One-electron Crystal Field Research Articles

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.

Spin-Hamiltonian Parameters of Gd3+ Ion in the Room Temperature Tetragonal Phase of BaTiO3

Abstract The spin-Hamiltonian parameters (g factors g||, g⊥, and zero-field splittings b0 2 , b0 4 , b4 4 , b0 6 , b4 6 ) of the 4f7 Gd3+ ion in the tetragonal phase of a BaTiO3 crystal are calculated through the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters are estimated from the superposition model with the structural data of the studied crystal. It is found that by using three adjustable intrinsic parameters Āk(R0) (k=2, 4, 6) in the superposition model, the seven calculated spin-Hamiltonian parameters are in good agreement with the experimental values, suggesting that the diagonalization method based on one-electron crystal field mechanism is effective in the studies of spin-Hamiltonian parameters for 4f7 ions in crystals.

Theoretical investigation on the spin-Hamiltonian parameters for Gd3+-doped molybdates AMoO4 (A=Ca, Sr, Ba, Pb)

In this paper the spin-Hamiltonian parameters, g factors g//, g⊥ and zero-field splittings b20, b40, b44, b60, b64, for Gd3+ ion in molybdates AMoO4 (A=Ca, Sr, Ba, Pb) are calculated by a diagonalization (of energy matrix) method based on one-electron crystal field mechanism. The crystal field parameters in the matrix are calculated from the superposition model. The results indicate that seven calculated spin-Hamiltonian parameters are in good agreement with the experimental values by using only three reasonable adjustable parameters (i.e., the intrinsic parameters Ak (R0), where k=2, 4, 6, in the superposition model). It is shown that the diagonalization method can be used to calculate and explain the spin-Hamiltonian parameters of Gd3+ ion in crystals. The results are discussed.

Spin-Hamiltonian parameters for the tetragonal [formula omitted] centers in CaF2 and SrF2 crystals

The spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splittings b20, b40, b44, b60, b64) of the tetragonal GdM3+–Fi- centers in CaF2 and SrF2 crystals at T≈1.8K are calculated from the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters used are estimated from the superposition model with the reported defect structural data obtained from the analyses of superhyperfire interaction constants at the same temperature. The calculated results are in reasonable agreement with the experimental values. It appears that the above defect structural data reported in the previous paper are suitable and the diagonalization (of energy matrix) method is effective to the studies of spin-Hamiltonian parameters for 4f7 ions in crystals.

An investigation of the spin-Hamiltonian parameters for Gd3+-doped YBa2Cu3O6+y (y = 0.06) superconductor

The spin-Hamiltonian parameters (g factors g∥ and g⊥ and zero-field splittings , , , and ) for Gd3+ ions at the tetragonal Y3+ site of YBa2Cu3O6+y (y = 0.06) superconductor are calculated together from a diagonalization (of the energy matrix) method based on the one-electron crystal field mechanism. In the method, a 56 × 56 energy matrix concerning the ground multiplet 8S7/2 and the excited multiplets 8L7/2 (where L = P, D, F, G, H, I) for 4f7 ions at a tetragonal crystal field and under an external magnetic field is constructed and used. The crystal field parameters in the energy matrix are obtained from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structure (characterized by the angular distortion Δθ) of the Gd3+ impurity centers in YBa2Cu3O6+y is also acquired from the calculation. The results are discussed.

Modeling of complex oxide materials from the first principles: systematic applications to vanadates RVO3 with distorted perovskite structure

"Realistic modeling" is a new direction of electronic structure calculations, where the main emphasis is made on the construction of some effective low-energy model entirely within a first-principle framework. Ideally, it is a model in form, but with all the parameters derived rigorously, on the basis of first-principles electronic structure calculations. The method is especially suit for transition-metal oxides and other strongly correlated systems, whose electronic and magnetic properties are predetermined by the behavior of some limited number of states located near the Fermi level. After reviewing general ideas of realistic modeling, we will illustrate abilities of this approach on the wide series of vanadates RVO3 (R= La, Ce, Pr, Nd, Sm, Gd, Tb, Yb, and Y) with distorted perovskite structure. Particular attention will be paid to computational tools, which can be used for microscopic analysis of different spin and orbital states in the partially filled t2g-band. We will explicitly show how the lifting of the orbital degeneracy by the monoclinic distortion stabilizes C-type antiferromagnetic (AFM) state, which can be further transformed to the G-type AFM state by changing the crystal distortion from monoclinic to orthorhombic one. Two microscopic mechanisms of such a stabilization, associated with the one-electron crystal field and electron correlation interactions, are discussed. The flexibility of the orbital degrees of freedom is analyzed in terms of the magnetic-state dependence of interatomic magnetic interactions.

