Atomic Multiplets Research Articles

Extracting the crystal electric field levels of Ce-4f1 states in CeB6 by atomic multiplet simulations

The crystal electric field (CEF) is vital in defining the low-energy electronic structure of lanthanide compound, and thus very essential in understanding the many-body physics of the strongly correlated 4 f electrons. Many efforts have been made to determine the low-energy electronic structure of the intrinsically correlated material CeB6 and its derived compounds. In this paper, we performed atomic multiplet (AM) simulations on the Ce-4f1 states in CeB6 and directly fitted them with previously reported resonant inelastic x-ray scattering spectroscopy (RIXS). The simulation results suggest that the discrepancy of excitations energies extracted from Raman spectroscopy and RIXS is a result of intrinsic varied crystal electric field strength, which can be reconciled by considering the enhanced CEF by eliminating the insulating scenario.

Mott Quantum Critical Points at Finite Doping.

We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded" so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin-the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling-is much more general. A strong analogy with cuprate superconductors is traced.

Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group.

In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin-orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.

AbInitio Multiplet-Plus-Cumulant Approach for Correlation Effects in X-Ray Photoelectron Spectroscopy.

The treatment of electronic correlations in open-shell systems is among the most challenging problems of condensed matter theory. Current approximations are only partly successful. Ligand-field multiplet theory has been widely successful in describing intra-atomic correlation effects in x-ray spectra, but typically ignores itinerant states. The cumulant expansion for the one-electron Green's function has been successful in describing shake-up effects but ignores atomic multiplets. More complete methods, such as dynamic mean-field theory can be computationally demanding. Here, we show that separating the dynamic Coulomb interactions into local and longer-range parts with abinitio parameters yields a combined multiplet-plus-cumulant approach that accounts for both local atomic multiplets and satellite excitations. The approach is illustrated in transition metal oxides and explains the multiplet peaks, charge-transfer satellites, and distributed background features observed in XPS experiment.

Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr2RuO4

We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diagonal Green's functions. For the archetypal correlated Hund's metal Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related to the van Hove singularity and the high-energy atomic multiplet excitations can be faithfully resolved. In particular, we show that while the spin-orbit coupling has only minor effects on the orbital-diagonal one-particle spectral functions, it has a more profound impact on the low-energy spin and orbital response functions.

Spectroscopic Determination of Key Energy Scales for the Base Hamiltonian of Chromium Trihalides

The van der Waals (vdW) chromium trihalides (CrX3) exhibit field-tunable, two-dimensional magnetic orders that vary with the halogen species and the number of layers. Their magnetic ground states with proximity in energies are sensitive to the degree of ligand-metal (p-d) hybridization and relevant modulations in the Cr d-orbital interactions. We use soft X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectroscopy at Cr L-edge along with the atomic multiplet simulations to determine the key energy scales such as the crystal field 10 Dq and interorbital Coulomb interactions under different ligand metal charge transfer (LMCT) in CrX3 (X= Cl, Br, and I). Through this systematic study, we show that our approach compared to the literature has yielded a set of more reliably determined parameters for establishing a base Hamiltonian for CrX3.

Hard x-ray photoemission spectroscopy of GdNi and HoNi

We study the electronic structure of GdNi and HoNi, which are magnetic materials with a Curie temperature ${T}_{c}=69$ and ${T}_{c}=36\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, respectively. These materials are useful for magnetic refrigerator applications at low temperature as they exhibit a large magnetocaloric effect near ${T}_{c}$. We have used hard x-ray photoemission spectroscopy (HAXPES) to investigate the core-level and valence-band electronic states of GdNi and HoNi. HAXPES measurements of the Gd and Ho $3d, 4d, 4p, 5p$, and $4s$ core-level spectra have been compared with atomic multiplet calculations of ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Ho}}^{3+}$ ionic configurations. The good match between the experimental and calculated spectra clarify the important role of spin-orbit coupling, as well as Coulomb and exchange interactions in the intermediate-coupling scheme. The core-level spectra also show plasmons in addition to the atomic multiplets. The Gd and Ho $4s$ spectra show clear evidence of exchange splitting. The Ni $2p$ and $3s$ spectra of GdNi and HoNi show a correlation satellite at a binding energy of 7 eV above their main peaks. The Ni $2p$ and Ni $3s$ spectra could be reproduced using charge transfer multiplet calculations. Valence-band HAXPES of GdNi and HoNi shows that the Gd $4f$ and Ho $4f$ features are also consistent with atomic multiplets and occur at high binding energies away from the Fermi level. The Ni $3d$ density of states are spread from the Fermi level to about 3 eV binding energy. The results indicate a partially filled Ni $3d$ band and show that the charge transfer model is not valid for describing the electronic structure of GdNi and HoNi.

