Multiplet Manifolds Research Articles

Site-selective excitation and polarized absorption and emission spectra of trivalent thulium and erbium in strontium fluorapatite

Polarized fluorescence spectra produced by site-selective excitation, and conventional polarized absorption spectra were obtained for Tm3+ and Er3+ ions individually incorporated into single crystals of strontium fluorapatite, Sr5(PO4)3F, also known as SFAP. Substitution of the trivalent rare earth ion for divalent strontium was achieved by passive charge compensation during Czochralski growth of the fluorapatite crystals. Spectra were obtained between 1780 and 345 nm at temperatures from 4 K to room temperature on crystals having the hexagonal structure [P63/m(C6h2)]. The polarized fluorescence spectra due to transitions from multiplet manifolds of Tm3+(4f12), including D21, G41, and H43 to manifolds H63 (the ground-state manifold), F43, H53, H43, and F33 were analyzed for the details of the crystal-field splitting of the manifolds. Fluorescence lifetimes were measured for Tm3+ transitions from D21, G41, and H43 at room temperature and from G41 at 16 K. Results of the analysis indicate that the majority of Tm3+ ions occupy sites having Cs symmetry. A point-charge lattice-sum calculation was made in which the crystal-field components, Anm, were determined assuming that trivalent thulium replaces divalent strontium in the metal site having Cs symmetry. Results support the conclusion that the nearest-neighbor fluoride (F−) is replaced by divalent oxygen (O2−), thus preserving overall charge neutrality and local symmetry. Crystal-field splitting calculations predict energy levels in agreement with results obtained from an analysis of the experimental data. By varying the crystal-field parameters, Bnm, we obtained a rms difference of 7 cm−1 between 43 calculated and experimental Stark levels for Tm3+(4f12) in Tm:SFAP. Absorption and fluorescence spectra are also reported for Er3+ ions in Er:SFAP. Measurement of the temporal decay of the room temperature fluorescence from the I11/24 and I13/24 manifolds yielded fluorescence lifetimes of 230±20 μs and 8.9±0.1 ms, respectively. The experimental Stark levels obtained from an analysis of the spectroscopic data were compared with a crystal-field splitting calculation. The initial set of Bnm parameters for Er3+(4f11) was established from the three-parameter theory and the final set of Bnm parameters obtained for Tm3+(4f12) in Tm:SFAP. The best overall agreement between calculated and experimental Stark levels is 8 cm−1 for 48 Stark levels, representing 12 observed multiplet manifolds of Er3+(4f11) in Er:SFAP.

Correlation-crystal-field `δ-function' analysis of Pr3+(4f2) energy-level structure

Inclusion of two-electron correlation-crystal-field (CCF) contributions to the model (energy-level) Hamiltonian has been shown to resolve disparities between calculated and observed energy-level splittings within problematic multiplet manifolds of Nd3+ and Er3+ systems. Application of these CCF terms to other problematic multiplets, such as the 1G4 and 1D2 multiplets of Pr3+ has not been feasible, owing to the fact that the number of applicable CCF terms far exceed the number of observed levels in these multiplets. However, this problem may be obviated by use of a simplified `δ-function' CCF model that assumes the dominant contributions to the CCF interactions come from paired electrons within the same orbital. In the present study, we examine the 4f2(Pr3+) electronic energy-level structures reported for Pr3+:LaCl3, Pr3+:GdCl3, Pr3+:Cs2NaYCl6 and Cs2NaPrCl6 systems and show that inclusion of δ-function CCF interaction parameters resolves the disparities between observed and calculated energy-level splittings for the problematic 1G4 and 1D2 multiplets of these systems.

