Crystal-field Energy Levels Research Articles

Spectroscopy and crystal-field analysis of low-symmetry Er[formula omitted] centres in K[formula omitted]YF[formula omitted] microparticles

K2YF5 crystals doped with lanthanide ions have a variety of possible optical applications. Owing to the low symmetry of the system, the crystal structure cannot be unambiguously determined by x-ray diffraction. However, electron-paramagnetic resonance studies have demonstrated that lanthanide ions substitute for yttrium in sites of Cs local symmetry. In this work, we use high-resolution absorption and laser spectroscopy to determine electronic energy levels for Er3+ ions in K2YF5 microparticles. A total of 39 crystal-field energy levels, distributed among 7 multiplets of the Er3+ ion, have been assigned. This optical data is used for crystal-field modelling of the electronic structure of Er3+ in K2YF5. Our model is fitted not only to the electronic energy levels, but also to the ground-state g-tensor. This magnetic-splitting data defines the axis system of the calculation, avoiding ambiguities associated with low-symmetry crystal-field fits.

High-resolution spectroscopy of LaAlO3-Pr3+ pseudo-cubic perovskite single crystals: Crystal-field parameters, hyperfine and deformation splittings

We report high-resolution measurements and analysis of the optical transmission and emission spectra of a concentration series of La(1-x)PrxAlO3 (x = 10−3, 9 ⋅ 10−3, and 2 ⋅ 10−2) single crystals in a wide frequency range ((2-27) ⋅ 103 cm−1) at temperatures 5–300 K, below the structural phase transition from the cubic Pm3‾m to the rhombohedral R3‾c phase. Pr3+ ions substitute for La3+ ions at sites with point symmetry D3. All recorded spectral lines are assigned to specific initial and final crystal-field (CF) energy levels, the scheme of CF levels is constructed and described by an appropriate set of CF parameters. The structural phase transition is accompanied by shear strains and the formation of ferroelastic twin domains of four types compressed along one of the four C3 axes in the parent cubic crystal lattice. Specific features of the measured spectra, namely, anomalous broadening of spectral lines and doublet structure of some lines corresponding to transitions between CF singlets and doublets, are considered as a result of interaction of 4f electrons with the field of random shear deformations competing at the boundaries of twin domains. Modeling of the observed line shapes was performed taking into account both hyperfine interactions and random lattice strains, as well as the effect of temperature. The width (6.6 ± 0.7)⋅10− 4 of the introduced two-dimensional distribution function of random strains was found from a comparison of simulated and measured profiles of the split spectral lines. The results of this work can be applied for quantitative assessment of crystal quality.

Laser site-selective spectroscopy and magnetic hyperfine splittings of Ho3+ doped Y2SiO5

Laser site-selective spectroscopy and high-resolution absorption measurements have been used to determine 51 crystal-field energy levels for one of the Ho3+ centres in Y2SiO5. This centre is denoted as Site 2 and has been tentatively assigned as the seven-fold coordinated centre. High resolution absorption measurements reveal complex hyperfine patterns that obey an approximate selection rule. The application of a magnetic field along the three optical axes reveals the presence of avoided crossings below 0.5 Tesla, in both the ground and excited states.

Zeeman spectroscopy and crystal-field analysis of low symmetry centres in Nd3+ doped Y2SiO5

We report on infrared to visible Zeeman absorption spectroscopy and parameterised crystal-field modelling of Nd3+ centres in Y2SiO5 through the use of experimentally inferred crystal-field energy levels and Zeeman directional electronic g values. We demonstrate that good agreement between the calculated and experimental crystal-field energy levels as well as directional Zeeman g values along all three crystallographic axes can be obtained. Further, we demonstrate that the addition of correlation crystal field effects successfully account for discrepancies that arise between the calculated and experimental values relevant to the 2H(2) multiplet in a one-electron crystal field model.