Microstructural, magnetic and crystal field investigations of nanocrystalline Dy 3+ doped zinc oxide

Dy 3+ doped zinc oxide was prepared by co-precipitation method. The as-prepared samples were annealed at different temperatures to obtain the samples with different particle sizes. The crystallographic phases of all the samples were confirmed by X-ray diffraction (XRD) patterns. Rietveld analysis of the XRD pattern of the sample annealed at 80 °C showed that most of the Dy 3+ ions were substituted in the Zn 2+ site of the hexagonal ZnO lattice. But in case of samples annealed at higher temperatures, a fraction of Dy 3+ ions comes out from the ZnO lattice and this fraction increases with the increase of annealing temperature. The sizes of nanoparticles and the lattice strains of all the samples were obtained from the Hall–Williamson plot. High resolution transmission electron microscopy showed that ZnO nanoparticles are more or less spherical. Magnetic susceptibilities ( χ) of some selected samples measured in the temperature range of 300–14 K indicate that the samples are paramagnetic. Values of χ were successfully fitted by Curie–Weiss law. A good theoretical simulation of χ of the sample annealed at 80 °C has been achieved using the one-electron crystal field interaction of the Dy 3+ ions with its diamagnetic neighbors in the hexagonal single crystal.

Magnetic susceptibilities, crystal field Stark energies, and hyperfine behavior of Sm3+ in hexagonal single crystals of Sm(CF3SO3)3⋅9H2O

Single crystals of samarium trifluoromethanesulfonate (SmTFMS) were prepared from the slow evaporation of the aqueous solution of SmTFMS. The crystals are elongated along the symmetry axis c of the hexagonal crystal. At room temperature, the c axis of the crystal sets parallel with the applied magnetic field which indicates that the susceptibility parallel to the c axis (χ∥) is greater than the susceptibility perpendicular to the c axis (χ⊥). χ∥ and χ⊥ were measured from 300 down to 14 K. Magnetic anisotropy (Δχ=χ∥−χ⊥) obtained from the values of χ∥ and χ⊥ was also checked by direct measurements of Δχ and both these results agreed very well. A crossover between χ∥ and χ⊥ has been observed at ∼56 K i.e., below this temperature χ∥<χ⊥. A good theoretical simulation of the observed magnetic data of SmTFMS has been achieved using the one-electron crystal field (CF) theory. Ordering effects in the observed magnetic data were not noticed down to the lowest temperature (∼14 K) attained, indicating the interionic interaction to be of predominantly dipolar type. To substantiate the CF analysis, the Raman and Fourier transform infrared (FTIR) spectra of the single crystal of SmTFMS were recorded in the wave number ranges of 100–1800 and 400–7000 cm−1, respectively. The calculated values of the CF Stark energies of all the excited multiplets are in agreement with those extracted from the Raman and FTIR spectra. Thermal variation of the calculated electronic specific heat shows Schottky anomaly at ∼8 K. The temperature dependences of quadruple splitting and hyperfine heat capacity were also studied.

Electronic Structure of U3+in Cs3Lu2Cl9and Cs3Y2I9Single Crystals

Low-temperature emission and polarized absorption spectra have been recorded for U(3+) ions diluted in Cs(3)Lu(2)Cl(9) and Cs(3)Y(2)I(9) host crystals. The experimental crystal-field levels were fitted to 13 parameters of a semiempirical Hamiltonian representing the combined atomic, one-electron crystal field (CF) as well as two-particle correlation crystal-field (CCF) operators. The red shift of the first f-d transitions from approximately 14,800 cm(-1) in the spectrum of U(3+):Cs(3)Lu(2)Cl(9) to as low as 11,790 cm(-1) in that of U(3+):Cs(3)Y(2)I(9) has been attributed to an increase in the covalence of the U(3+)-X(-) bonds. Comparison of the differences in the Coulomb repulsion strength between U(3+) and Er(3+) ions in Cs(3)Lu(2)Cl(9) and Cs(3)Y(2)I(9) crystals suggests that the 5f electrons of U(3+) ions are more 3d-like than 4f. The CF splitting of the (2)H(9/2) and (4)F(5/2) multiplets is unexpectedly larger for U(3+):Cs(3)Y(2)I(9) than for U(3+):Cs(3)Lu(2)Cl(9), which may be viewed as a result of the proximity of f-d states. For a correct description of the energy level structure of the (2)H(9/)(2) and (4)F(5/2) multiplets, the inclusion of CCF terms in the parametric Hamiltonian has proved to be essential. The larger f-f transition intensities for U(3+):Cs(3)Y(2)I(9) were also considered to be a consequence of the red shift of the first f-d states. The inadequacy in determination of the minor atomic parameters (other than parameters for Coulomb and spin-orbit interactions) and the insufficient inclusion of the influence of excited configuration in the applied CF Hamiltonian are assumed to be the main deficiencies preventing a better agreement between the experimental and calculated energies of CF levels.