Characterization and analysis of the 4 f-electronic states of trivalent holmium in yttrium scandium gallium garnet

The electronic energy-level structure of Ho 3+-doped yttrium scandium gallium garnet (Ho: YSGG) is examined over the 0–41,600cm −1 spectral range. Data obtained from a combination of optical absorption, emission and emission excitation spectra measurements are used to locate and assign 232 of the 465 crystal-field (Stark) levels predicted to be split out of the 45 lowest-energy 4 f 10[SL]J multiplet manifolds of Ho 3+ in Ho: YSGG. The experimentally characterized energy-level structure is analyzed in terms of a model Hamiltonian defined to represent the major atomic-like (isotropic) interactions that contribute to the LS(term) and J(multiplet) structure of 4 f 10(Ho 3+), as well as the anisotropic crystal-field interactions that determine the splittings between Stark levels within the [SL]J multiplet manifolds of 4 f 10 (Ho 3+). A parameterized form of the model Hamiltonian is used to perform parametric fits of calculated to observed energy-level data, and the results obtained from these data fits show a root-mean-square deviation of < 9 cm −1 between the calculated and experimentally determined energies. The crystal-field interaction strengths and anisotropies determined in the present study for Ho 3+ in YSGG are compared to those determined previously for Ho 3+ in YAG (yttrium aluminum garnet, Y 3Al 5O 12) and for Er 3+ in both YSGG and YAG. These comparisons show small but clearly measurable differences between the crystal-field interactions operative in YSGG vs YAG (for both Ho 3+ and Er 3+ dopant ions). The most significant differences between the results obtained from comparative crystal-field analyses of the Ho 3+ vs Er 3+ systems are seen in the two-electron correlation-crystal-field (CCF) contributions to energy-level structure. Whereas CCF interactions appear to play a very important role in determining the energy-level structures of several 4 f 11(Er 3+) multiplet manifolds, no evidence is found for strong CCF effects on the energy-level structures of 4 f 10(Ho 3+) multiplet manifolds.

Polarized Optical Spectra, Transition Line Strengths, and the Electronic Energy-Level Structure of Eu(dpa)33- Complexes in Single Crystals of Hexagonal Na3[Yb0.95Eu0.05(dpa)3]·NaClO4·10H2O

Polarized optical absorption and emission measurements are used to locate and assign 52 crystal-field energy levels split out of the 4f6 electronic configuration of Eu3+ in single crystals of Na3[Yb0.95Eu0.05(dpa)3]·NaClO4·10H2O (where dpa ≡ dipicolinate dianion ≡ 2,6-pyridinedicarboxylate). In these crystals, each Eu3+ is coordinated to three dipicolinate (dpa) ligands, and the tris-terdentate Eu(dpa)33- chelate structures have trigonal-dihedral (D3) symmetry. The combined optical absorption and emission measurements provide access to the energy-level structures of 27 different 4f6[SL]J multiplet manifolds of Eu3+, and 21 of these multiplet manifolds are represented among the 52 crystal-field levels that are characterized with respect to both location (energy) and symmetry properties. The energy-level data obtained from experiment are analyzed in terms of a model Hamiltonian that includes consideration of both isotropic and nonisotropic 4f-electron/crystal-field interactions. A parametrized form of this Hamiltonian is used to perform parametric fits of calculated-to-experimental energy-level data, and the results obtained from these data fits show a root mean square (rms) deviation of 9.8 cm-1 between calculated and observed energies. The Hamiltonian parameters evaluated from the energy-level analyses provide information about both the anisotropies and the overall strength of the 4f-electron/crystal-field interactions that contribute to the energy-level structure of Eu(dpa)33- complexes. In addition to energy-level data, the absorption measurements performed in this study permit the quantitative determination of relative optical line strengths for 22 different Stark-level-to-Stark-level transitions observed in the low-temperature axial absorption spectra of Eu(dpa)33- in Na3[Yb0.95Eu0.05(dpa)3]·NaClO4·10H2O.

