Multiplet Calculations Research Articles

Nano‐Size Effects on Decay Dynamics of Photo‐Excited Polarons in CeO2

AbstractThe study of polaron dynamics in complex materials has garnered significant attention owing to its implications for various technological applications, including catalysis, solid‐state devices, and energy storage. This paper investigates the photo‐excited electron and hole polaron dynamics in cerium dioxide (CeO2) using time‐resolved X‐ray absorption spectroscopy, with an emphasis on the nano‐size effect. Additionally, density functional theory and multiplet calculations have been utilized to reveal the photo‐excited polaron dynamics in CeO2 single crystal (SC) and nanocrystal (NC). The electron polaron is observed to decay into a deep trap site with a short duration of ≈5 ps, while electrons in the traps stay for more than 1400 ps. The most significant observation is the behavior of holes in NC, which tends to stay longer (≈150 ps) compared to SC (<10 ps) suggesting hole existence more at the surface than at bulk. The fast dissociation of the electron polarons the prolonged lifetime of the electrons above the Fermi level and the enhanced hole lifetime at the surface are proposed to be among the various factors that influence the high reactivity of CeO2.

X-ray spectroscopic investigation of crystal fields in Ce2Rh1−xIrxIn8 heavy fermions

The higher dimensionality in the crystal fields of the Ce2MIn8 (M=Rh,Ir) compounds and its interplay with hybridization and disorder are key ingredients to understand the complex phase diagrams by this family, which have been explored extensively by macroscopic techniques. Here, we present an investigation of the crystal-electric field schemes of Ce2Rh1−xIrxIn8 using x-ray absorption spectroscopy. Our full multiplet calculations for the 4f1 configuration of Ce3+ to describe the temperature-dependent linear dichroism in Ce2MIn8 are consistent with a Γ71=1−α2·|∓32〉−|α|·|±52〉 ground state containing a predominant |±3/2〉 contribution that increases further with x. This enhancement is believed to favor superconductivity in Ce-based heavy fermion materials, observed in previous results in the CeMIn5 family. Our recent observations shed light on the unexpected emergence of the ambient-pressure superconducting dome in the center of the composition phase diagram and its subsequent suppression on the Ir-rich side due to the early onset of fluctuations associated with the structurally more disordered state, inferred from previous neutron magnetic diffraction experiments. Published by the American Physical Society 2024

A New High-Valent Fe Redox Couple in Intercalation Electrodes

The overwhelming majority of layered oxide cathode materials are based on the redox activity of expensive and scarce transition metals like Co and Ni. While the Fe-redox based material LiFePO4 has become increasingly attractive due to its low cost, its low gravimetric energy density and relatively low operating voltage limit its use cases. A high-voltage Fe-based layered oxide cathode would provide high energy density utilizing the redox-activity of the most abundant transition metal in Earth’s crust, but such a material that provides stable and reversible electrochemical performance remains elusive. Indeed, high-voltage Fe-redox in oxides is plagued by cation disorder and oxygen dimerization, which leads to capacity fading and large voltage hysteresis (> 1 V).[1]In contrast, the layered oxide cathode Li4FeSbO6 (equivalently, Li[Li1/3Fe1/3Sb1/3]O2, abbreviated LFSO) exhibits <0.2 V of hysteresis, and a discharge plateau at 4.2 V versus Li/Li+ with two-electron capacity.[2] Both the exceptional electrochemical reversibility of this material and its phase separating nature upon (de)intercalation raise questions about the origin of these properties that are unusual for layered Fe oxide cathodes. In this work, we will discuss our efforts to probe the electronic structure of LFSO with Fe L–edge x–ray absorption (XAS) and 57Fe Mössbauer spectroscopy, as well as O K–edge resonant inelastic x–ray scattering spectroscopy (RIXS). The combination of these element-specific and valence-state sensitive techniques, in conjunction with charge-transfer multiplet and density functional theory calculations, allows us to reveal the electronic structure changes at Fe and O as a function of state of charge for the first time. Correlating these electronic structure changes with synchrotron diffraction measurements, we reveal a unique redox compensation mechanism that readily rationalizes the exceptional electrochemical reversibility, unlocking a new direction for high-voltage, Fe-based redox systems.

Origin of Magnetism in a Supposedly Nonmagnetic Osmium Oxide.

