Spin-correlated Crystal Field Research Articles

Evidence for a spin-correlated crystal field - two-photon spectroscopyof thulium III in the elpasolite Cs2NaYCl6:Tm

We present two-photon excitation spectra for thulium III in the elpasoliteCs2NaYCl6:Tm. 37 out of the total of 40 crystal-field (CF) levelshave been assigned, with the aid of a one-electron CF Hamiltonian,representing the most extensive data set so far reported for Tm III at acubic site. Deviations from the predictions of the one-electron CF modelare unusually large, the effective fourth-rank CF parameter being 60%larger for the singlet states than for the triplet states. This isdiscussed in terms of a spin-polarized covalency that is more pronounced inthe singlet states of the metal ion.

Simulation of optical and magnetic properties of neodymium (4f 3) in the solid state: extreme sensitivity to the wave vector’s composition

The optical absorption spectra of neodymium at 4 K are reproduced with a very good agreement between calculation and experiment (15<rms<20 cm −1). The wavefunctions which are obtained as a result of the energy calculation can be used to compute other physical properties. Among them we consider the paramagnetic susceptibility and the electron paramagnetic resonance. We report the results of these calculations concerning six compounds (Nd 2O 2S, A-Nd 2O 3, NdOCl, NdOF, Nd 3+:LaCl 3 and NdF 3) for which the optical absorption spectra were thoroughly interpreted. We notice that these properties, depending on the point symmetry of the neodymium, are very sensitive to the values of the coefficients of the kets in the wavefunctions. These wavefunctions are extremely dependent on the crystal field parameters (cfps). A regard on the magnetic properties is very useful to determine if a set of crystal field parameters which fits the overall Stark levels is also convenient for the ground state ( 4I 9/2). A comparison is also made between cfps determined from atomic positions in the structure (Simple Overlap Model) and phenomenological cfps. We also consider the effect of the spin-correlated crystal field (SCCF) through the action of its radial contribution represented by the c k parameters ( k=2,4,6).

Spin-correlated crystal field analysis of lanthanide elpasolites

Using extensive two-photon spectroscopic data sets for the lanthanide ions Sm(III), Eu(III) and Tb(III) at cubic sites, we report the results of spin-correlated crystal field (SCCF) analysis. We show these calculations to be consistent with the chemical expectations of radial wavefunction expansion and charge transfer.

Spectra, energy levels, and transition line strengths forSm3+:Y3Al5O12

Optical spectra and energy levels of the sextet, quartet, and doublet states of ${\mathrm{Sm}}^{3+}$ ${(4f}^{5})$ incorporated into single crystals of ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ $({\mathrm{Sm}}^{3+}:\mathrm{Y}\mathrm{A}\mathrm{G}),$ where YAG denotes yttrium aluminum garnet, are reported and analyzed at wavelengths between 560 and 280 nm. The analysis of energy (Stark) levels is based on a model Hamiltonian consisting of Coulombic, spin-orbit, and interconfigurational terms for the ${4f}^{5}$ atomic configuration of ${\mathrm{Sm}}^{3+}$ and crystal-field terms in ${D}_{2}$ symmetry (the site symmetry of the ${\mathrm{Sm}}^{3+}$ ions in the garnet lattice). The Hamiltonian also includes contributions arising from the spin-correlated crystal field. Because of the strength of the crystal field, the entire energy matrix is diagonalized within the complete ${4f}^{5}$ ${\mathrm{SLJM}}_{J}$ basis set representing 73 LS states, 198 ${}^{2S+I}{L}_{J}$ multiplets, and 1001 doubly degenerate crystal-quantum states. In ${D}_{2}$ symmetry, all Stark levels are characterized by the same irreducible representation ${(}^{2}{\ensuremath{\Gamma}}_{5}).$ Optimization between 314 calculated-to-observed Stark levels was carried out with a final rms deviation of 10 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Eigenvectors obtained from the crystal-field splitting analysis are used to calculate transition line strengths originating from the ground-state Stark level to Stark levels in excited manifolds. The calculated line strengths are compared with experimental line strengths obtained from the absorption spectrum at 3.8 K. The line-strength analysis is useful in identifying individual excited Stark levels associated with sextet, quartet, and doublet states strongly mixed by the crystal field.

Two-photon spectroscopy of samarium(III) in the elpasolite Cs2NaYCl6:Sm3+

We present polarized two-photon excitation (TPE) spectra for samarium(III) f5 in the elpasolite Cs2NaYCl6. Approximately 80 levels have been assigned up to 29 000 cm-1 with the aid of a one-electron crystal field Hamiltonian, representing the most complete and extensive data set so far reported for Sm(III) at a cubic site. Deviations from the predictions of one-electron theory are discussed in terms of the spin correlated crystal field (SCCF).