Polarized Optical Absorption and Emission Spectra and the Electronic Energy-Level Structure of Tb(dpa)33- Complexes in Na3[Yb0.95Tb0.05(dpa)3]·NaClO4·10H2O

Polarized optical absorption and emission measurements are used to locate and assign 60 crystal-field energy levels split out of the 4f8 electronic configuration of Tb3+ in single crystals of Na3[Yb0.95Tb0.05(dpa)3]·NaClO4·10H2O (where dpa ≡ dipicolinate dianion ≡ 2,6-pyridinedicarboxylate). In these crystals, each Tb3+ ion is coordinated to three dipicolinate (dpa) ligands, and the tris-terdentate Tb(dpa)33- chelate structures have trigonal-dihedral (D3) symmetry. The combined optical absorption and emission measurements provide access to the energy-level structures of the 17 lowest-energy 4f8[SL]J multiplet manifolds of Tb3+, and all of these multiplet manifolds are represented among the 60 crystal-field levels that are characterized with respect to both location (energy) and symmetry properties. The energy-level data obtained from experiment are analyzed in terms of a model Hamiltonian that includes consideration of both isotropic and nonisotropic 4f-electron/crystal-field interactions. A parametrized ...

Electronic absorption spectra, optical line strengths, and crystal-field energy-level structure of Nd3+ in hexagonal [Nd(H2O)9](CF3SO3)3

Abstract Optical absorption measurements are used to locate and assign 79 crystal-field (Stark) levels split out of the 4f 3 electronic configuration of Nd 3+ in single crystals of neodymium nonahydrate tris(trifluoromethanesulfonate), [Nd(H 2 O) 9 ](CF 3 SO 3 ) 3 , denoted hereafter as NdTRF. Line strengths are determined for 56 transitions between Stark levels. Single crystals of NdTRF have hexagonal, P6 3 /m(C 6h 2 ) space-group symmetry, and each Nd 3+ ion is coordinated to nine water molecules in a slightly distorted tri-capped trigonal prism structure of C 3h symmetry. The energy-level structure of 4f 3 (Nd 3+ ) in NdTRF is analyzed in terms of a model Hamiltonian that includes consideration of both one-electron crystal-field and two-electron correlation-crystal-field interactions, the latter interactions making important contributions to the energy-level structures of several 4f 3 [ SL ] J multiplet manifolds. Line strength data obtaibned for NdTRF is analyzed in terms of a general 4f → 4f transition intensity model in which the details of the 4f-electron/crystal-field/electric-dipolar radiation-field interactions are represented in parametric form. The derived parameters provide information about structural properties and interaction mechanisms that contribute to 4f → 4f transition intensities. The general crystal-field and intensity parameters are further analyzed in terms of a set of ‘intrinsic’ parameters that are related to contributions from individual Nd 3+ OH 2 pairwise interactions.

Electronic spectra, optical activity, and crystal-field energy-level structure of Dy3+ in trigonal Na3[Dy(oda)3].cntdot.2NaClO4.cntdot.6H2O crystals

Optical absorption and emission measurements are used to locate and assign 152 crystal-field energy levels split out of the 4f{sup 9} electronic configuration of Dy{sup 3+} in Na{sub 3}[Dy(oda){sub 3}]{center_dot}2NaClO{sub 4}{center_dot}6H{sub 2}O (where oda denotes an oxydiacetate ligand). The absorption measurements span the 230-1800 nm wavelength range, and they encompass all optical transitions that may occur between the {sup 6}H{sub 15/2} ground multiplet and 63 different excited multiplet manifolds of the 4f{sup 9}(Dy{sup 3+}) electronic configuration.