High-pressure structural transition and magnetic phase diagram of CuB2O4

Noncentrosymmetric $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$ is a prototypical system with interacting spin sublattices of different dimensionality, exhibiting diverse magnetic structures and magnetic phase transitions. Here we report pressure-induced structural evolution of $\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4}$ and its effect on the magnetic phase diagram. Powder x-ray diffraction (XRD), Raman scattering, and infrared phonon measurements have been performed under high pressure at room temperature. Although XRD shows lattice stability up to $\ensuremath{\sim}25\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, Raman and IR phonon measurements reveal structural anomaly near 3 GPa, followed by a structural phase transition at $\ensuremath{\sim}12\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. Pressure evolution of the zero-phonon lines in the low-temperature optical absorption studies helps identifying the symmetry change of the Cu sites modifying the crystal-field energy levels at the structural transition. High-pressure magnetization measurements have been performed with magnetic field applied perpendicular to the tetragonal $c$ axis. With increasing pressure the saturation magnetization of the commensurate weak ferromagnetic phase increases with systematic reduction of its turnup critical field. Pressure-induced systematic suppression of the dc susceptibility in this phase is attributed to the reduced critical field, indicating pressure-driven enhanced stability of the weak ferromagnetic phase at high pressure. Whereas, below 10 K the critical field of the incommensurate-commensurate transition increases with pressure, indicating enhanced stability of the incommensurate helical order at high pressure.

An inelastic neutron scattering investigation of holmium orthoferrite

The inelastic neutron scattering spectra recorded in this study and elsewhere provide a useful set of crystal-field (CF) energy levels for the ground J = 6 term of Ho3+ in HoFeO3. The resolution of the low-energy, temperature-dependent pseudo-quadrupole ground state splitting and magnon peaks is consistent with the self-ordering of the Ho3+ sublattice at T Ho ∼ 8–10 K and supports earlier electron spin resonance investigations of the Ho3+ magnon behaviour. Systematic analysis of the grouped singlet CF levels of Ho3: HoFeO3, in conjunction with the CF Kramers doublet levels of the neighbouring Er3+: ErFeO3, has yielded possible sets of CF parameters for the two systems.

Precise determination of the low-energy electronuclear Hamiltonian of LiY1−xHoxF4

We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY$_{1-x}$Ho$_{x}$F$_{4}$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the $^6\mathrm{Li}$ and $^7\mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants ${A_J=0.02703\pm0.00003}$ $\textrm{cm}^{-1}$ and ${B= 0.04 \pm0.01}$ $\textrm{cm}^{-1}$, respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the $^5I_8$ ground state manifold, including the (non-linear) hyperfine corrections. The latter match the measurement-based estimates. The scale of the non-linear hyperfine corrections sets an upper bound for the inhomogeneous line widths that would still allow for unique addressing of a selected hyperfine transition. e.g. for quantum information applications. Additionally, we establish the far-infrared, low-temperature refractive index of LiY$_{1-x}$Ho$_{x}$F$_{4}$.

Simulating excited-state absorption spectra in upconverting lanthanide doped nanoparticles: KY3F10:Er3+

High-resolution absorption and laser-excited fluorescence studies of KY3F10:Er3+ core-only nanoparticles are presented. A total of 49 crystal-field energy levels, distributed amongst 13 multiplets of the Er3+ ion, have been deduced for the C4v point group symmetry centre in this material. A parametrized, single-electron crystal-field calculation provides an excellent approximation to the experimental data with optimized crystal fit parameters that are comparable to the bulk KY3F10:Er3+ crystal. Simulated spectra, based upon wavefunctions derived from the crystal-field calculations, unequivocally demonstrate that excited-state absorption is the predominant upconversion mechanism in this material – agreeing well with upconversion excitation spectra obtained for Yb3+ co-doped samples.

Ab initio non-covalent crystal field theory for lanthanide complexes: a multiconfigurational non-orthogonal group function approach.

We present a multiconfigurational ab initio methodology based on non-orthogonal fragments for the calculation of crystal field energy levels and magnetic properties of lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach consists of two steps. In the first step, appropriate ab initio wave functions for the various ionic fragments (lanthanide ions and coordinating ligands) are optimized separately, accounting for the influence of the surrounding environment within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGFs), and reduced to an effective (2J + 1)-dimensional non-orthogonal configuration interaction (CI) problem via Löwdin-partitioning. Within the proposed formalism, the projected non-orthogonal CI Hamiltonian can be expanded to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions provide systematic approximations to the crystal field energies and wave functions. We present here a preliminary implementation of the proposed MC-NOGF method developed for first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach, Fragment Ab Initio Model Potential (FAIMP) approximation, and the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We found that the energies and magnetic properties of 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method compare remarkably well with those obtained using the full CAHF/CASCI-SO method including metal-ligand covalency, thus exposing the predominantly electrostatic character of the metal-ligand interactions, and are superior to those obtained using the FAIMP approach, which in its iteratively optimised variant was believed to date to be the best ab initio description of non-covalent metal-ligand interactions.

