Low-symmetry Crystal Field Research Articles

Optical Lines in Europium and Terbium-Activated Yttrium Tantalate Phosphor: Combined Experimental and Group-Theoretical Analysis

The rare-earth ions in crystals such as terbium (YTaO4:Tb3+) and europium (YTaO4:Eu3+)-activated yttrium tantalate phosphors have a number of attractive features that predetermine their crucial role in practical application in contemporary optoelectronic devices. In this article, we employ the group-theoretical arguments aimed to reveal the group-theoretical classification of the crystal field levels and selection rules for the allowed optical transition between the crystal field components of Tb3+ and Eu3+ of the low symmetry crystal field in the activated yttrium tantalate phosphors. We also establish possible polarization rules for the lines corresponding to the allowed transitions. We deduce the symmetry-assisted results for the selection rules in the optical transitions accompanied by the absorption/emission of the vibrational quanta. The selection rules for the vibronic satellites of the zero-phonon lines are expected to be useful for the identification of the lines in the spectra of rare-earth ions with a weak vibronic coupling. The results of the low-temperature measurements of photoluminescence under the 325 nm excitation are in compliance with the group-theoretical analysis. The aim of the paper is to establish symmetry-assisted results that are the background of the quantitative crystal field theory based on the quantum-mechanical consideration.

Charge Transfer Transitions and Circular Magnetooptics in Ferrites

The concept of charge transfer (CT) transitions in ferrites is based on the cluster approach and takes into account the relevant interactions, such as the low-symmetry crystal field, spin–orbital, Zeeman, exchange and exchange-relativistic interactions. For all its simplicity, this concept yields a reliable qualitative and quantitative microscopic explanation of spectral, concentration, temperature and field dependencies of optic and magneto-optic properties ranging from the isotropic absorption and optical anisotropy to circular magneto-optics. In this review paper, starting with a critical analysis of the fundamental shortcomings of the “first-principles” density functional theory (DFT-based) band theory, we present the main ideas and techniques of the cluster theory of the CT transitions to be main contributors to circular magneto-optics of ferrites. Numerous examples of comparison of cluster theory with experimental data for orthoferrites, iron garnets and other ferrites are given.

The influence of nd0 transition metal cations on the Eu3+ asymmetry ratio R=I(5D0−7F2)I(5D0−7F1) and crystal field splitting of 7F1 manifold in pyrochlore and zircon compounds

This paper examines the influence of transition metal cations with empty nd0 cores on the Eu3+ asymmetry ratio R=I(5D0−7F2)I(5D0−7F1) and the magnitude of crystal field splitting of the 7F1 manifold (ΔΕ; 7F1). Two families of compounds that crystallize with the pyrochlore and zircon structures are considered. The pyrochlores under consideration have the general formula La2M2O7 (M = Hf, Zr, Sn). Comparison of the Eu3+ optical properties indicate that R increases in order La2Sn2O7 < La2M2O7 (M = Hf, Zr) while (ΔΕ; 7F1) varies as La2M2O7 (M = Hf, Zr) < La2Sn2O7. The strength of M-O covalent bonding is responsible for these trends. The M-cations in La2M2O7 (M = Hf, Zr) have empty nd0 orbitals that participate strongly in covalent bonding with oxide anions, while the covalent contribution to the Sn4+-O2- bonding is weak due to filled Sn4+ 4d10 core. Mulliken charge calculations of the cations and anions in isostructural pyrochlore compounds are interpreted to indicate the presence of a stronger low-symmetry crystal field component that increases the asymmetry ratio in compounds with cations having empty ndo cores. This stronger covalent bonding is also responsible for decreasing (ΔΕ; 7F1). The second family of compounds under consideration crystallize in the zircon structure with the general formula YZO4 (Z = P, V). Comparison of Mulliken charges of cations and anions in these compounds indicates strong covalent bonding in the vanadate because it contains V5+ transition metal cation with empty 3d0 orbital. It leads to R(YPO4) < R(YVO4) and [YVO4: (ΔΕ; 7F1)] < [YPO4: (ΔΕ; 7F1)]. It is concluded that in isostructural family of compounds, the covalent bonding within the crystal framework determines R and (ΔΕ; 7F1).