Electronic energy-level structure of trivalent holmium in yttrium aluminum garnet

The optical-absorption spectrum of Ho3+:Y3Al5O12 (Ho:YAG) has been analyzed between 220 and 2160 nm under variable temperature conditions between 4 and 60 K. Measurements between 220 and 470 nm were obtained from a Ho:YAG crystal that contained 15 at. % holmium. A crystal containing 0.5 at. % holmium was used to obtain the spectrum between 470 and 2160 nm. Within the temperature and total spectral range, more than 1500 transitions due to Ho3+(4f10) were observed and attributed to transitions between individual crystal-field (Stark) levels of the ground-state multiplet 5I8, and 49 different excited multiplet manifolds, 4f10(2S+1LJ), of trivalent holmium. From an analysis of these transitions it was possible to establish 419 of the 486 Stark levels predicted below 45 000 cm−1. This large number of experimentally characterized energy levels provided a suitable basis for a detailed analysis of the 4f10(Ho3+) electronic state structure in Ho:YAG. The analysis was carried out using a model Hamiltonian that assumes D2 site symmetry for the Ho3+ ions and incorporates all of the interactions known to have a significant influence on the 4fN electronic state structure of trivalent lanthanide ions in crystalline hosts. The radial-dependent parts of the interaction terms in the model Hamiltonian are represented in parametric form, and the resulting parameters are used as variables in fitting calculated-to-experimental energy-level data. The parametric fits of energy-level data yield a rms deviation of ∼11 cm−1 between the calculated and observed locations of the 419 experimentally assigned levels (between 0 and 45 000 cm−1), and both the isotropic and anisotropic (crystal-field) interaction parameters of the model Hamiltonian are well characterized by these data fits. Among the 50 4f10[SL]J multiplet manifolds represented in the energy-level analysis, only three show major discrepancies between calculated and observed crystal-field splitting energies. The three problematic multiplet regions are: (5G6, 5F1), centered at 22 258 cm−1, 5G5, centered at ∼24 040 cm−1; and (5G3, 3L9), centered close to 28 950 cm−1. These same multiplet regions have posed problems in energy-level analyses of Ho3+(4f10) in other systems. The possible influence of correlation crystal-field (CCF) interactions on these multiplet manifolds is explored in the present study, but CCF effects appear to be small. Overall, the model Hamiltonian derived gives an excellent representation of 4f10(Ho3+) energy-level structure in Ho:YAG, and the eigenvectors of this Hamiltonian should provide a satisfactory basis for future calculations and modeling studies of Ho:YAG optical and magneto-optical properties.

Energy-level and line-strength analysis of optical transitions between Stark levels in Nd3+:Y3Al5O12.

Results obtained from optical absorption measurements on ${\mathrm{Nd}}^{3+}$:${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ (Nd:YAG) at 10 and 29 K are reported and analyzed. The low-temperature (10 K) absorption spectrum shows transitions from the lowest Stark component of the $^{4}$${\mathit{I}}_{9/2}$ (ground) multiplet to 133 of the 155 crystal-field (Stark) levels predicted to be located between 3900 and 40 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, spanning 35 excited multiplet manifolds of ${\mathrm{Nd}}^{3+}$(4${\mathit{f}}^{3}$). Among the 133 transitions observed in the 10-K absorption spectrum, 97 are sufficiently well resolved to permit quantitative determination of transition line strengths. Energy levels for the $^{4}$${\mathit{I}}_{9/2}$ and $^{4}$${\mathit{I}}_{11/2}$ multiplets are taken from previously obtained optical emission measurements, and the resulting 144-level data set is analyzed in terms of a model Hamiltonian that assumes ${\mathrm{D}}_{2}$ site symmetry for the ${\mathrm{Nd}}^{3+}$ ions in Nd:YAG. Inclusion of two-electron correlation crystal-field (CCF) interaction terms in the model Hamiltonian explains the crystal-field splittings of several anomalous multiplets, and reduces the rms deviation between calculated and observed energies (for 144 levels) from 28 to 14 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The optical line-strength data obtained in this study are analyzed in terms of an f-f transition intensity model developed by us in previous work. This model has broad applicability in analyses of f-f intensity data for transitions between Stark levels. Emission branching ratios for transitions from the $^{4}$${\mathit{F}}_{3/2}$ multiplet are calculated and compared with literature values.