A supposedly nonmagnetic 5d^{1} double perovskite oxide is investigated by a combination of spectroscopic and theoretical methods, namely, resonant inelastic x-ray scattering, x-ray absorption spectroscopy, magnetic circular dichroism, and multiplet ligand-field calculations. We found that the large spin-orbit coupling admixes the 5d t_{2g} and e_{g} orbitals, covalency raises the 5d population well above the nominal value, and the local symmetry is lower than O_{h}. The obtained electronic interactions account for the finite magnetic moment of Os in this compound and, in general, of 5d^{1} ions. Our results provide direct evidence of elusive Jahn-Teller distortions, hinting at a strong electron-lattice coupling.

Valence-state mixing and reduced magnetic moment in Fe3−δGeTe2 single crystals with varying Fe content probed by x-ray spectroscopy

We present a spectroscopic study of the magnetic properties of Fe3−δGeTe2 single crystals with varying Fe content, achieved by tuning the stoichiometry of the crystals. We carried out x-ray absorption spectroscopy and analyzed the x-ray circular magnetic dichroism spectra using the sum rules, to determine the orbital and spin magnetic moments of the materials. We find a clear reduction of the spin and orbital magnetic moment with increasing Fe deficiency. Magnetic susceptibility measurements show that the reduction in magnetization is accompanied by a reduced Curie temperature. Multiplet calculations reveal that the Fe2+ state increasingly mixes with a higher valence state when the Fe deficiency is increased. This effect is correlated with the weakening of the magnetic moment. As single crystals are the base material for exfoliation processes, our results are relevant for the assembly of 2D magnetic heterostructures.

Using Iron L-Edge and Nitrogen K-Edge X-ray Absorption Spectroscopy to Improve the Understanding of the Electronic Structure of Iron Carbene Complexes.

Iron-centered N-heterocyclic carbene compounds have attracted much attention in recent years due to their long-lived excited states with charge transfer (CT) character. Understanding the orbital interactions between the metal and ligand orbitals is of great importance for the rational tuning of the transition metal compound properties, e.g., for future photovoltaic and photocatalytic applications. Here, we investigate a series of iron-centered N-heterocyclic carbene complexes with +2, + 3, and +4 oxidation states of the central iron ion using iron L-edge and nitrogen K-edge X-ray absorption spectroscopy (XAS). The experimental Fe L-edge XAS data were simulated and interpreted through restricted-active space (RAS) and multiplet calculations. The experimental N K-edge XAS is simulated and compared with time-dependent density functional theory (TDDFT) calculations. Through the combination of the complementary Fe L-edge and N K-edge XAS, direct probing of the complex interplay of the metal and ligand character orbitals was possible. The σ-donating and π-accepting capabilities of different ligands are compared, evaluated, and discussed. The results show how X-ray spectroscopy, together with advanced modeling, can be a powerful tool for understanding the complex interplay of metal and ligand.

Differences in the Ti4+/Ti3+ Redox Reactions between Li4Ti5O12 and LiTi2(PO4)3 Observed By Soft X-Ray Spectroscopy

Clarification of the redox reaction in electrode materials for Li-ion batteries is essential to obtain strategies to improve the performances such as charge-discharge capacity, voltage and cyclability. We focus on the difference in voltage, i.e., redox potential between Li4Ti5O12 (LTO) and LiTi2(PO4)3 (LTP). Spinel-type LTO with a redox potential around 1.5 V vs Li/Li+ is one of the anode materials [1], while the main redox potential of LTP (NASICON-type structure) is around 2.4 V vs Li/Li+ [2]. Although the difference in redox potential is as large as ~0.9 V, it has been thought to be that Ti4+/Ti3+ redox couple is identical for both LTO and LTP. Here, we demonstrate the electronic-structure analysis of LTO and LTP by using soft X-ray absorption spectroscopy (XAS) and soft X-ray photoemission spectroscopy (XPS). Operando Ti L 2,3-edge XAS by use of an all-solid-state cell [3,4] successfully revealed reversible Ti4+/Ti3+ redox reactions by discharge/charge for both materials, but the XAS line shapes were different. By analyzing the spectra using multiplet calculation [5], differences in the crystal-field splitting for the TiO6 octahedron and O 2p -> Ti 3d charge-transfer (CT) effect were found. The different CT effect was also confirmed by Ti 2p-3d resonant XPS measurements for the initial-state LTO and LTP samples. Moreover, the difference in redox potential is mostly explained by the energy levels of the pre-edge structures in the O K-edge XAS calibrated with the O 1s XPS spectra. In the presentation, the understandings of the spectroscopic results will be discussed in detail.

