyte systems for Li–O2 batteries. We have employed nonresonant inelastic X-ray scattering (NIXS), which is a hard X-ray photon-in photon-out technique to monitor low energy core–shell excitations and to obtain bulk sensitive information on the solid discharged products in Li–O2 batteries using various electrolyte solvent/salt combinations. NIXS measurements were performed on cathodes after discharging the Li–O2 cells using low discharge current (∼25 mA/g of carbon). NIXS results reveal that, even in cells containing current state-of-the-art electrolytes, the oxygen in the discharged products is bound predominantly to species other than a peroxide or lithia. This finding shows that electrolyte decomposition is a significant pathway during discharge of Li–O2 batteries using ether and oligoether substituted silane based electrolytes.

Nonresonant inelastic x-ray scattering from actinides and rare earths

Calculated multiplet spectra are presented for the electric-multipole transitions in nonresonant inelastic x-ray scattering (NIXS) at the ${O}_{4,5}$ edges of actinides and the ${N}_{4,5}$ edges of rare earths. The multiplet structure is characteristic for the $f$ count as well as for the angular momentum coupling. As a remarkable peculiarity, the calculations for the actinide ${O}_{4,5}$ edge show that the higher multipole spectra resemble $jj$ coupling, whereas the dipole spectrum is close to $LS$ coupling. The exchange integral ${G}^{1}(5d,5f)$ is responsible for a shift of $\ensuremath{\sim}$15 eV of the dipole spectrum to higher energy. This high energy is conserved by a sum rule for the average energy of the accessible final states. In the higher multipole spectra, where the allowed final states are different, the splitting by the $5d$ spin-orbit interaction exceeds that of the electrostatic interaction. This leads to a distinct spin-orbit-split doublet structure, with a broad first peak and a narrower second peak. According to the spin-orbit sum rule, the $5f$ spin-orbit interaction per hole is linearly related to the core-level branching ratio, where the proportionality factor is opposite in sign for the $k=3$ and 5 spectra. Compared to the $k=3$ spectrum, the $k=5$ spectrum has overall a lower intensity in the low-energy region but a higher intensity in the high-energy region, especially for the heavier elements in the series. The NIXS at the rare-earth ${N}_{4,5}$ edge is quite different since the electrostatic and core spin-orbit splitting in the $k=3$ and 5 spectra are of similar size. The pre-edge region of the rare-earth spectra, where the linewidth is narrow, shows a rich multiplet structure that depends strongly on the initial-state $J$ value.

Systematic Trends in Non-resonant Inelastic X-ray Scattering of Actinides

ABSTRACTNonresonant inelastic x-ray scattering (NIXS) measurements probing the 5d → 5f electronic transitions at the uranium O4,5 edges in a localized electron system such as UO2 show a good agreement with many-electron atomic spectral calculations. The higher multipole spectra are split into two peaks that can be assigned as the 5d5/2 and 5d3/2 structures, despite the large electrostatic interactions. A new sum rule for the branching ratio of spin-orbit split core levels in electric multipole spectra, which generalizes the sum rule for dipole transitions in x-ray absorption spectroscopy, allows for a systematic analysis of the NIXS spectra. The branching ratio is linearly proportional to the expectation value of the angular part of the spin-orbit interaction in the initial state, where the rank of the multipole determines the coefficient of the linear dependence. This spin-orbit sum rule can be an important diagnostic tool for high-energy spectroscopies.

Structure of Lithium Peroxide

The reliable identification of lithium oxide species, especially lithium peroxide (Li2O2), is of vital importance to the study of Li-air batteries. Previous X-ray diffraction studies of Li2O2 resulted in the proposal of two disparate structures by Féher and Föppl. In this Letter, we assess these competing Li2O2 structures using a combination of the following X-ray and first-principles techniques: (i) high-energy X-ray diffraction (XRD), (ii) comparisons of the measured nonresonant inelastic X-ray scattering (NIXS) spectra with those computed from first principles using the Bethe-Salpeter equation (BSE), and (iii) comparison of thermochemistry data with the formation enthalpies obtained from density functional theory (DFT) calculations using a hybrid functional. All three approaches result in the identification of Föppl’s proposal as the more appropriate structure for Li2O2. The measured and computed spectra and data presented in this Letter are useful as benchmarks for future characterization of Li2O2.

Reexamining the Lyman-Birge-Hopfield band of N2

Motivated by fundamental molecular physics and by atmospheric and planetary sciences, the valence excitations of N${}_{2}$ gas have seen several decades of intensive study, especially by electron-energy-loss spectroscopy (EELS). It was consequently surprising when a comparison of nonresonant inelastic x-ray scattering (NIXS) and nonresonant EELS found strong evidence for violations of the first Born approximation for EELS when leaving the dipole scattering limit. Here we reassess the relative strengths of the constituent resonances of the lowest-energy excitations of N${}_{2}$, encompassed by the so-called Lyman-Birge-Hopfield (LBH) band, expanding on the prior, qualitative interpretation of the NIXS results for N${}_{2}$ by both quantifying the generalized oscillator strength of the lowest-energy excitations and also presenting a time-dependent density functional theory (TDDFT) calculation of the $q$ dependence of the entire low-energy electronic excitation spectrum. At high $q$, we find that the LBH band has an unexpectedly large contribution from the octupolar $w{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Delta}}_{u}$ resonance exactly in the regime where theory and EELS experiment for the presumed-dominant $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ resonance have previously had substantial disagreement, and also where the EELS results must now be expected to show violations of the Born approximation. After correcting for this contamination, the $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ generalized oscillator strength from the NIXS results is in good agreement with prior theory. The NIXS spectra, over their entire $q$ range, also find satisfactory agreement with the TDDFT calculations for both bound and continuum excitations.