Ab initio calculation of the electron capture spectrum of 163Ho: Auger–Meitner decay into continuum states

Determining the electron neutrino mass by electron capture in 163Ho relies on an accurate understanding of the differential electron capture nuclear decay rate as a function of the distribution of the total decay energy between the neutrino and electronic excitations. The resulting spectrum is dominated by resonances due to local atomic multiplet states with core holes. Coulomb scattering between electrons couples the discrete atomic states, via Auger–Meitner decay, to final states with free electrons. The atomic multiplets are above the auto-ionisation energy, such that the delta functions representing these discrete levels turn into a superposition of Lorentzian, Mahan- and Fano-like line-shapes. We present an ab initio method to calculate nuclear decay modifications due to such processes. It includes states with multiple correlated holes in local atomic orbitals interacting with unbound Auger–Meitner electrons. A strong energy-dependent, asymmetric broadening of the resonances in good agreement with recent experiments is found. We present a detailed analysis of the mechanisms determining the final spectral line-shape and discuss both the Fano interference between different resonances, as well as the energy dependence of the Auger–Meitner Coulomb matrix elements. The latter mechanism is shown to be the dominant channel responsible for the asymmetric line-shape of the resonances in the electron capture spectrum of 163Ho.

Molecular Beam Epitaxy of Two-Dimensional Vanadium-Molybdenum Diselenide Alloys.

Two-dimensional (2D) alloys represent a versatile platform that extends the properties of atomically thin transition-metal dichalcogenides. Here, using molecular beam epitaxy, we investigate the growth of 2D vanadium-molybdenum diselenide alloys, VxMo1-xSe2, on highly oriented pyrolytic graphite and unveil their structural, chemical, and electronic integrities via measurements by scanning tunneling microscopy/spectroscopy, synchrotron X-ray photoemission, and X-ray absorption spectroscopy (XAS). Essentially, we found a critical value of x = ∼0.44, below which phase separation occurs and above which a homogeneous metallic phase is favored. Another observation is an effective increase in the density of mirror twin boundaries of constituting MoSe2 in the low V concentration regime (x ≤ 0.05). Density functional theory calculations support our experimental results on the thermal stability of 2D VxMo1-xSe2 alloys and suggest an H phase of the homogeneous alloys with alternating parallel V and Mo strips randomly in-plane stacked. Element-specific XAS of the 2D alloys, which clearly indicates quenched atomic multiplets similar to the case of 2H-VSe2, provides strong evidence for the H phase of the 2D alloys. This work provides a comprehensive understanding of the thermal stability, chemical state, and electronic structure of 2D VxMo1-xSe2 alloys, useful for the future design of 2D electronic devices.

Electronic structure investigation of GdNi using x-ray absorption, magnetic circular dichroism, and hard x-ray photoemission spectroscopy

GdNi is a ferrimagnetic material with a Curie temperature Tc = 69 K which exhibits a large magnetocaloric effect, making it useful for magnetic refrigerator applications. We investigate the electronic structure of GdNi by carrying out x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) at T = 25 K in the ferrimagnetic phase. We analyze the Gd M$_{4,5}$-edge ($3d$ - $4f$) and Ni L$_{2,3}$-edge ($2p$ - $3d$) spectra using atomic multiplet and cluster model calculations, respectively. The atomic multiplet calculation for Gd M$_{4,5}$-edge XAS indicates that Gd is trivalent in GdNi, consistent with localized $4f$ states. On the other hand, a model cluster calculation for Ni L$_{2,3}$-edge XAS shows that Ni is effectively divalent in GdNi and strongly hybridized with nearest neighbour Gd states, resulting in a $d$-electron count of 8.57. The Gd M$_{4,5}$-edge XMCD spectrum is consistent with a ground state configuration of S = 7/2 and L=0. The Ni L$_{2,3}$-edge XMCD results indicate that the antiferromagnetically aligned Ni moments exhibit a small but finite magnetic moment ( $m_{tot}$ $\sim$ 0.12 $\mu_B$ ) with the ratio $m_{o}/m_{s}$ $\sim$ 0.11. Valence band hard x-ray photoemission spectroscopy shows Ni $3d$ features at the Fermi level, confirming a partially filled $3d$ band, while the Gd $4f$ states are at high binding energies away from the Fermi level. The results indicate that the Ni $3d$ band is not fully occupied and contradicts the charge-transfer model for rare-earth based alloys. The obtained electronic parameters indicate that GdNi is a strongly correlated charge transfer metal with the Ni on-site Coulomb energy being much larger than the effective charge-transfer energy between the Ni $3d$ and Gd $4f$ states.

Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet-Triplet Energy Gaps.