Optical spectra, energy levels, and emission intensity calculations of trivalent thulium ions in gadolinium scandium gallium garnet

Absorption spectra of trivalent thulium ions in gadolinium scandium gallium garnet are reported between 1.9 and 0.25 μm at 4 K. Laser-induced fluorescence was observed at 4 K from the 1D2, 1G4, and 3H4 (4 and 300 K) manifolds. Site-selective excitation experiments reveal large fractions of thulium ions in both regular D2 sites and alternate sites. A crystal-field splitting calculation was carried out in which a parameterized Hamiltonian (including Coulombic, spin-orbit, and crystal-field terms in D2 symmetry) was diagonalized for all multiplet manifolds of the Tm3+ (4f12) configuration. The rms deviation between 56 experimental and calculated Stark levels was 10 cm−1. Calculations were carried out to predict branching ratios for emission from the 3H4 manifold to the 3H5, 3F4, and 3H6 manifolds, as well as line-to-line transition probabilities for transitions between the 3H4 manifold and the 3H5 manifold.

Energy levels and correlation crystal-field effects in Er3+-doped garnets.

The crystal-field energy-level structures of three different ${\mathrm{Er}}^{3+}$-doped garnet systems are analyzed and compared in this study. The garnet hosts are ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ (YAG), ${\mathrm{Y}}_{3}$${\mathrm{Sc}}_{2}$${\mathrm{Al}}_{3}$${\mathrm{O}}_{12}$ (YSAG) doped with ${\mathrm{Tm}}^{3+}$ as a sensitizer ion, and ${\mathrm{Y}}_{3}$${\mathrm{Sc}}_{2}$${\mathrm{Ga}}_{3}$${\mathrm{O}}_{12}$ (YSGG) doped with ${\mathrm{Cr}}^{3+}$ as a sensitizer ion. The focus is on energy levels assigned to ${\mathrm{Er}}^{3+}$ ions substituted for ${\mathrm{Y}}^{3+}$ at dodecahedral (${\mathit{D}}_{2}$ symmetry) sites in the cubic garnet lattices. Analyses are carried out on experimental energy-level data that span up to 29 different $^{2\mathit{S}+1}$${\mathit{L}}_{\mathit{J}}$ multiplet manifolds (between 0 and 44 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) of the ${\mathrm{Er}}^{3+}$ 4${\mathit{f}}^{11}$ electronic configuration. These data include the locations of 117 crystal-field levels of ${\mathrm{Er}}^{3+}$ in YAG, 109 levels of ${\mathrm{Er}}^{3+}$ in YSAG, and 92 levels of ${\mathrm{Er}}^{3+}$ in YSGG.The energy-level analyses are based on the use of a parametrized model Hamiltonian for the 4${\mathit{f}}^{11}$ electronic configuration of ${\mathrm{Er}}^{3+}$ in a crystal field of ${\mathit{D}}_{2}$ symmetry. The model Hamiltonian includes both atomic (``free-ion'') and crystal-field interactions, parametrized to fit calculated eigenvalues to experimentally observed energies. The crystal-field part of the Hamiltonian is defined to include the standard one-electron interaction operators, as well as additional operators that provide a partial, phenomenological consideration of electron-correlation effects in the 4f-electron--crystal-field interactions. The latter, correlation crystal-field (CCF) interactions, are introduced to address crystal-field splittings within several J-multiplet manifolds that are poorly represented by one-electron crystal-field interaction models. Inclusion of CCF terms in the model Hamiltonian leads to dramatic improvement in the fits between calculated and observed crystal-field splittings within the problematic multiplet manifolds. All of the energy-level analyses reported in this study were carried out within commensurate parametrization schemes, and the Hamiltonian parameters derived from these analyses provide a suitable basis for comparing the 4f-electron--crystal-field interaction properties of ${\mathrm{Er}}^{3+}$ in YAG, YSAG, and YSGG. These analyses are based entirely on experimental data that specify the locations of energy levels, but do not provide any explicit information about the angular momentum (${\mathit{JM}}_{\mathit{J}}$) compositions of the crystal-field wave functions.