Abnormal reduction and luminescence properties of Sm2+-doped Sr5(PO4)3Cl prepared by solution combustion synthesis

Sm-doped Sr5(PO4)3Cl was prepared by a solution combustion synthesis in the air atmosphere. The pure hexagonal phases of the samples were confirmed via the XRD, Raman, and FT-IR measurements. The typical microrod shape of the products was also demonstrated by SEM, TEM, and HRTEM images. The spectral properties and lifetimes were applied to characterize the luminescence of the samples as-prepared and subsequently heated in the air atmosphere. The luminescence of as-prepared Sm-doped Sr5(PO4)3Cl contains a broad emission band and a group of narrow lines, which are ascribed to the radiative transitions of 4f5d→4f and 5D0→7FJ (J = 0, 1, 2) of Sm2+ ions, respectively. It indicates that the Sm3+ can be successfully reduced to Sm2+ ions in hexagonal Sr5(PO4)3Cl prepared by combustion synthesis. The temperature dependent luminescence spectra and decay curves of Sm2+ were measured in a very wide temperature region from 10 K to 300 K. The thermal quenching and activation energy of Sm2+ doped Sr5(PO4)3Cl were reported. The crystal field energy level diagram and excitation mechanism of Sm2+ ions-doped Sr5(PO4)3Cl were characterized by the high resolution luminescence at low temperature. The luminescence of Sm2+ in Sr5(PO4)3Cl shows a great dependence on heating temperature in the air atmosphere (50–700 °C). The heating treatments at the elevated temperature depress Sm2+ emission along with the appearance of Sm3+ ions. The temperature-induced changes in the modification of the spectral components could be applied as potential luminescence thermometry.

Laser site-selective spectroscopy of Nd3+-doped Y2SiO5

We report on laser site-selective spectroscopy, as well as high resolution, infrared to optical absorption, of both the six and seven -fold coordinated, C1 symmetry sites for Nd3+ doped Y2SiO5. A total of fifty three crystal-field energy levels have been determined for both sites. We also present the temperature dependencies of the spectral linewidth and line position as measured in absorption. The coupling coefficients due to Raman two-phonon and direct one-phonon processes are interpreted in terms of the phonon energies contributing and their roles in the phonon energy distribution of Y2SiO5. Finally, we analyse direct non-radiative relaxation processes as inferred from the temperature-dependent fluorescence lifetimes.

Quasi-two-dimensional magnetic correlations inNi2P2S6probed byP31NMR

Detailed $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements are presented on well-characterized single-crystals of antiferromagnetic van der Waals ${\mathrm{Ni}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$. An anomalous breakdown is observed in the proportionality of the NMR shift $K$ with the bulk susceptibility $\ensuremath{\chi}$. This so-called $K$--$\ensuremath{\chi}$ anomaly occurs in close proximity to the broad peak in $\ensuremath{\chi}(T)$, thereby implying a connection to quasi-two-dimensional (2D) magnetic correlations known to be responsible for this maximum. Quantum chemistry calculations show that crystal field energy level depopulation effects cannot be responsible for the $K$--$\ensuremath{\chi}$ anomaly. Appreciable transferred hyperfine coupling is observed, which is consistent with the proposed Ni--S--Ni super- and Ni--S--S--Ni super-super-exchange coupling mechanisms. Magnetization and spin-lattice relaxation rate (${T}_{1}^{\ensuremath{-}1}$) measurements indicate little to no magnetic field dependence of the N\'eel temperature. Finally, ${T}_{1}^{\ensuremath{-}1}(T)$ evidences relaxation driven by three-magnon scattering in the antiferromagnetic state.

Investigations of crystal-field energy levels and microscopic spin-Hamiltonian parameters of Mn4+ ions in pyrochlore hosts Y2Ti2O7 and Y2Sn2O7