The Influence of Lattice Vibrations on Spin-Correlated Crystal Fields I: An Intersite Mechanism for a Dynamic Lattice

The role of lattice vibrations in providing additional contributions to spin correlated crystal fields has been investigated in the context of the calculation of zero field splittings for S-state ions. A many-electron theory, due to Stevens, which was originally developed to study exchange interactions in magnetic insulators has previously been used to study inter-site modifications to spin-correlated crystal fields in a static lattice. The present paper develops a methodology for the incorporation of lattice vibrations using a similar technique and an iterative form of perturbation theory for effective operators.

The Influence of Lattice Vibrations on Spin-Correlated Crystal Fields II: Application to Gd3+ in Lanthanum Ethylsulphate: The Structure and Classification of Matrix Elements

The Influence of Lattice Vibrations on Spin-Correlated Crystal Fields II: Application to <font>Gd³⁺</font> in Lanthanum Ethylsulphate: The Structure and Classification of Matrix Elements

The Influence of Lattice Vibrations on Spin-Correlated Crystal Fields III: Application to Gd3+ in Lanthanum Ethylsulphate: The Lattice and Comparison with Experiment

The Influence of Lattice Vibrations on Spin-Correlated Crystal Fields III: Application to <font>Gd³⁺</font> in Lanthanum Ethylsulphate: The Lattice and Comparison with Experiment

Effects of electron correlation in crystal-field splittings of Sm2+ in MFCl-type hosts.

Effects of pressure on the crystal-field splittings of the $^{5}$${\mathit{D}}_{1}$ and $^{7}$${\mathit{F}}_{1}$ multiplets were studied for ${\mathrm{Sm}}^{2+}$ in MFCl (M=Ba, Sr, and Ca). A comparison with experimental data from the literature for ${\mathrm{Eu}}^{3+}$ in different compounds at ambient pressure and partly under pressure shows that the splittings of $^{5}$${\mathit{D}}_{1}$ and $^{7}$${\mathit{F}}_{1}$ are successfully explained in the case of ${\mathrm{Eu}}^{3+}$ by the spin-correlated crystal-field (SCCF) model, when a constant SCCF parameter ${\mathit{c}}_{2}$=-0.007(3) is used. For ${\mathrm{Sm}}^{2+}$, however, the experimental results cannot be described by the same SCCF model. In fact, the pressure dependence of the splittings in the two multiplets $^{5}$${\mathit{D}}_{1}$ and $^{7}$${\mathit{F}}_{1}$ for ${\mathrm{Sm}}^{2+}$:BaFCl to ${\mathrm{Sm}}^{2+}$:CaFCl deviates extremely not only from the predictions of the conventional crystal-field models but also from the SCCF model, but these results are qualitatively explained when a significant configuration interaction between the 4${\mathit{f}}^{6}$ and 4${\mathit{f}}^{5}$5${\mathit{d}}^{1}$ configurations is taken into account. The present study shows that this 4f-5d configuration interaction results in very important contributions to correlation crystal fields for ${\mathrm{Sm}}^{2+}$ due to the close energetic proximity of these two configurations.

An electron paramagnetic resonance study of Er3+ in Bi4Ge3O12 single crystals

The X-band electron paramagnetic resonance study of Er-doped Bi4Ge3O12 single crystals at 5 K is reported. The spectra have been attributed to Er3+ ions in the Bi3+ site, confirming the assumed trigonal site symmetry of Er3+ in previous crystal-field analysis. A detailed study of the measured g-factor values indicates that corrections to the existing crystal-field parameters Bnm should be performed. It is suggested that corrections to the sixth-rank parameters are particularly important, in agreement with spin-correlated crystal-field (SCCF) effects for Er3+.

Correlations between orthorhombic crystal field parameters for rare-earth (fn) and transition-metal (dn) ions in crystals: REBa2Cu3O7-x, RE2F14B, RE-garnets, RE:LaF3and MnF2

Spectroscopic properties of rare-earth (RE) and transition-metal (TM) ions in orthorhombic symmetry sites in crystals are considered. Correlations between orthorhombic crystal field (CF) parameters are studied. The intrinsic limit on the asymmetry parameter λ = B 2 2/B 2 0 (k = B 22/B 20) is used to unify the six equivalent ways of presentation of CF parameters. Implications for analysis of the one-electron CF data as well as SCCF (spin-correlated CF) data are discussed, including the corresponding error analysis. Our results indicate that the SCCF data must be treated with caution. A multiple correlation fitting technique is suggested to increase the reliability of CF data. Correlations between several CF parameters sets for REBa2Cu3O7-x , RE2Fe14B, RE-garnets, RE:LaF3, and MnF2 are established. It is shown that the arbitrary ways of presentation of the experimental orthorhombic CF parameters should be replaced by a well defined standard form thus helping to avoid the present inconsistencies. The propose...