Theoretical Analysis of Anomalous Emission of Eu2+ in Crystals By First-Principles Calculation

The 5d-4f transition energies of lanthanides are very versatile, especially the 4f65d1-4f75d0 transition energy of Eu2+ has high luminescence efficiency and is used in various luminescent materials such as phosphors like SrxCa1-xAlSiN3: Eu2+, scintillators, and solid-state lasers, etc. However, there are materials that do not undergo pure 5d-4f transitions, showing the so-called anomalous luminescence instead. The anomalous luminescence is caused by the formation of excitons due to the overlap of the 5d level of Eu2+ with the conduction band and the transition of electrons from the conduction band to the 4f level, resulting in a shift to a lower energy than the general 5d-4f transition energy. A more detailed analysis of this phenomenon is important for the development of novel luminescent materials using Eu2+.In this study, we aimed to theoretically analyze the anomalous luminescence based on first-principles electronic structure calculations. The model clusters of Eu2+-doped crystals consisting of Eu2+ at the substitution site and the surrounding ions were created. Then molecular orbital calculations were performed by the relativistic discrete-variational Xα (DV-Xα) method and subsequently multiplet calculations were performed by the relativistic discrete-variational multi-electron (DVME) method. These first-principles calculations were carried out for Eu2+-doped crystals that show anomalous luminescence and those that do not show anomalous luminescence, and the electronic states of these materials were compared in detail.

Core level excitation spectra of La and Mn ions in LaMnO3

Manganese-based perovskite is popular for research on ferromagnetic materials, and its spectroscopic studies are essential for understanding its electronic structure, dielectric, electrical, and magnetic properties. In this paper, the M-edge spectra of La ions and the M-edge, L-edge, and K-edge spectra of Mn ions in LaMnO3 are calculated by considering both the free-ion multiplet calculation and the crystal field effects. We analyze spectral shapes, identify peak origins, and estimate the oxidation states of La and Mn ions in LaMnO3 theoretically. It is concluded that La ions in LaMnO3 predominantly exist in the trivalent state, while Mn ions exist primarily in the trivalent state with a minor presence of tetravalent ions. Furthermore, the calculated spectra are in better conformity with the experimental spectra when the proportion of Mn3+ is 90% and Mn4+ is 10%. This article enhances our comprehension of the oxidation states of La and Mn within the crystal and also provides a valuable guidance for spectroscopic investigations of other manganates.

Two-dimensional Kβ-Kα fluorescence spectrum by nonlinear resonant inelastic X-ray scattering

High sensitivity of the Kβ fluorescence spectrum to electronic state is widely used to investigate spin and oxidation state of first-row transition-metal compounds. However, the complex electronic structure results in overlapping spectral features, and the interpretation may be hampered by ambiguity in resolving the spectrum into components representing different electronic states. Here, we tackle this difficulty with a nonlinear resonant inelastic X-ray scattering (RIXS) scheme, where we leverage sequential two-photon absorption to realize an inverse process of the Kβ emission, and measure the successive Kα emission. The nonlinear RIXS reveals two-dimensional (2D) Kβ-Kα fluorescence spectrum of copper metal, leading to better understanding of the spectral feature. We isolate 3d-related satellite peaks in the 2D spectrum, and find good agreement with our multiplet ligand field calculation. Our work not only advances the fluorescence spectroscopy, but opens the door to extend RIXS into the nonlinear regime.

Precise dd excitations and commensurate intersite Coulomb interactions in the dissimilar cuprates YBa2Cu3O7–y and La2–xSrxCuO4

Using high-resolution extreme ultraviolet resonant inelastic X-ray scattering (EUVRIXS) spectroscopy at Cu M-edge, we observed the doping dependent spectral shifts of inter-orbital (dd) excitations of YBa_2Cu_3O_(7-x) and La_(2-x)Sr_xCuO_4. With increasing hole doping level from undoped to optimally doped superconducting compositions, the leading edge of dd excitations is found to shift towards lower energy loss in a roughly linear trend that is irrespective to the cuprate species. The magnitude of energy shift can be explained by including a 0.15 eV Coulomb attraction between Cu 3d_(x^2-y^2) electrons and the doped holes on the surrounding oxygens in the atomic multiplet calculations. The consistent energy shift between distinct cuprate families suggests that this inter-site Coulomb interaction energy scale is relatively material-independent, and provides an important reference point for understanding charge density wave phenomena in the cuprate phase diagram.