Energy levels and upconversion fluorescence in trivalent thulium-doped yttrium scandium aluminum garnet

Absorption spectra of Tm3+ ions in yttrium scandium aluminum garnet are reported between 1.9 and 0.25 μm at 4 K. Laser-excited fluorescence was observed at 4 K from Tm3+(4f12) multiplet manifolds 1D2, 1G4, 3F2, and 3H4 to the ground-state manifold 3H6. Emission from 1D2 and 1G4 also includes transitions to Stark levels in manifolds 3F4 and 3H5. Upconversion excited fluorescence was observed between 1D2 and 3F4 at 10 K. Analysis of the fluorescence emission confirms assignments given to individual Stark levels based on an analysis of the absorption spectra. A crystal-field splitting calculation was carried out in which a parameterized Hamiltonian (including Coulombic, spin-orbit, and crystal-field terms in D2 symmetry) was diagonalized for all multiplets of the Tm3+(4f12) configuration. The rms deviation between 42 experimental and calculated Stark levels was 8 cm−1.

Analysis of the optical spectra of trivalent holmium in yttrium scandium gallium garnet

The absorption spectrum of Ho3+ ions in yttrium scandium gallium garnet (Ho3+:YSGG) is reported at 4 K between 1.93 and 0.28 μm. Laser excitation spectra and laser-excited fluorescence spectra from Ho3+(4f10)2S+1LJ multiplet manifolds 5F4, 5S2, and 5F3 to the ground-state manifold 5I8 were obtained at 4, 8, and 70 K. Unresolved emission is observed from Ho3+ ions in slightly disturbed cation (Y3+) sites along with emission coming from Ho3+ ions occupying the regular cation (Y3+) sites having D2 symmetry. Temperature-dependent transitions (hot bands) observed in absorption at 8 and 70 K establish experimental crystal-field split (Stark) levels in 24 excited manifolds and the seven lowest energy Stark levels in 5I8 (Z1=0, Z2=6, Z3=17, Z4=29, Z5=87, Z6=95, and Z7=102, all in cm−1). An algorithm is used to establish D2 symmetry labels Γ1, Γ2, Γ3, or Γ4 of individual experimental Stark levels. These levels are compared with results obtained from a calculation in which a parameterized Hamiltonian was diagonalized within the 50 lowest multiplet manifolds of Ho3+(4f10). Comparison between 157 experimental Stark levels and the corresponding predicted levels out of a total of 486 calculated levels yields a root-mean-square deviation of 5 cm−1.

Spectroscopic analysis of Tm3+:NaLa(MoO4)2

Absorption spectra of trivalent thulium (Tm3+, 4f12) doped double molybdate NaLa(MoO4)2 (NLM) are reported between 370 and 2000 nm at approximately 16 K. Laser-excited fluorescence spectra obtained at 4.2 K from multiplet manifolds 1G4 and 3H4 to manifolds 3F4 and the ground state 3H6 are also reported. The observed spectra are broad in this disordered host as compared with the spectra observed for Tm3+:YAG (yttrium aluminum garnet). The observed crystal field splitting of the multiplet manifolds in Tm3+:NLM is in reasonable agreement with the calculated splitting based on smoothed crystal field parameters obtained from an analysis of Nd3+:NLM and Er3+:NLM. The smaller crystal field splitting in Tm3+:NLM as compared with Tm3+:YAG may discourage cross-relaxation from the 3H4 to the 3F4 manifold in this host. This in turn may favor laser operation on the 3H4→3F4 transitions over the 3F4→3H6 transitions.

