We demonstrate how ab initio cluster calculations including the full Coulomb vertex can be done in the basis of the localized, generalized Wannier orbitals which describe the low-energy density functional (LDA) band structure of the infinite crystal, e.g. the transition metal 3d and oxygen 2p orbitals. The spatial extend of our 3d Wannier orbitals (orthonormalized Nth order muffin-tin orbitals) is close to that found for atomic Hartree-Fock orbitals. We define Ligand orbitals as those linear combinations of the O 2p Wannier orbitals which couple to the 3d orbitals for the chosen cluster. The use of ligand orbitals allows for a minimal Hilbert space in multiplet ligand-field theory calculations, thus reducing the computational costs substantially. The result is a fast and simple ab initio theory, which can provide useful information about local properties of correlated insulators. We compare results for NiO, MnO and SrTiO3 with x-ray absorption, inelastic x-ray scattering, and photoemission experiments. The multiplet ligand field theory parameters found by our ab initio method agree within ~10% to known experimental values.
A method is developed to calculate the ligand field (LF) parameters and the multiplet spectra of local magnetic centers with open $d$- and $f$-shells in solids in a parameter-free way. This method proceeds from density functional theory and employs Wannier projections of nonmagnetic band structures onto local $d$- or $f$-orbitals. Energies of multiplets and optical, as well as X-ray spectra are determined by exact numerical diagonalization of a local Hamiltonian describing Coulomb, LF, and spin-orbit interactions. The method is tested for several 3$d$- and 5$f$-compounds for which the LF param…
Using the recently developed method we calculate the crystal field parameters in yttrium and lutetium aluminum garnets doped with seven trivalent Kramers rare-earth ions. We then insert calculated parameters into the atomic-like Hamiltonian taking into account the electron-electron, spin-orbit and Zeeman interactions and determine the multiplet splitting by the crystal field as well as magnetic $\hat{g}$ tensors. We compare calculated results with available experimental data.
We analyze the magnetic form factor of Cu$^{2+}$ in low-dimensional quantum magnets by taking the metal-ligand hybridization into account explicitly. In this analysis we use the form of magnetic Wannier orbitals, derived from the first-principles calculations, and identify the contributions of different atomic sites. Having performed local density approximation calculations for cuprates with different types of ligand atoms, we discuss the influence of the on-site Coulomb correlations on the structure of the magnetic orbital. The typical composition of Wannier functions for copper oxides, chlor…
Two-dimensional transition metal dichalcogenides (TMDs) exist in two polymorphs, referred to as $1T$ and $1H$, depending on the coordination sphere of the transition metal atom. The broken octahedral and trigonal prismatic symmetries lead to different crystal and ligand field splittings of the $d$ electron states, resulting in distinct electronic properties. In this work, we quantify the crystal and ligand field parameters of two-dimensional TMDs using a Wannier-function approach. We adopt the methodology proposed by Scaramucci et al. [A. Scaramucci et al., J. Phys.: Condens. Matter 27, 175503…
We investigate the magnetic properties of archetypal transition-metal oxides MnO, FeO, CoO and NiO under very high pressure by x-ray emission spectroscopy at the Kβline. We observe a strong modification of the magnetism in the megabar range in all the samples except NiO. The results are analyzed within a multiplet approach including charge-transfer effects. The pressure dependence of the emission line is well accounted for by changes of the ligand field acting on the d electrons and allows us to extract parameters like local d-hybridization strength, O-2p bandwidth and ionic crystal field acro…
A method to calculate the crystal field parameters {\it ab initio} is proposed and applied to trivalent rare earth impurities in yttrium aluminate and to Tb$^{3+}$ ion in TbAlO$_3$. To determine crystal field parameters local Hamiltonian expressed in basis of Wannier functions is expanded in a series of spherical tensor operators. Wannier functions are obtained by transforming the Bloch functions calculated using the density functional theory based program. The results show that the crystal field is continuously decreasing as the number of $4f$ electrons increases and that the hybridization of…
We discuss the calculation of resonant inelastic x-ray scattering (RIXS) with Xclaim, a multi-plaform code for the calculation of core-hole spectroscopy based on a ligand-field multiplet model. RIXS can be calcuated with a ligand-field model with ligands for the L$_{2,3}$, M$_{2,3}$, $K_α$ and $K_β$ edges for $d$-valence metals. In addition, the program brings the possibility of fully diagonalizing the hamiltonian to classify the excited states. The command line use of xclaim is described for scripting purposes to help in automatizing the results that can be obtained with the graphical interfa…
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 (LFMT) 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 Greens 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 problematic. Here we show th…
The crystal field parameters of 13 trivalent lanthanide ions substituted for La in LaF$_3$ were calculated using the combination of the band structure and Wannier function calculations. Performing an atomic exact diagonalization with thus obtained crystal-field parameters we compute the crystal-field splitting of atomic multiplets. The calculation is compared with the available experimental results and a good agreement is found.