Thermal, nonlinear, magnetic and faraday rotation properties of sol-gel diamagnetic glass /NaYF4: Fe, Ho3+: Role of magnetic ions

Ho3+ owns the biggest magnetic moment, stark splitting of energy and low-symmetry D2 crystal field which make Ho3+ high polarizable and has been studied as dopant in several magnetic crystals. For the first time, Ho3+ doped sol-gel synthesized diamagnetic glass for nonlinear, magnetic and magneto optical study was reported. This paper reports the synthesis, structure, morphology and magnetization of hexagonal NaYF4:Fe, Ho nanorods and importantly, the influence of NaYF4:Fe, Ho to the thermal, nonlinear, magnetic and Faraday rotation of diamagnetic glasses through varies techniques such as X-ray diffraction, scanning electron microscopy, Raman spectra, Ultraviolet–visible spectra, different scanning calorimetry, thermal mechanical analysis, Z-scan, superconducting quantum interference device magnetometry and Verdet constant measurement. Experimental results discovered that the doping of Ho3+ and Fe3+ ions disturbed the self-assembly of NaYF4 while suppressed the length of nanorod. Due to its nanoscale, magnetization of NaYF4:Fe, Ho changed from diamagnetic to superparamagnetic. The doping of NaYF4:Fe, Ho increased the thermal stability and third nonlinearity. Glass with different amount of doping presented diamagnetism and paramagnetism due to the strongest magnetic moment, increased polarizability, electron transition of Ho3+ and d-d exchange of Fe3+ ions in glass matrix. Glass doped 2% of NaYF4:Fe, Ho glass showed the best magnetic, magneto optical performance and improved thermal stability and nonlinearity which can be ideal candidate for photonics, nonlinear and magneto optical applications.

Occupation switching of d orbitals in vanadium dioxide probed via hyperfine interactions

Metal-insulator transition was microscopically investigated by orbital-resolved nuclear magnetic resonance (OR-NMR) spectroscopy in a single crystal of vanadium dioxide VO$_2$. Observations of the anisotropic $^{51}$V Knight shift and the nuclear quadrupole frequency allow us to evaluate orbital-dependent spin susceptibility and $d$ orbital occupations. The result is consistent with the degenerated $t_{2g}$ orbitals in a correlated metallic phase and the $d$ orbital ordering in a nonmagnetic insulating phase. The predominant orbital pointing along the chain facilitates a spin-singlet formation triggering metal-insulator transition. The asymmetry of magnetic and electric hyperfine tensors suggests the $d$ orbital reformation favored by a low-symmetry crystal field, forming a localized molecular orbital. The result highlights the cooperative electron correlation and electron-phonon coupling in Mott transition with orbital degrees of freedom.

Dispersion dependences for polariton-axion waves in tryptophan crystals

Dispersion dependences of electromagnetic waves in tryptophan crystals are constructed taking into account photon-axion conversion processes in the low-symmetry tryptophan crystal field. It is shown that a peculiarity associated with the intersection of dispersion curves of electromagnetic and axion waves appears in the frequency range of unitary polaritons, corresponding to the unity refractive index. In the intersection region, hybrid polariton-axion quasiparticles called axitons are formed. The dispersion relation for axitons in the visible and infrared spectral regions is derived. The conditions for photon-axion conversion near the exciton absorption edge of tryptophan in the ultraviolet spectral region are determined.

Efficient real-frequency solver for dynamical mean-field theory

We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks roughly spaced by the band width divided by the number of bath sites. The self-consistency cycles are fully performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on Ligand Field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling and low symmetry crystal-fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.