The mixed-reference spin-flip (MRSF) time-dependent density functional theory (TDDFT) method eliminates the notorious spin contamination of SF-TDDFT, thus enabling identification of states of proper spin-symmetry for automatic geometry optimization and molecular dynamics simulations. Here, we analyze and optimize the MRSF-TDDFT in the calculations of the vertical excitation energies (VEEs) and the singlet-triplet (ST) gaps. The dependence of the obtained VEEs and ST gaps on the intrinsic parameters of the MRSF-TDDFT method is investigated, and prescriptions for the proper use of the method are formulated. For VEEs, MRSF-TDDFT displays similar or better accuracy than SF-TDDFT (ca. 0.5 eV), while considerably outperforming the LR-TDDFT for the ST gaps. As a result, a new functional of STG1X (dubbed here), especially for ST gaps is suggested on the basis of splitting between the components of the atomic multiplets.

Direct observation of spin-orbit-induced 3d hybridization via resonant inelastic extreme ultraviolet scattering on an edge-sharing cuprate

Author(s): Malvestuto, M; Caretta, A; Casarin, B; Ciprian, R; Dell'Angela, M; Laterza, S; Chuang, YD; Wurth, W; Revcolevschi, A; Wray, LA; Parmigiani, F | Abstract: Using high resolution resonant inelastic x-ray scattering measurements, we have observed that the orbital excitations of the quasi-1D spin chain compound CuGeO3 has nontrivial and noticeable orbital mixing effects from 3d valence spin-orbit coupling. In particular, the SOC leads to a significant correction of dz2 state, which has a direct interplay with the low energy physics of cuprates. Guided by atomic multiplet based modeling, our results strongly support a 3d spin-orbit mixing scenario and explore in detail the nature of these excitations.

Charge States of Cations in Lithium–Nickel Phosphates LiNiPO4 Doped with Manganese and Cobalt

Using Ni, Mn, and Co L2,3-edge soft X-ray absorption spectra supported by calculations of atomic multiplets with allowance for the crystal field and charge transfer, the charge states of cations in doped phosphates LiNiPO4, LiNi0.9Co0.1PO4, and LiNi0.9Mn0.1PO4 are determined. It is established that nickel, manganese, and cobalt ions are in the divalent high-spin state and have an octahedral oxygen environment. Oxygen K-edge X-ray absorption spectra showed the absence of impurity states in the energy gap of manganese- or cobalt-doped lithium nickel phosphates.

Anomalous orbital structure in two-dimensional titanium dichalcogenides

Generally, lattice distortions play a key role in determining the electronic ground states of materials. Although it is well known that trigonal distortions are generic to most two dimensional transition metal dichalcogenides, the impact of this structural distortion on the electronic structure and topological properties has not been understood conclusively. Here, by using a combination of polarization dependent X-ray absorption spectroscopy (XAS), X-ray photoelectron spectroscopy (XPS) and atomic multiplet cluster calculations, we have investigated the electronic structure of titanium dichalcogenides TiX2 (X = S, Se, Te), where the magnitude of the trigonal distortion increase monotonically from S to Se and Te. Our results reveal the presence of an anomalously large crystal field splitting. This unusual kind of crystal field splitting is likely responsible for the unconventional electronic structure of TiX2 compounds and ultimately controls the degree of the electronic phase protection. Our findings also indicate the drawback of the distorted crystal field picture in explaining the observed electronic ground state and emphasize the key importance of trigonal symmetry, metal-ligand hybridization and electron-electron correlations in defining the electronic structures at the Fermi energy.

Ab initio interaction potentials of the Ba, Ba+ complexes with Ar, Kr, and Xe in the lowest excited states.

The complexes of the Ba atom and Ba+ cation with the rare gas atoms Ar, Kr, and Xe in the states associated with the 6s → 5d, 6p excitations are investigated by means of the multireference configuration interaction techniques. Scalar relativistic potentials are obtained by the complete basis limit extrapolation through the sequence of aug-cc-pwCVnZ basis sets with the cardinal numbers n = Q, T, 5, combined with the suitable effective core potentials and benchmarked against the coupled cluster with singles, doubles, and non-iterative triples calculations and the literature data available for selected electronic states. Spin-orbit coupling is taken into account by means of the state-interacting multireference configuration interaction calculations performed for the Breit-Pauli spin-orbit Hamiltonian. The results show weak spin-orbit coupling between the states belonging to distinct atomic multiplets. General trends in the interaction strength and long-range anisotropy along the rare gas series are discussed. Vibronic spectra of the Ba and Ba+ complexes in the vicinity of the 1S → 1P° and 2S → 2P° atomic transitions and diffusion cross sections of the Ba(1S0, 3DJ) atom in high-temperature rare gases are calculated. Comparison with available experimental data shows that multireference calculations tend to underestimate the interaction strength for excited complexes.

