Michael F. Reid

Energy levels of lanthanide ions in the cubic Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ (doped) systems

The best available energy level data for the cubic Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ (doped) systems are collected together and summarized. These data are analyzed in terms of a parametric model which assumes an octahedral (Oh) site symmetry for the Ln3+ ions and a 4 f N ‘‘free‐ion’’ Hamiltonian similar to that used previously in energy level analyses of the LaCl3:Ln3+ systems. The empirical energy level data are fit to the parametrized 4 f N Hamiltonian, and the resulting ‘‘best‐fit’’ parameter sets and calculated energy levels are presented and discussed.

Electric dipole intensity parameters for lanthanide 4f → 4f transitions

A general parametrization scheme for the electric dipole intensities of lanthanide 4f → 4f crystal‐field transitions is proposed. This parametrization is sufficiently general to accommodate any 4f → 4f intensity mechanism based on the ‘‘one‐electron’’ and ‘‘one‐photon’’ approximations for lanthanide‐ligand‐radiation field interactions. It includes as a subset, the familiar Judd–Ofelt–Axe intensity parameters, AtpΞ(t, λ), but introduces additional parameters which are shown to be essential in cases where the lanthanide‐ligand pairwise interactions cannot be assumed to be cylindrically symmetric. Expressions are given for calculating the general intensity parameters in terms of two specific intensity mechanisms. Special consideration is given to the effects of ligand polarizability anisotropy on the intensity parameters. A set of ‘‘intrinsic’’ intensity parameters are also introduced. These parameters are defined within the context of the ‘‘superposition’’ model for lanthanide‐ligand interactions, and are i...

Correlation crystal field analyses with orthogonal operators

The construction of orthogonal operators to represent correlation crystal field (CCF) effects in the f N configuration of lanthanide and actinide ions is discussed. The approach of B. R. Judd [J. Chem. Phys. 66, 3163 (1977)] is extended to make all the operators orthogonal. The spin‐correlated crystal field (SCCF) parametrization that has been successful in removing several long‐standing anomalies from crystal field fits involves only two of the two‐electron orthogonalized operators. We calculate values of the orthogonal CCF parameters from recent ab initio results. On the basis of these calculations the sixth rank SCCF operators are predicted to be very important. Fits using various combinations of the CCF parameters are reported for Ho3+ and Gd3+in LaCl3. For these systems we only obtain consistent results for the parameters associated with the sixth rank SCCF.

Phenomenological spin-correlated crystal-field analyses of energy levels in Ln3+:LaCl3 systems

The best energy level data available in the literature for the Ln3+:LaCl3 systems are analyzed in terms of an electronic hamiltonian that includes isotropic (free-ion) and crystal-field interaction parameters for C3h site symmetry. The crystal-field hamiltonian is defined to include spin-correlated crystal-field (SCCF) interaction terms, and analyses are carried out with and without consideration of these SCCF terms. The analyses reported here yield improved calculated-vs.-experimental energy level fits (compared to fits reported previously in the literature). For example, for Ho3+:LaCl3, the value of sigma is improved from 7.8 to 4.9 cm−1 for 168 crystal-field levels. In each case, inclusion of the SCCF terms improves the calculated-vs.-experimental energy level data fits. Ratios of the SCCF vs. one-electron crystal-field parameters are reported and compared for each system.

Analysis of spectral data and comparative energy level parametrizations for Ln3+ in cubic elpasolite crystals

Abstract Comparative analyses have been made of the 4f n lanthanide ion (Ln 3+ ) energy level structures in a variety of cubic elpasolite crystals. The systems can be grouped into two sets, namely (i) Ln 3+ in the neat compounds: Cs 2 NaLnCl 6 (LnCeYb, except for Nd, Pm and Sm), Cs 2 LiErCl 6 Cs 2 NaLnBr 6 (LnPr, Ho, Tm), Cs 2 KPrF 6 and Rb 2 NaEuF 6 ; and (ii) Ln 3+ diluted into elpasolite host crystals: Cs 2 NaYCl 6 :Ln 3+ (LnPr, Sm, Eu), Cs 2 NaGdCl 6 :Ln 3+ (LnHo, Nd) and Cs 2 KYF 6 :Eu 3+ . New energy level data obtained from low temperature absorption, emission and electronic Raman studies are presented for these systems to provide more accurate and extensive data sets. The new energy level data were analysed in terms of a 4f n “free-ion” Hamiltonian and a parametric crystal field Hamiltonian model, with octahedral ( O h ) site symmetry for the Ln 3+ ion. The empirical energy level data were fitted to the parametrized total Hamiltonian and the resulting “best-fit” parameter sets are presented and discussed. Examination of the parameter values obtained from least-squares fittings reveals significant differences in the crystal field perturbations experienced by the 4f electrons of Ln 3+ at octahedral sites: the fluoride ligands interact with the 4f electrons somewhat more strongly than do the bromide ligands. The phenomenological (fitted) crystal field parameters of Cs 2 NaLnCl 6 do not exhibit a clear trend across the series of lanthanide elements, partly because of the uncertainty in determination due to the term dependence. The magnitude of the B k 0 ( k = 4,6) parameters follow different patterns in the LaCl 3 :Ln 3+ , LaF 3 :Ln 3+ and LiYF 4 :Ln 3+ systems. However, the magnitudes of the “free-ion” parameters resulting from free variation in the elpasolite system data fits exhibit clearer trends and the spin-orbit coupling constant is found to fit well to a second-order polynomial in atomic number. The standard deviations of the data fits as defined herein are between 0 and 43 cm −1 , so that the energy level schemes of the Ln 3+ ions in elpasolite lattices are reasonably well reproduced.