X-ray-photoemission-spectroscopy study of the electronic structure of Am metal and AmHx (for x

In order to test the proposal that the anomalous valence-level photemission spectrum of Am results from a divalent (5${\mathit{f}}^{7}$) surface layer, we have performed variable-takeoff-angle experiments on the metal. 4f spectra obtained at 10\ifmmode^\circ\else\textdegree\fi{} and 85\ifmmode^\circ\else\textdegree\fi{} off normal showed no significant difference in the intensity of the 5${\mathit{f}}^{7}$ (i.e., f-screened) satellite, which is not consistent with an electronically altered surface. Core and valence spectra of a hydrided sample were also obtained for comparison. Pronounced differences in the 5f-derived multiplet manifold were evident, and suggest that alternate screening channels are responsible for the additional features in the metal spectrum. Differences in the metal and hydride 4f peak shapes and satellite intensities are discussed.

Energy levels and crystal quantum states of trivalent holmium in yttrium aluminum garnet

Absorption spectra of Ho3+ ions in yttrium aluminum garnet (Ho3+:YAG) are reported between 2.16 and 0.23 μm at various temperatures between 4 K and room temperature. Laser-excited excitation spectra and emission spectra from the 5F4 and 5S2 multiplet manifolds to the ground state manifold 5I8 were obtained at 4, 20, and 55 K. The majority of Ho3+ ions substitute for Y3+ ions in sites of D2 point-group symmetry in the lattice. Over 1000 temperature-dependent transitions (hot bands) establish 280 experimental Stark levels of the 4 f 10(2S+1LJ) multiplet manifolds. Symmetry labels Γ1, Γ2, Γ3, or Γ4, appropriate to D2 symmetry, have been assigned to Stark levels up to 43 000 cm−1. Experimental levels are compared with results obtained from a theoretical calculation. The model Hamiltonian includes Coulombic, spin-orbit, and interconfiguration interaction terms for the 4 f 10 atomic configuration of Ho3+ and crystal-field terms in D2 symmetry. The Hamiltonian was diagonalized within the 50 lowest 2S+1LJ manifolds in a LSJMJ basis set that includes 486 calculated levels. Comparison between 151 experimental Stark levels and the corresponding levels of the lowest 199 calculated levels yields an rms deviation of 4.3 cm−1.

Crystals field energy levels and transition line strengths of neodymium in trigonal Na 3[Nd(oxydiacetate) 3]·2NaClO 4·6H 2O

Locations and assignments of 119 crystal-field levels are reported for Nd 3+ in the trigonal Na 3[Nd(oxydiacetate) 3]·2NaClO 4·6H 2O levels span 34 of the 37 J-multiplet manifolds split out of the 4f 3 electronic configuration of Nd 3+ between 0 and 40000 cm −1, and they were located and assigned from axial and orthoaxial (σ- and π-polarized) absorption measurements performed on single crystals at temperatures between 4.2 and 300 K. The energy level data are analyzed in terms of a parameterized model Hamiltonian for the 4f 3 electronic configuration, assumed to be perturbed by a crystal field of trigonal dihedral (D 3) symmetry. Parametric fits of calculated to empirical energy level data yields rms deviations (between calculated and observed energies) of ≈ 14 cm −1 for 119 levels and ≈ 12 cm −1 for the subset of 71 levels that derive from multiplet manifolds with J ⩽ 9/2. The Hamiltonian parameter values obtained from these energy level analyses are reported and are compared with results obtained from similar analyses of Nd 3+ in other crystals and of other Ln 3+ ions in the Na 3[Ln(oxydiacetate) 3]. 2NaClO 4·6H 2O system. In addition to energy level locations and assignments, quantitatively determined line strengths are reportedfor 47 trans low-temperature π-polarized orthoaxial absorption spectra. All of these transitions originate in the ground crystal-field level of the 4I 9 2 (ground) multiplet, and each occurs via a predominantly electric-dipole mechanism.