The Inherent Single‐Molecule Magnet Character of Trivalent Uranium

SMMs are often based on transition-metal clusters, but significant attention has recently focused on complexes of single and multiple lanthanoid ions, because the crystal-field splitting of the lowest Russell–Saunders multiplet engenders large magnetic anisotropies. [5–11] These anisotropies are responsible for high relaxation barriers and therefore slow magnetic relaxation. However, well isolated high-spin ground states are difficult to achieve within polynuclear lanthanoid SMMs because the valence 4f orbitals have limited radial extension and are usually energetically incompatible with ligand orbitals. These inherent 4f orbital properties give predominantly ionic interactions and results in weak magnetic exchange coupling with neighboring spin centers, with very few exceptions. [7, 12] In principle, actinoids, and in particular uranium, possess properties that render these ions ideal candidates from which to construct SMMs. This is because, compared to the lanthanoids, uranium exhibits enhanced crystal field splitting, [13, 14] as well as increased covalency, the latter enabling significant spin couplings in polynuclear systems, [15] and therefore both stronger magnetic exchange and anisotropies can be envisaged. This premise was realized recently with reports of several closely related single-ion pyrazolylborate uranium(III) complexes which were shown to display SMM behavior. [14, 16–20] In addition, two neptunium complexes were shown to display slow relaxation of the magnetization. [15, 21] The fact that all uranium(III) SMMs reported to date are closely related to each other raises the question as to how sensitive SMM behavior in trivalent uranium is to the composition of the coordination sphere and its symmetry. SMM behavior in all published examples is much more pronounced in an external field than in zero field, which suggests that quantum tunneling of the magnetization plays a significant role in shortening the relaxation times. However, in principle, low-symmetry crystal field components cannot induce tunneling of the magnetization, because uranium(III) is a Kramers half-integer angular momentum ion. Also the nuclear spin I = 0o f 238 U cannot induce tunneling of the

Crystal-field analysis for RE3+ ions in laser materials: III. Energy levels for Nd3+ and Er3+ ions in LaAlO3, YAlO3, and LaGaO3 single crystals – Combined approach to low symmetry crystal field parameters

Crystal field (CF) analysis of energy levels for Nd3+ and Er3+ ions in LaAlO3, YAlO3, and LaGaO3 single crystals is presented. It is shown that a combined approach comprising the ascent/descent in symmetry (ADS) method combined with superposition model (SPM) analysis can be successfully used for analysis of low-symmetry systems. The present ADS/SPM approach is less labor and time consuming as compared, e.g., with Monte-Carlo method and it also allows maintaining the relationship between the crystallographic axis system and the nominal axis systems of fitted CFP sets. For orthogallates and orthoaluminates the actual Cs symmetry, resulting from distortion of perovskite structure, may be successfully approximated for both systems by the ADS chain C4v↔C3 (D3)↔Cs or C3 (D3)↔Cs symmetry. The possibility of using of approximated symmetries for orthogallates or orthoaluminates can be useful for interpretation of energy levels for this family of compounds of technological importance, particularly in the case when the number of available experimental energy levels is insufficient for full Cs parameterization. The novel aspect of the combined ADS/SPM approach is that possible higher symmetry approximations employing also the axis systems oriented differently than for the actual symmetry are searched for, taking advantages of the transformation properties of CF parameters sets.

A Model of Spin Crossover in Manganese(III) Compounds: Effects of Intra- and Intercenter Interactions

A microscopic approach to the problem of cooperative spin crossover in the [MnL2]NO3 crystal, which contains Mn(III) ions as structural units, is elaborated on, and the main mechanisms governing this effect are revealed. The proposed model also takes into account the splitting of the low-spin 3T1 (t(2)(4)) and high-spin 5E (t(2)(3)e) terms by the low-symmetry crystal field. The low-spin → high-spin transition has been considered as a cooperative phenomenon driven by interaction of the electronic shells of the Mn(III) ions with the all-around full-symmetric deformation that is extended over the crystal lattice via the acoustic phonon field. The model well explains the observed thermal dependencies of the magnetic susceptibility and the effective magnetic moment.

Faraday Rotation Caused by Mixed Valence Centers in Magnetic Crystals

The peculiarities of the Faraday rotation in the imperfect garnet-type crystals for which the lattice irregularities are represented by the mixed valence clusters of transition metal ions are analyzed. The model takes into account the cubic and low symmetry crystal fields acting on the metal ions and migration of the “extra” hole. The electric dipole transitions in these types of clusters with migrating hole coupled to the spin core through the double exchange mechanism are shown to lead to a significant magnetooptical activity in the visible range of spectrum. The intensity of these transitions can be comparable or higher than those for the magnetic dipole ones in the same range of frequencies.

Study of optical spectra and thermal shifts of R1-line of LaAlO3:Cr3+

Based on the strong scheme of ligand field theory and the non-coupling trigonal bases, the d 3 complete energy matrix was constructed, which include the cubic crystal field, coulomb interactions, spin-orbit coupling, and low-symmetry crystal field. By means of diagonalizing the complete d 3 energy matrix (DCEM), the energy levels, wavefunctions and crystal-field parameters of LaAlO3:Cr3+ at normal pressure have been calculated. In terms of these results, the g factor of the ground state under normal pressure and low temperature has been calculated and proved to be consistent with experiment data. By taking into account the wavefunctions and Thermal Shift theory, the thermal shifts of R 1-line of LaAlO3:Cr3+ were calculated and the related parameters were determined. All the results are in good agreement with the experimental ones. Furthermore, the results show the physical origin and micro-mechanism of R 1-line thermal shifts more completely.