We report x-ray absorption and x-ray linear dichroism measurements at the Fe L2,3 edges of the geometrically frustrated systems of potassium and hydronium iron jarosite. Comparison with simulated spectra, involving ligand-field multiplet calculations modelling the 3d-2p hybridization between the iron ion and the oxygen ligands, has yielded accurate estimates for the ligand metal-ion hybridization and the resulting single-ion crystal field anisotropy energy. Using this method we provide an experimentally verified scenario for the appearance of a single-ion anisotropy in this nominally high-spin…
We investigate the cause of exchange anisotropy in a family of copper-based, quasi-two-dimensional materials with very similar geometries. This family differs mainly in the inter-layer separation, but have very different magnetic interactions even within the basal plane. We use density functional theory and Wannier functions to parameterize two complimentary tight-binding models and show that the superexchange between the Cu(II) ions is dominated by a through-space interaction between hybrid Cu-pyrazine orbitals centered on the copper atoms. We find no correlations between the strength of this…
Xclaim (x-ray core level atomic multiplets) is a graphical interface for the calculation of core-hole spectroscopy and ground state properties within a charge-transfer multiplet model taking into account a many-body hamiltonian with Coulomb, spin-orbit, crystal-field, and hybridization interactions. Using Hartree-Fock estimates for the Coulomb and spin-orbit interactions and ligand field parameters (crystal-field, hybridization and charge-transfer energy) the program can calculate x-ray absorption spectroscopy (XAS), x-ray photoemission spectroscopy (XPS), photoemission spectrospcy (PES) and i…
We have investigated the electronic structure of Sr2IrO4 using core level resonant inelastic x-ray scattering. The experimental spectra can be well reproduced using ab initio density functional theory based multiplet ligand field theory calculations, thereby validating these calculations. We found that the low-energy, effective Ir t2g orbitals are practically degenerate in energy. We uncovered that covalency in Sr2IrO4, and generally in iridates, is very large with substantial oxygen ligand hole character in the Ir t2g Wannier orbitals. This has far reaching consequences, as not only the onsit…
Evidence for Many-Body States in NiPS$_3$ Revealed by Angle-Resolved Photoelectron Spectroscopy
Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）；RWTH-Aachen University（亚琛工业大学）；Technion, Haifa（海法理工学院）；Forschungszentrum Jülich（于利希研究中心）；University of Trieste（的里雅斯特大学）；Elettra – Sincrotrone Trieste S.C.p.A.（Elettra-的里雅斯特同步辐射中心）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
We revisit the problem of the spectra of two holes in a CuO$_{2}$ layer, modeled as a Cu-d$^{8}$ impurity with full multiplet structure coupled to a full O-2p band as an approximation to the local electronic structure of a hole doped cuprate. Unlike previous studies that treated the O band as a featureless bath, we describe it with a realistic tight binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-2p band structure. We also find (i) that only the ligand O-2p orbitals play an essential role, withi…
The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is able to treat both strongly correlated insulators and metals. Several interfaces between LDA and DMFT have been used, such as (N-th order) Linear Muffin Tin Orbitals or Maximally localized Wannier Functions. Such schemes are however either complex in use or additional simplifications are often performed (i.e., the atomic sphere approximation). We present an alt…
Using a combination of X-ray absorption spectroscopy experiments with first principle calculations, we demonstrate that insulating KCuO_2 contains Cu in an unusually-high formal-3+ valence state, the ligand-to-metal (O to Cu) charge transfer energy is intriguingly negative (Delta~ -1.5 eV) and has a dominant (~60%) ligand-hole character in the ground state akin to the high Tc cuprate Zhang-Rice state. Unlike most other formal Cu^{3+} compounds, the Cu 2p XAS spectra of KCuO_2 exhibits pronounced 3d^8 (Cu^{3+}) multiplet structures, which accounts for ~40% of its ground state wave-function. Ab-…
X-ray absorption spectroscopy measured at the $L$-edge of transition metals (TMs) is a powerful element-selective tool providing direct information about the correlation effects in the $3d$ states. The theoretical modeling of the $2p\rightarrow3d$ excitation processes remains to be challenging for contemporary \textit{ab initio} electronic structure techniques, due to strong core-hole and multiplet effects influencing the spectra. In this work we present a realization of the method combining the density-functional theory with multiplet ligand field theory, proposed in Haverkort et al. (https:/…
We report on a combined experimental and theoretical study on CrI3 single crystals by employing the polarization dependence of resonant inelastic X-ray scattering (RIXS). Our investigations reveal multiple Cr 3d orbital splitting (dd excitations) as well as magnetic dichroism (MD) in the RIXS spectra which is evidence of spin-flip in the dd excitation. Interestingly, the dd excitation energies are similar on both sides of the ferromagnetic transition temperature, TC of 61 K, although MD in RIXS is predominant at 0.4 tesla magnetic field below TC. This demonstrates that the ferromagnetic supere…