Absorption spectra and electron correlation of the trivalent holmium ion in LiYF4

The optical absorption spectrum of Ho3+ in LiYF4 and its Zeeman effect in magnetic fields along the crystal c axis were studied in the range from 15400 to 28500 cm-1. The quantum numbers mu of all crystal field components of Ho3+ were determined using linearly and circularly polarized transitions from the ground state. The correlated and spin-correlated crystal fields were used for a fitting procedure of the energy levels.

Comparative analysis of Nd3+(4f3) energy levels in four garnet hosts.

nets Y3A1)012 (YAG), Y3Sc~A1,0„(YSAG), Gd3Sc~Ga30l2 (GSGG), and LagLu2Ga30]2 (LLGG). The majority of Nd'+ ions substitute for Y'+, Gd'+, or La'+ ions in sites of D2 point-group symmetry in the lattice. Individual Stark levels within each manifold have been identified experimentally up to 40000 cm ' and compared with results obtained from a theoretical calculation. The model Hamiltonian includes Coulombic, spin-orbit, and interconfiguration interaction terms for the 4f atomic configuration of Nd'+ and crystal-field terms in D2 symmetry, including spin-correlated crystal-field (SCCF) contributions. The Hamiltonian was diagonalized within the complete 4f SLJMJ basis set which includes 364 states. Comparison between 148 (Nd: YAG), 140 (Nd: YSAG), 143 (Nd:GSGG), and 107 (Nd:LLGG) observed and calculated Stark levels (without SCCF) yields rms deviations of 18, 19, 17, and 16 cm, respectively. Results indicate that SCCF contributions yield modest improvement in the calculated value of the overall crystal-field splitting of the energy levels.

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.

Phenomenological spin-correlated crystal-field analyses of energy levels in Ln 3+:LaCl 3 systems

The best energy level data available in the literature for the Ln 3+:LaCl 3 systems are analyzed in terms of an electronic hamiltonian that includes isotropic (free-ion) and crystal-field interaction parameters for C 3 h 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 Ho 3+:LaCl 3, 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.

Spin-correlated crystal fields: A study of two-body and relativistic effects for Gd3+ in lanthanum ethylsulphate

Matrix elements of a spin-correlated crystal field (SCCF) operator have been evaluated using exact calculations for two-body double tensor operators and compared with earlier approximate calculations for Gd3+ in lanthanum ethylsulphate. In this latter case reductions to products of matrix elements of one-body operators were used. These approximations are shown to be accurate for the determination of zero-field splittings (ZFS) only to within 40%. Nonstandard rank combinations resulting from relativistic effects have also been incorporated which are shown to yield negligible contributions to the ZFS. The two-body form of the SCCF has been made relativistic as well in order to investigate the importance of new tensorial terms for the calculations of the ZFS. Again, their contribution has been shown to be very small.

Index of authors and papers

Matrix elements of a spin-correlated crystal field (SCCF) operator have been evaluated using exact calculations for two-body double tensor operators and compared with earlier approximate calculations for Gd3+ in lanthanum ethylsulphate. In this latter case reductions to products of matrix elements of one-body operators were used. These approximations are shown to be accurate for the determination of zero-field splittings (ZFS) only to within 40%. Nonstandard rank combinations resulting from relativistic effects have also been incorporated which are shown to yield negligible contributions to the ZFS. The two-body form of the SCCF has been made relativistic as well in order to investigate the importance of new tensorial terms for the calculations of the ZFS. Again, their contribution has been shown to be very small.

The effect of spin polarisation on the crystal field and the S ground-state splitting of Mn2+

A configuration interaction calculation and a covalency model derivation for Mn2+ are presented, giving estimates of the ck parameters describing the spin-correlated crystal field (SCCF). Expressions for the SCCF contributions to the S ground-state splitting of Mn2+ are also given.

Spin-correlated crystal-field analysis and temperature-dependent paramagnetic susceptibility of neodymium gallium garnet

The crystal-field energy levels and temperature-dependent paramagnetic susceptibility of neodymium gallium garnet (NdGG), Nd 3Ga 5O 12, are analyzed in terms of a model Hamiltonian defined to include spin-correlated crystal-field (SCCF) effects. A parametrized form of this Hamiltonian is used to fit the energies reported for 104 crystal-field levels split out of 30 different multiplets of the Nd 3+ (4 f 3) electronic configuration. Comparisons of energy level fits carried out with and without the inclusion of SCCF terms in the model Hamiltonian suggest the possible importance of SCCF effects in NdGG. Temperature-dependent paramagnetic susceptibility data are also reported for NdGG, and these data are reasonably well accounted for by calculations based on the eigenvalues and eigenvectors obtained from the crystal-field analyses.