Local electronic structure ofFe2+impurities in MgO thin films: Temperature-dependent soft x-ray absorption spectroscopy study

We report on the local electronic structure of Fe impurities in MgO thin films. Using soft x-ray absorption spectroscopy (XAS) we verified that the Fe impurities are all in the 2+ valence state. The fine details in the line shape of the Fe $L_{2,3}$ edges provide direct evidence for the presence of a dynamical Jahn-Teller distortion. We are able to determine the magnitude of the effective $D_{4h}$ crystal field energies. We also observed a strong temperature dependence in the spectra which we can attribute to the thermal population of low-lying excited states that are present due to the spin-orbit coupling in the Fe 3d. Using this Fe$^{2+}$ impurity system as an example, we show that an accurate measurement of the orbital moment in Fe$_3$O$_4$ will provide a direct estimate for the effective local low-symmetry crystal fields on the Fe$^{2+}$ sites, important for the theoretical modeling of the formation of orbital ordering.

Optical Transitions and Enhanced Angular Overlap Model for the Low Symmetry Europium(III) System

Absorption, emission, and excitation spectra covering a wide energy range of 3000−58000 cm−1 for the Eu3+ ion in the low symmetry system K5Li2EuF10 have been reported. The emission spectra have been analyzed by taking into account the influence of the temperature onto the luminescence from the 5D0,1,2 multiplets. The observed energy intervals in transition bands characteristic for the europium ion have been assigned and modeled using a multistep approach developed for this system. A risk of producing numerical artifacts in the multidimensional parameter space has been minimized by its strong reduction based on the enhanced angular overlap model and standardization of the low symmetry crystal field. The reported results are satisfactory (the final rms error of the fitting below 9.2 cm−1), consistent in each step of the procedure and in line with the microscopic physicochemical picture of the crystal field effective interaction.

Magnetooptical activity of spinel type crystals with complex mixed-valence lattice irregularities

In this Letter we analyze the peculiarities of the Faraday rotation in the imperfect spinel type crystals for which the lattice irregularities are represented by the mixed valence clusters of transition metal ions. A such kind of complex system with the electronic configuration d 5 ( t 2 g 3 e g 2 ) − d 5 ( t 2 g 3 e g 2 ) − d 4 ( t 2 g 2 e g 2 ) (for example, Mn 2 + Mn 2 + Mn 3 + ) is considered in detail. The model takes into account the cubic and low symmetry crystal fields acting on the metal ions, migration of the “extra” hole as well as the orientational degeneracy (hidden optical anisotropy). The electric dipole transitions in these types of clusters with migrating hole coupled to the spin core through the double exchange mechanism are shown to lead to a significant magnetooptical activity in the visible range of spectrum. The intensity of these transitions can be comparable or higher than those for the magnetic dipole ones in the same range of frequencies. The electric dipole mechanism of the magnetooptical effects manifests itself in a highly anisotropic character of the spectra.

Photoluminescence investigations of cubic boron nitride doped with neodymium during high-pressure synthesis

Micropowders of cubic boron nitride doped with neodymium are prepared under high-pressure and high-temperature conditions. The phase composition of the micropowders is studied using X-ray diffractometry and X-ray fluorescence analysis. The photoluminescence, photoluminescence excitation spectra, and the life-time of the 4F3/2 excited state of Nd ions introduced into cubic boron nitride are investigated. In photoluminescence spectra of the micropowders, structured bands are recorded in the range of the 4F3/2 → 4I9/2 and 4F3/2 → 4I11/2 electronic transitions. A higher intensity of the first structured band indicates that the corresponding photoluminescence in cubic boron nitride doped with neodymium is excited by the “three-level scheme.” It is demonstrated that an increase in the concentration of the neodymium compound in the growth batch leads to the formation of two luminescence centers Nd1 and Nd2 formed by neodymium ions located in different low-symmetry crystal fields in the micropowders. This is confirmed by X-ray diffraction investigations and the study of the photoluminescence decay curves. The 4F3/2 short-lived state is assigned to the Nd ions forming the Nd1 centers, and the long-lived state is attributed to the Nd ions forming the Nd2 centers.