We investigate the crystal-field energy levels and the microscopic origin of spin-Hamiltonian parameters (SHPs), i.e. g-factors and zero-field splitting parameter D, for the ground state 4A2g(4F) of Mn4+ impurity ions at trigonal sites in host pyrochlores, Y2Ti2O7 and Y2Sn2O7. The total Hamiltonian includes the electrostatic and crystal-field (CF) Hamiltonians, and the magnetic interactions, i.e. spin-orbit, spin-spin, spin-other-orbit, and orbit-orbit couplings. The calculations are performed under the complete diagonalization method and microscopic spin-Hamiltonian (CDM/MSH) program. The calculated CF levels agree reasonably well with the observed energy levels for Mn4+ ions in these compounds. The SHPs are evaluated with the CDM/MSH wave functions as well as by a perturbation loop theory method (PLTM). The g-factors of Mn4+ in Y2Ti2O7 and Y2Sn2O7 using PLTM are close to those evaluated by CDM, while the PLTM value of D shows appreciable difference with the CDM value. This evidences that the g-factors depend predominately on the lower states, while the higher energy states significantly affect the D value. The contributions of spin-spin, spin-other-orbit, and orbit-orbit couplings to the CF energy levels and the SHPs are discussed.

Unifying analyses of the crystal field energy levels and EPR g factors for the trigonal Co2+ tetrahedral center in β˝-alumina

The crystal field energy levels (obtained from the optical spectra) and g factors g//, g⊥ (obtained from EPR spectra) for the Co2+ ion at the trigonal Al3+ tetrahedral site in β˝-alumina crystal are unifiedly analyzed with the full diagonalization (of energy matrix) method founded on the two-spin-orbit-parameter model (which contains the contributions from both the spin-orbit parameters of central dn ion and ligand ion via covalence effect). The results display that by applying only three adjustable parameters, the observed ten spectral data (eight crystal field energy levels and two g factors) can be rationally interpreted, confirming the availability of this full diagonalization method in the united analyses of optical and EPR data. The large impurity-generated angular distortion and hence the large trigonal distortion [which correspond to the large g-factor anisotropy and large ground state splitting ΔE(4A2)] of the Co2+ tetrahedral center in β˝-alumina are also gained. The outcomes are discussed.

Modeling spin Hamiltonian parameters for Fe2+ adatoms on Cu2N/Cu(1 0 0) surface: Semiempirical microscopic spin Hamiltonian approach

Abstract Transition metal atoms adsorbed on surfaces (adatoms) behave like magnets in nanoscale and have potential applications in quantum computing. Scanning tunneling microscopy and inelastic tunneling spectroscopy studies yield the spin Hamiltonian parameters. Semi-empirical approach based on crystal-field and microscopic spin Hamiltonian theory is employed for modeling of the zero field splitting parameters b k q , and Zeeman g-factors for Fe2+(S = 2) adatoms on Cu2N/Cu(1 0 0) surface. These parameters are determined for wide ranges of the microscopic parameters: the spin-orbit (λ), spin-spin (ρ) coupling constants, and crystal-field energy levels (Di) within the 5D multiplet. Matching theoretical and experimental 2nd-rank parameters ( b 2 0 , b 2 2 ) yields suitable values of {λ, ρ, Di}. For the first time, also the 4th-rank parameters ( b 4 q ) as well as the g-factors and their ρ-contributions are estimated. Using EasySpin program we show that the transition energies and mixing coefficients obtained using only b 2 q differ significantly from those using both ( b 2 q , b 4 q ). This indicates that b 4 q significantly affect the spin energy levels. Hence interpretations of experimental data may be inaccurate if b 4 q are neglected. Our approach enables bridging the gap between semi-empirical and DFT/ab-initio methods and may be utilized for Fe2+(S = 2) adatoms on other surfaces and Fe2+-based molecular nanomagnets.

Modeling Spin Hamiltonian Parameters for Fe2+ (S = 2) Adatoms on Cu2N/Cu(100) Surface Using Semiempirical and Density Functional Theory Approaches

Transition metal atoms adsorbed on surfaces (adatoms) behaving like magnets are important for potential applications in quantum computing and memory storage. Better insight into their magnetic properties, described by spin Hamiltonian (SH) parameters, is essential. Comprehensive modeling of SH parameters for Fe2+ with spin S = 2 adatoms on various surfaces is carried out using two approaches: (1) semiempirical CF/MSH [based on crystal field (CF) and microscopic spin Hamiltonian (MSH) theory], and (2) density functional theory (DFT). Here preliminary results of modeling of zero-field splitting parameters (ZFSPs) for Fe2+ on Cu2N/Cu(100) surface [for short Fe2+@Cu2N/Cu(100)] are presented. We focus on the orthorhombic second-rank ZFSPs in the conventional notation (D, E) measured for Fe2+@Cu2N/Cu(100). The fourth-rank ZFSP in the Stevens notation ( $$B_{k}^{q}$$ , k = 2, 4) measured for Fe2+ on CuN/Cu(100) surface are considered elsewhere. Using the CF/MSH approach within 5D approximation, the ZFSPs (k = 2, 4) and Zeeman g-factors are calculated for wide range of the microscopic parameters: spin–orbit (λ), spin–spin (ρ) coupling constants, and the crystal field energy levels (∆i). The ρ-contributions and the fourth-rank ZFSPs are found important. Computations of the ZFSPs (D, E) are done using the SIESTA code by mapping of the physical energy levels to those of effective ZFS Hamiltonian. Comparison of the results enables bridging the gap between DFT methods and CF/MSH ones. The present results will also be utilized in ongoing studies of adatoms on other surfaces, single molecule magnets and single-ion magnets.