Analysis of the Absorption and Emission Spectra of U3+ in CsCdBr3 Single Crystal

Laser selective excitation and emission spectra as well as σ- and π-polarized absorption spectra have been recorded for U 3 + ions diluted in a CsCdBr 3 host crystal. Three distinct U 3 + sites were observed. For the principal site, which was attributed to a symmetric dimer center, 45 crystal-field energy levels in the 0-13250 cm - 1 energy range were assigned. These experimentally determined levels were fitted to thirteen parameters of a semiempirical Hamiltonian representing the combined atomic, one-electron crystal field as well as two-particle correlation crystal-field (CCF) operators, with an rms deviation of 41 cm - 1 . Above 14000 cm - 1 strong electric-dipole allowed 5f 3 -5f 2 6d 1 transitions were observed. The lifetime of the 4 G 7 / 2 fluorescing level has been measured for each of the three U 3 + sites at liquid-helium temperatures and are 2.5, 4.3, and 7.6 μs. The emission is strongly influenced by temperature due to strong phonon coupling of the 5f 3 states with the nearby 5f 2 6d 1 states. Visible upconversion fluorescence observed when pumping the 4 I 9 / 2 - ( 4 F 7 / 2 + 4 I 1 5 / 2 ) absorption transitions of the principal site A is attributed to excited-state absorption (ESA).

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.

Two-photon spectroscopy of europium(III) elpasolites

We present polarized two-photon excitation (TPE) spectra, including Zeeman data, for europium(III) in the elpasolites Cs2NaEuCl6 and Cs2NaYF6:Eu3+. Approximately 80 and 60 levels of unambiguous symmetry have been assigned respectively in each compound up to 32 000 cm-1 with the aid of a one-electron crystal field Hamiltonian. This represents the most complete and extensive data set so far reported for Eu(III) at a cubic site. Comparisons are made between comparable data sets for Eu(III) f6 and Tb(III) f8. Deviations from the predictions of the one-electron crystal field model are discussed in terms of the spin correlation 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).

Magnetism of neodymium trifluoromethanesulfonate nonahydrate and effects of the crystal field

The principal magnetic susceptibilities of neodymium trifluoromethanesulfonate nonahydrate (NdTFMS) were measured between 300.0 and 12.5 K. The hexagonal crystal structure of NdTFMS is very similar to that of the hydrated rare-earth ethylsulfates with the Nd 3+ ion occupying a site of C 3h symmetry. An excellent description of the observed results was obtained using one-electron crystal field theory with the set of parameters derived from a fit to the observed absorption spectra. No ordering effects were noticed indicating the interionic interaction to be of predominantly dipolar type. The g-values were calculated to be 3.81 and 2.02 for g ∥ and g ⊥, respectively. The nuclear quadrupole splitting, and the electronic and nuclear heat capacities were also computed.

Energy levels of terbium(III) in the elpasolite Cs2NaTbCl6

Polarized two-photon excitation (TPE) and emission spectra have been used to locate, and identify the symmetry of, more than 100 energy levels of terbium(III) in the elpasolite Cs2NaTbCl6. These are assigned with the aid of a one-electron crystal field Hamiltonian. In many cases the assignments were verified by modelling the Zeeman interaction. Systematic deviations from the predictions of the one-electron model provide evidence for electron correlation induced by the crystal field (CCF).