Analysis of the crystal‐field spectra of the actinide tetrafluorides. I. UF4, NpF4, and PuF4

An interpretation of the low‐temperature absorption spectra of AnF4 (An=U, Np, Pu) is presented. Using an effective operator Hamiltonian with orthogonalized free‐ion operators and initializing crystal‐field parameter values based on a superposition model calculation for An4+ sites with C2 symmetry, good agreement between the model calculations and experimentally observed absorption band structure could be obtained. Correlations with published magnetic and heat capacity measurements are discussed.

Free‐ion, crystal‐field, and spin‐correlated crystal‐field parameters for lanthanide ions in Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ systems

Free‐ion and crystal‐field energy parameters for trivalent lanthanide ions (Ln3+) in Cs2NaLnCl6 and Cs2NaYCl6 are presented and discussed. Spin‐correlated crystal‐field parameters are determined for those systems for which sufficient data are available. The superposition model is used to compare the crystal‐field interactions in the Cs2NaYCl6:Ln3+ and LaCl3:Ln3+ systems.

Comparison of calculated and experimental 4f → 4f intensity parameters for lanthanide complexes with isotropic ligands

Calculations of 4f → 4f electric dipole intensity parameters are reported for six different lanthanide (III) systems whose solid‐state structures and optical spectra have been well characterized. In each case, the ligands are considered to have isotropic electronic charge distributions, and the 4f → 4f intensity parametrization is expressed in terms of the parameters Aλλ±1,p(λ=2, 4, and 6), which have been defined in a previous paper (see paper I). The calculations include contributions to these parameters from both the static‐coupling and dynamic‐coupling intensity mechanisms. Comparisons between the calculated and empirically determined signs of the Aλλ±1,p parameters suggest that, in most cases, the dynamic‐coupling mechanism makes the dominant contributions to the Aλλ+1,p parameters. The empirically determined signs of the Aλλ−1,p parameters correlate with those calculated on the basis of the static‐coupling mechanism. For isotropic ligands, the dynamic‐coupling mechanism cannot contribute to the Aλλ−...

Correlation-crystal-field analysis of Nd3+(4f3) energy-level structures in various crystal hosts

We have performed an in-depth correlation-crystal-field (CCF) analysis of the energy-level structures in 10 Nd3+(4f3) crystal systems: NdF3, Nd2Te4O11, NdVO4, NdPO4, Nd3+:LiYF4, Nd3+:LaVO4, Nd3+:LaCl3, Nd3+:BaY2F8, Nd3+:YAlO3 and Nd3+:LuA1O3. A model Hamiltonian employing 20 free-ion parameters, appropriate one-electron crystal-field interaction parameters and also selected two-particle CCF interaction parameters was diagonalized within the complete 364 SLJMJ basis set of the 4f3 electronic configuration. Inclusion of the fourth-rank g2(4), g10A(4) and g10B(4) CCF operators in the phenomenological energy-level fits yields an overall improved agreement between calculated and empirical energy levels besides eliminating major discrepancies between calculated and observed crystal-field splittings within the anomalous 2H(2)11/2 multiplet of Nd3+ ion. The fits are also in qualitative agreement with the ab initio calculations of CCF effects for lanthanide ions.

Comprehensive Spectroscopic Determination of the Crystal Field Splitting in an Erbium Single-Ion Magnet

The electronic structure of a novel lanthanide-based single-ion magnet, {C(NH2)3}5[Er(CO3)4]·11H2O, was comprehensively studied by means of a large number of different spectroscopic techniques, including far-infrared, optical, and magnetic resonance spectroscopies. A thorough analysis, based on crystal field theory, allowed an unambiguous determination of all relevant free ion and crystal field parameters. We show that inclusion of methods sensitive to the nature of the lowest-energy states is essential to arrive at a correct description of the states that are most relevant for the static and dynamic magnetic properties. The spectroscopic investigations also allowed for a full understanding of the magnetic relaxation processes occurring in this system. Thus, the importance of spectroscopic studies for the improvement of single-molecule magnets is underlined.