Origin of the Ground Kramers Doublets for Co2+(3d7) Ions with the Effective Spin 3/2 Versus the Fictitious \u2018Spin\u2019 \xbd

Experimental spectroscopic and magnetic data for Co2+(3d7) ions in various systems are reviewed and critically examined. The focus is on Co2+ ions with the electronic spin S = 3/2, properties of which may be interpreted using the spin Hamiltonian with the effective S̃ = 3/2 or the fictitious ‘spin’ S (S′) = ½. Possible distinct ground states of Co2+(3d7) ions arising from crystal field energy levels are discussed. Distinctions between the concepts of the effective spin S̃ and the fictitious ‘spin’ S′ are outlined to clarify the terminological confusion encountered in literature. Sample cases of the ground state assignments and options for the ‘spin’ S′ = ½ origin are considered for better understanding of the Co2+ ions local environment in various systems, including low symmetry cases. Present study is motivated by potential applications of Co2+(S̃ = 3/2) complexes exhibiting very large or moderate zero-field splitting as molecular nanomagnets.

Analysis of the optical band positions for manganese (IV) ions in trigonal barium titanium hexafluoride and barium silicon hexafluoride crystals

The optical band positions (or crystal field energy levels) of manganese (IV) ions in trigonal barium titanium hexafluoride and barium silicon hexafluoride crystals are computed from the full diagonalization (of energy matrix) method founded on the two-spin–orbit-parameter model which consists of the effects from both the spin–orbit parameters of dn ion and ligand ions. The computed results are in rational agreement with the experimental values. It is found that the large difference of first excited state splitting ΔE (2E) between the manganese (IV)-doped barium titanium hexafluoride and barium silicon hexafluoride crystals is owing mainly to the great difference of trigonal distortion between the fluorine octahedral clusters in the two host crystals.

Crystal field in NdPd5Al2 investigated by inelastic neutron scattering

We report on inelastic neutron scattering measurements of the antiferromagnetic NdPd5Al2 compound. NdPd5Al2 crystallizes in the tetragonal I4/mmm space group and exhibits a distinct uniaxial anisotropy due to crystal field effects. In this study, we have revealed the crystal field energy levels of NdPd5Al2 composed of five Kramers doublets. The corresponding four inelastic excitations are located at energies 3.0 meV, 7.4 meV, 8.6 meV and 17.1 meV. We additionally interpreted the neutron spectra within a crystal field model. It has been established that the crystal field parameters found by a Monte Carlo technique and the derived ground-state wavefunctions consisting primarily of the states reproduce correctly magnetic susceptibility data.

Identification of local structures around Ce3+ centers in potassium magnesium fluoride

Several Ce3+ centers were experimentally found in Ce3+-doped potassium magnesium fluoride (KMgF3) crystal by electron-spin resonance (ESR) spectra, but there was no definite conclusion about the charge-compensating mechanism. In the present work, we carried out a comprehensive investigation on local structures around Ce3+ centers in the host, based on a combination of first-principles calculations and phenomenological analyses. The site occupation preference, crystal-field energy levels and spectral parameters (e.g. crystal-field parameters, and g factors) for Ce3+ ions in the host were derived, which are compatible with previously measured excitation and ESR spectra. Accordingly, four Ce3+ centers (at K+ sites) observed in ESR spectra are assigned successfully. In particular, the Ce3+ center previously thought to be associated with a Mg2+ site is reassigned to a K+ site, in agreement with the results of defect formation energy calculations. The presented calculations together with optical and ESR spectroscopy techniques may offer cross check for reliable determination of impurity sites in luminescent materials.