Application of the correlation-crystal-field delta-function model in analyses of Pr 3+(4f 2) energy-level structures in crystalline hosts

The 4f 2 electronic energy-level structures observed for Pr 3+ in seven different crystalline host materials are analyzed and compared. The analyses are based on a model Hamiltonian that includes consideration of both one-electron crystal-field (CF) and two-electron correlation-crystal-field (CCF) interactions. Special attention is given to the importance of CCF interactions in determining the crystal-field energy-level structures observed within particular anomalous multiplet manifolds of Pr 3+, such as the 1D 2 and 1G 4 multiplets, which typically exhibit crystal-field energy-level structures that cannot be explained in terms of `standard' one-electron CF interaction models. It is shown in the present study that the apparently anomalous behavior of these multiplets can be explained in terms of two-electron CCF effects. It is further shown that the relevant CCF effects can be satisfactorily modeled by use of a highly restricted `delta-function' form of the general two-electron CCF model Hamiltonian, where the dominant two-electron correlation effects are assumed to arise from spin-paired electrons occupying the same angular orbital. Incorporation of this restricted CCF model Hamiltonian into the modeling calculations requires the introduction of only one or two additional parameters beyond those required for the standard one-electron CF modeling calculations, and satisfactorily resolves the major discrepancies between observed and calculated crystal-field splittings for the anomalous 1D 2 and 1G 4 multiplet manifolds in the energy-level structures of LaCl 3:Pr 3+, GdCl 3:Pr 3+, Cs 2NaPrCl 6, Cs 2NaYCl 6:Pr 3+, LiYF 4:Pr 3+, LiBiF 4:Pr 3+, and CsCdBr 3:Pr 3+.

Co- and Counterrotation of Magnetic Axes and Axial Ligands in Low-Spin Ferriheme Systems

The orientation of the principal axes of the g tensor with respect to the relationship of axial ligand planes to the porphyrin nitrogens has been studied in the framework of the one-electron crystal field model for tetragonal and rhombic low-spin d5 complexes such as ferriheme centers. All five d atomic orbitals were taken into account for two different ground-state electronic configurations, the “normal” (dxy)2(dxz,dyz)3 and the “novel” (dxz,dyz)4(dxy)1 configurations. The expressions for the g tensor, g values, and magnetic axes were derived on the basis of first-order perturbation theory. The conditions for co- and counterrotation of magnetic axes with rotation of planar axial ligands away from the porphyrin nitrogens toward the meso positions and beyond, as well as the order of g values, have been analyzed. It is found that counterrotation is the only possibility for the (dxz,dyz)4(dxy)1 configuration and that it is also by far more common for the (dxy)2(dxz,dyz)3 electron configuration. The possibili...

Energy levels of terbium(III) in the elpasolite Cs2NaTbF6

Polarized two-photon excitation (TPE) and emission spectra are presented for terbium(III) in the elpasolite Cs2NaTbF6. Almost 90 levels of unambiguous symmetry have been assigned up to 35 000 cm−1 with the aid of a one-electron crystal field Hamiltonian. This represents the most complete and extensive data set so far reported for a lanthanide ion at a cubic site. Large deviations from the predictions of the one-electron crystal field model are observed in the splitting of a number of multiplets. These are discussed in terms of the correlation crystal field (CCF).

Non-integral expansion method of f(R)YLM(Θ,φ) functions about a displaced centre

The transformation properties of f(R)YMM(Θ,φ) functions under translation of the reference system along the z axis, apart from those in relation to rotation of the system, have to be known to formulate the effective one-electron crystal field hamiltonian. The classical solution of the problem for a general radial function f(R) in the form of expansion into the spherical harmonic series has been given by Sharma in 1976. Another method avoiding integration but making use of the simple translational behaviour of the multipole functions R−(L + 1)YLM(Θ,Φ), and reduction of the Kronecker products of spherical harmonics, is presented. The method allows one to find the expansion of the f(R)YLM(Θ,Φ) function by means of the 3-j symbols only. The method is applicable to a wide class of radial functions which can be expanded into a power series. Moreover, in the case of crystal field potential, it gives a clear survey of the contributions of each local potential moment to the crystal field parameters.

Comparative correlation crystal field analysis of Er 3+ (4f 11) in garnet hosts

Comparative correlation crystal field (CCF) analyses of the Er 3+ (4f 11) energy level structure in YAG, LuAG, ErAG, ErGG, YSAG and YSGG systems are reported. These analyses are based on the use of a phenomenological Hamiltonian model that includes 20 free-ion parameters and the nine one-electron crystal field parameters plus one two-particle CCF parameter. The present analyses are carried out with a uniform Hamiltonian model and common crystal field levels spanning the lowest 12 multiplets. Comparison between the observed and calculated crystal field levels yields good agreement with rms deviations between 7.7 cm −1 (Er:ErGG) and 11.5 cm −1 (Er:YAG). The fits are in qualitative agreement with ab initio calculations of CCF effects and also with the results of CCF of the Nd 3+ ion.