Electronic properties of ultra-thin YCrO3 films

We report on the heteroepitaxial stabilization of YCrO3 ultra-thin films on LSAT (001) substrate. Using a combination of resonant X-ray absorption spectroscopy (XAS) and atomic multiplet cluster calculation, the electronic structure of YCrO3 thin film was investigated. Polarization dependent Cr L3,2 edge XAS measurements reveal the presence of x-ray linear dichroism spectrum uncharacteristic of a 3d3 electronic system in an octahedral crystal field. Atomic multiplet calculation demonstrates the critical importance of charge transfer energy, coulomb correlation strength, and hopping interaction in realizing this dichroism spectrum.

Fingerprints of spin-orbital polarons and of their disorder in the photoemission spectra of doped Mott insulators with orbital degeneracy

We explore the effects of disordered charged defects on the electronic excitations observed in the photoemission spectra of doped transition metal oxides in the Mott insulating regime by the example of the $R_{1-x}$Ca$_x$VO$_3$ perovskites, where $R=$La,$\dots$,Lu. A fundamental characteristic of these vanadium $d^2$ compounds with partly filled $t_{2g}$ valence orbitals is the persistence of spin and orbital order up to high doping, in contrast to the loss of magnetic order in high-$T_c$ cuprates at low defect concentration. We demonstrate that the disordered electronic structure of doped Mott-Hubbard insulators can be obtained with high precision within the unrestricted Hartree-Fock approximation. In particular: (i) the atomic multiplet excitations in the inverse photoemission spectra and the various defect-related states and satellites are well reproduced, (ii) a robust Mott gap survives up to large doping, and (iii) we show that the defect states inside the Mott gap develop a soft gap at the Fermi energy. The soft defect states gap can be characterized by a shape and a scale parameter extracted from a Weibull statistical sampling of the density of states near the chemical potential. We demonstrate that charge defects trigger small spin-orbital polarons, with their internal kinetic energy responsible for the opening of the soft defect states gap. The small size of spin-orbital polarons is inferred by an analysis of the inverse participation ratio which explains the origin of the robustness of spin and orbital order. Using realistic parameters for La$_{1-x}$Ca$_x$VO$_3$, we show that its soft gap is well reproduced as well as the marginal doping dependence of the position of the chemical potential relative to the center of the lower Hubbard band.

Hallmarks of Hunds coupling in the Mott insulator Ca2RuO4

A paradigmatic case of multi-band Mott physics including spin-orbit and Hund’s coupling is realized in Ca2RuO4. Progress in understanding the nature of this Mott insulating phase has been impeded by the lack of knowledge about the low-energy electronic structure. Here we provide—using angle-resolved photoemission electron spectroscopy—the band structure of the paramagnetic insulating phase of Ca2RuO4 and show how it features several distinct energy scales. Comparison to a simple analysis of atomic multiplets provides a quantitative estimate of the Hund’s coupling J=0.4 eV. Furthermore, the experimental spectra are in good agreement with electronic structure calculations performed with Dynamical Mean-Field Theory. The crystal field stabilization of the dxy orbital due to c-axis contraction is shown to be essential to explain the insulating phase. These results underscore the importance of multi-band physics, Coulomb interaction and Hund’s coupling that together generate the Mott insulating state of Ca2RuO4.

Field-induced exciton condensation in LaCoO3

Motivated by recent observation of magnetic field induced transition in LaCoO3 we study the effect of external field in systems close to instabilities towards spin-state ordering and exciton condensation. We show that, while in both cases the transition can be induced by an external field, temperature dependencies of the critical field have opposite slopes. Based on this result we argue that the experimental observations select the exciton condensation scenario. We show that such condensation is possible due to high mobility of the intermediate spin excitations. The estimated width of the corresponding dispersion is large enough to overrule the order of atomic multiplets and to make the intermediate spin excitation propagating with a specific wave vector the lowest excitation of the system.

Racah Materials: Role of Atomic Multiplets and Intermediate Valence in f-Electron Systems

ABSTRACT The electronic structure of PuB6, an actinide analog of SmB6 , was investigated making use of a combination of the density functional theory (DFT), and the exact diagonalization (ED) of an effective discrete Anderson impurity model. Intermediate valence ground state with the f-shell occupation n4f =5.5 for the Pu atom in PuB6 is calculated. The 5f-shell magnetic moment is completely compensated by the moment carried by the electrons in the conduction band. Already in DFT, PuB6 is an insulator with a small amount of holes near the X-point, and the indirect band gap of ≈60 meV. This band gap becomes direct in DFT+ED calculations supporting the idea of “topological Kondo insulator” in PuB6. Connection between the electronic structure of PuB6 and δ-Pu is established. We propose that these materials belong to a new class of intermediate valence “Racah” materials with the multi-orbital “Kondo-like” singlet ground-state.