Evolution of orbital excitations from insulating to superconducting MgTi2O4 films

Spinel oxides are well-known functional materials but rarely show superconductivity. Recently, emergent superconductivity was discovered in ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$, which is attributed to the increase of electron doping and the suppression of orbital order. Here, we utilized Ti $L$-edge resonant inelastic x-ray scattering to study the orbital excitations in superconducting (SC) and insulating ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$ films. We find that the spectral weight of orbital excitations is enhanced and the energy of ${t}_{2g}$ intraband excitation is softened in the SC film compared to the insulating one, suggesting higher electron doping and a suppressed orbital order gap in the SC sample. These observations were further supported by our multiplet calculations using the minimal two-site model. Our results provide spectroscopic evidence for the competition between orbital order and superconductivity in ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$ and shed light on searching for novel superconductors in spinel oxides.

Fitting Multiplet Simulations to L-Edge XAS Spectra of Transition-Metal Complexes Using an Adaptive Grid Algorithm.

A new methodology based on an adaptive grid algorithm followed by an analysis of the ground state from the fit parameters is presented to analyze and interpret experimental XAS L2,3-edge data. The fitting method is tested first in a series of multiplet calculations for d0-d7 systems and for which the solution is known. In most cases, the algorithm is able to find the solution, except for a mixed-spin Co2+ Oh complex, where it instead revealed a correlation between the crystal field and the electron repulsion parameters near spin-crossover transition points. Furthermore, the results for the fitting of previously published experimental data sets on CaO, CaF2, MnO, LiMnO2, and Mn2O3 are presented and their solution discussed. The presented methodology has allowed the evaluation of the Jahn-Teller distortion in LiMnO2, which is consistent with the observed implications in the development of batteries, which use this material. Moreover, a follow-up analysis of the ground state in Mn2O3 has demonstrated an unusual ground state for the highly distorted site which would be impossible to optimize in a perfect octahedral environment. Ultimately, the presented methodology can be used in the analysis of X-ray absorption spectroscopy data measured at the L2,3-edge for a large number of materials and molecular complexes of first-row transition metals and can be expanded to the analysis of other X-ray spectroscopic data in future studies.

Theory of circular dichroism in angle-resolved resonant photoemission from magnetic surfaces

A theoretical method is presented for angle-resolved photoemission at the transition metal $L$-edge resonance. It combines atomic multiplet calculations for the second-order resonant photoemission amplitude on the core-level site and a single scattering calculation of the photoelectron final state. The theory is applied to a magnetized Ni(111) surface excited with circularly polarized x rays at the Ni ${L}_{2,3}$-edge resonance with a focus on the circular dichroism (CD) signal. Good agreement with available experimental data is achieved. It is shown that the CD pattern is composed of a slowly varying magnetic signal induced by the atomic resonant process and a signal of fast angular modulations that are due to the interference of primary and scattered waves, known as the Daimon effect. The two types of CD signals are found to be nearly additive. At the Ni ${L}_{2}$-edge resonance, the angular dependence of the magnetic CD is well described by a simple expression known from x-ray magnetic CD. At the ${L}_{3}$ edge, however, the angular dependence is more complex and shows a pronounced final state multiplet dependence. With the present theory, it becomes possible to extract element- and site-selective magnetic information of surfaces from the CD in angle-resolved resonant photoemission data.

Erbium and thulium on MgO(100)/Ag(100) as candidates for single atom qubits

Lanthanide atoms on surfaces are prospective platforms for realizing atomic-scale quantum logic units. Here, the authors combine scanning tunneling microscopy, x-ray magnetic circular dichroism, density functional theory, and atomic multiplet calculations to identify the quantum level structure of erbium and thulium atoms on MgO(100)/Ag(100), and to estimate their performance as spin qubits. Their analysis reveals that both atoms have a ground state that is suitable to perform efficient quantum coherent operations.