Comparative Crystal‐Field Analyses of 4fN Energy Levels in LiYF4:Ln3+ Systems

AbstractComparative analyses of the 4fN(Ln3+) energy level structures in a series of LiYF4:Ln3+ systems are reported. These analyses focus on empirical energy level data currently available in the literature for the Pr3+, Nd3+, Eu3+, Dy3+, Ho3+, Er3+, and Tm3+ systems, and they are based on the use of a phenomenological Hamiltonian that permits trans‐series comparisons of 4f‐electron/crystal‐field interactions. Spin‐correlated crystal‐field (SCCF) interactions are considered in the phenomenological energy level analyses of the Pr3+, Nd3+, Er3+, and Tm3+ systems. Differences between analyses carried out with and without inclusion of SCCF effects are most apparent for the Er3+ and Tm3+ systems. For these systems, inclusion of SCCF effects leads to significant improvement in agreement between calculated and observed crystal‐field splittings within certain multiplet manifolds. The calculated crystal‐field energy level structures within the 1G4 and 1D2 multiplets of Tm3+ and the lowest‐energy 2H11/2 multiplet of Er3+ exhibit particular sensitivity to the SCCF components of the model Hamiltonian. Comparisons between the present work and previously reported analyses of LiYF4:Ln3+ systems are presented.

Spin‐Correlated Crystal‐Field Analyses of the 4f2(Pr3+) Energy Levels in LiYF4:Pr3+ and LiBiF4:Pr3+

AbstractComparative analyses of the 4f2(Pr3+) energy level structure in LiYF4:Pr3+ and LiBiF4:Pr3+ are reported. These analyses are based on a phenomenological crystal‐field model that includes some (partial) consideration of electron‐correlation effects in the 4f‐electron‐crystal‐field interactions. Parametric fits of calculated‐to‐experimental energy level data are reported for a 48‐level data set for LiYF4:Pr3+, a 38‐level data set for LiBiF4:Pr3+, and a data set that contains 37 levels assigned in common for the two systems. The 4f2 energy level structure is qualitatively similar in the two systems, but the LiYF4:Pr3+ system exhibits slightly stronger crystal‐field interactions. Inclusion of spin‐correlated crystal‐field (SCCF) interactions in the phenomenological energy level analyses produces slightly improved agreement between calculated and empirical results, but it does not resolve major discrepancies between calculated and observed crystal‐field splittings within the 1G4 and 1D2 multiplet manifolds.

Optical absorption spectra, crystal-field analysis, and electric dipole intensity parameters for europium in Na 3[En(ODA) 3]-2NaClO 4·6H 2O

Locations and assignments of 61 crystal-field levels are reported for Eu 3+ in the trigonal Na 3[Eu(oxydiacetate) 3]· 2NaClO 46H 2O system. These energy levels span the 0-37400 cm − energy region, and they were located and assigned from optical emission spectra and from axial and orthoaxial (σ and π-polarized) absorption measurements on single crystals. The assigned crystal-field levels span 22 different multiplet manifolds, with principal parentages derived from seven different f 6 Russell-Saunders terms ( 2F, 5D, 5L, 5H, 5F, 5I, and 5K). The assigned levels are analyzed in terms of a 26-parameter electronic Hamiltonian in which six of the parameters are defined to represent the 4f-electron/crystal-field interactions for Eu 3+ ions located at sites with trigonal dihedral (D 3) symmetry. Quantitative line intensities are reported for 39 individual 4f→4f (crystal-field) transitions observed in the low-temperature (10 K) absorption spectra, and these intensity data are analyzed in terms of a general parametric model for 4f→4f transition intensities in lanthanide systems. The energy and intensity parameterizations provide a basis for calculating the 4f→4f absorption spectra of Eu 3+ in Na 3[Eu(oxydiacetate) 3]· 2NaClO 4·6H 2O over a wide spectral range and excellent agreement between calculated and experimentally measured spectra is obtained. Several of the intensity parameters determined to be important in this study carry information of particular significance to understanding the structural and mechanisticbases of lanthanid