Highly Anisotropic Exchange Interactions in a Trigonal Bipyramidal Cyanide-Bridged NiII3OsIII2 Cluster

This article is a part of our efforts to control the magnetic anisotropy in cyanide-based exchange-coupled systems with the eventual goal to obtain single-molecule magnets with higher blocking temperatures. We give the theoretical interpretation of the magnetic properties of the new pentanuclear complex {[Ni(II)(tmphen)(2)](3)[Os(III)(CN)(6)](2)} x 6 CH(3)CN (Ni(II)(3)Os(III)(2) cluster). Because the system contains the heavy Os(III) ions, spin-orbit coupling considerably exceeds the contributions from the low-symmetry crystal field and exchange coupling. The magnetic properties of the Ni(II)(3)Os(III)(2) cluster are described in the framework of a highly anisotropic pseudo-spin Hamiltonian that corresponds to the limit of strong spin-orbital coupling and takes into account the complex molecular structure. The model provides a good fit to the experimental data and allows the conclusion that the trigonal axis of the bipyramidal Ni(II)(3)Os(III)(2) cluster is a hard axis of magnetization. This explains the fact that in contrast with the isostructural trigonal bipyramidal Mn(III)(2)Mn(II)(3) cluster, the Ni(II)(3)Os(III)(2) system does not exhibit the single-molecule magnetic behavior.

Local lattice distortion near the tetragonal Cr3+-(0) center in a Cs2CdCl4 crystal

The perturbation formulas of electron paramagnetic resonance parameters D, g // and g ⊥ for a 3d3 ion in a tetragonal octahedral field are established on the basis of Zhao's semi-SCF d-orbit wave functions model. In these formulas, the parameters related to the contributions from the configuration interaction, covalency effect and low-symmetry crystal field can be estimated from the optical spectra and the structural data of the system under study. According to these formulas, the local tetragonal distortion of the Cr3+-(0) center in a Cs2CdCl4 crystal was determined by fitting the calculated to the experimental values. The results showed that these local values of Cs2CrCl4(R 1≈ 0.254 nm and R 2≈ 0.233 nm) were different from those of the host crystal.

Microscopic mechanisms of spin-dependent electric polarization in3doxides

We address a systematic microscopic theory of spin-dependent electric polarization in $3d$ oxides starting with a generic three-site two-hole cluster. A perturbation scheme realistic for $3d$ oxides is applied which implies the quenching of orbital moments by low-symmetry crystal field, strong intra-atomic correlations, the $dp$-transfer effects, and rather small spin-orbital coupling. An effective spin operator of the electric-dipole moment is deduced incorporating both nonrelativistic $\ensuremath{\propto}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{s}}}_{1}\ensuremath{\cdot}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{s}}}_{2})$ and relativistic $\ensuremath{\propto}[{\mathbf{s}}_{1}\ifmmode\times\else\texttimes\fi{}{\mathbf{s}}_{2}]$ terms. The nonrelativistic electronic polarization mechanism related to the effects of the redistribution of the local on-site charge density due to $pd$ covalency and exchange coupling is believed to govern the multiferroic behavior in $3d$ oxides. The relativistic exchange-dipole moment is mainly stems from the nonrelativistic one due to the perturbation effect of Dzyaloshinsky-Moriya coupling and is estimated to be a weak contributor to the electric polarization observed in the most of $3d$ multiferroics.

Extracting structural information from low symmetry crystal field parameters: Pr4+ in BaPrO3

Abstract Recent literature survey has revealed several crystal field parameter (CFP) datasets for rare-earth (RE) ions at orthorhombic, monoclinic, and triclinic symmetry sites, which cannot be directly compared. Triclinic CFPs include for a given rank ( k = 2, 4, 6) all components (− k ≤ q ≤ + k ). Depending on the axis system chosen, the low symmetry effects involved in the symbolic, fitted, or model CFPs may be only apparent and not actual . In order to extract useful structural information involved in the low symmetry CFPs, an approach comprising three methods is proposed: (1) the principal values of the 2nd-rank CFPs and the orientation of their principal axis system (AS) w.r.t. the original or crystallographic AS; (2) the pseudosymmetry axes method; (3) the closeness factors. This approach is applied to reanalyze the CFPs for Pr 4+ in BaPrO 3 .