EELS post-processing and multiplet calculation for Ce4+, Ce3+ valency determination in nanomaterials

EELS post-processing and multiplet calculation for Ce4+, Ce3+ valency determination in nanomaterials

Charge transfer effects and O2- vacancies in pure CuO nanofibers and enriched with 3.0% Mn

This research shows the relationship between oxygen vacancies and the charge transfer effects generated from the synthesis process using the electrospinning method in an uncontrolled atmosphere for copper oxide nanofibers (CuO NFs) pure and enriched with 3.0% Mn. The thermal measurements obtained through TGA-DSC allowed finding the calcination temperature and obtaining the tenorite structure with monoclinic phase at 700 °C. In addition, the combination of x-ray photoelectron spectrum (XPS) with the multiplet calculation using Cowan's codes suggests that the charge transfer effects play an important role in CuO NFs. After XPS analysis was possible to determine the presence of oxygen vacancies (Vo) and oxygen adsorbed (Ao) in the XPS O 1s region placed at 532 eV. The synthesized materials show a mixture of oxides, and a single oxidation state for Cu3+ in a superlattice according to the selected area electron diffraction (SAED) analysis. Finally, the CuO NFs enriched with 3.0% show the presence of Mn4+ and Mn3+ according to the XPS Mn 2p region analysis.

Spin excitations of individual magnetic dopants in an ionic thin film

Individual magnetic transition metal dopants in a solid host usually exhibit relatively small spin excitation energies of a few meV. Using scanning tunneling microscopy and inelastic electron tunneling spectroscopy (IETS) techniques, we have observed a high spin excitation energy around 36 meV for an individual Co substitutional dopant in ultrathin NaCl films. In contrast, the Cr dopant in the NaCl film shows much lower spin excitation energy around 2.5 meV. Electronic multiplet calculations combined with first-principles calculations confirm the spin excitation induced IETS, and quantitatively reveal the out-of-plane magnetic anisotropies for both Co and Cr. They also allow reproducing the experimentally observed redshift in the spin excitations of Co dimers and ascribe it to a charge and geometry redistribution.

Dispersionless orbital excitations in (Li,Fe)OHFeSe superconductors

The superconducting critical temperature Tc of intercalated iron-selenide superconductor (Li,Fe)OHFeSe (FeSe11111) can be increased to 42 from 8 K of bulk FeSe. It shows remarkably similar electronic properties as the high-Tc monolayer FeSe and provides a bulk counterpart to investigate the origin of enhanced superconductivity. Unraveling the nature of excitations is crucial for understanding the pairing mechanism in high-Tc iron selenides. Here we use resonant inelastic x-ray scattering (RIXS) to investigate the excitations in FeSe11111. Our high-quality data exhibit several Raman-like excitations, which are dispersionless and isotropic in momentum transfer in both superconducting 28 K and 42 K samples. Using atomic multiplet calculations, we assign the low-energy ~0.3 and 0.7 eV Raman peaks as local eg − eg and eg − t2g orbital excitations. The intensity of these two features decreases with increasing temperature, suggesting a dominating contribution of the orbital fluctuations. Our results highlight the importance of the orbital degree of freedom for high-Tc iron selenides.

Spin-orbit coupling and crystal-field splitting in Ti-doped Ca2RuO4 studied by ellipsometry

In Ca2RuO4, the competition of spin-orbit coupling $\zeta$ and tetragonal crystal field splitting $\Delta_{CF}$ has been discussed controversially for many years. The orbital occupation depends on $\Delta_{CF}/\zeta$, which allows us to address this ratio via the optical spectral weights of the lowest intersite Mott-Hubbard excitations. We study the optical conductivity of Ca$_2$Ru$_{0.99}$Ti$_{0.01}$O$_4$ in the range of 0.75 - 5 eV by ellipsometry, using the large single crystals that can be grown for small Ti concentrations. Based on a local multiplet calculation, our analysis results in $2.4 \leq \Delta_{CF}/\zeta \leq 4$ at 15 K. The dominant crystal field yields a ground state close to xy orbital order but spin-orbit coupling is essential for a quantitative description of the properties. Furthermore, we observe a pronounced decrease of $\Delta_{CF}$ with increasing temperature, as expected based on the reduction of octahedral distortions.