Modeling Spectroscopic Properties of Ni2+ Ions in the Haldane Gap System Y2BaNiO5.

Modeling of spin Hamiltonian parameters enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions in crystals. In this paper, based on the crystallographic data and utilizing the point-charge model and superposition model, the crystal field parameters (CFPs) are estimated for Ni2+(3d8) ions in the Haldane gap system Y2BaNiO5. The CFPs serve as input for the perturbation theory expressions and the crystal field analysis package for microscopic spin Hamiltonian modeling of the zero-field splitting parameters (ZFSPs) D and E. Results of an extensive literature search of the pertinent crystallographic data, experimental ZFSPs, and model parameters are briefly outlined. The modeling aims at verification of the experimental 'single ion anisotropy' parameters and explanation of the controversy concerning the maximal rhombic distortion |E/D| ≈1/3 reported for Ni2+ ions in Y2BaNiO5. The preliminary results call for reanalysis of some magnetic studies of the Haldane gap systems.

Optical spectra and energy levels analysis of the 4f(N) ions doped into Ba2YCl7.

Absorption emission and excitation spectra are measured and analyzed to achieve assignments of energy levels for 4f(N) ions in Ba(2)YCl(7):RE(3+) (RE = Pr, Nd, Tb, Dy, Ho, Er, and Tm) crystals. The experimental energy levels were analyzed in terms of the usual free-ion parameters and the crystal field (CF) ones, B(kq), in the Wybourne notation. The orthorhombic C(2v) symmetry is shown to be a good approximation of the actual triclinic C(1) site symmetry at the metal center. The starting values of the CF parameters B(kq) used for fittings for the studied crystals were obtained from superposition model analysis. A good agreement between the calculated and experimental energy levels was obtained with rms deviations in the range from 6.8 cm(-1) (for Ho(3+)) to 14.1 cm(-1) (for Pr(3+)). The fitted sets of B(kq) parameters are, in general, consistent across the 4f(N) series. This study has enabled determination and discussion of the trends in variation of the free-ion parameters and CF ones across the 4f(N) series. The CF parameter set and energy level structure obtained for Nd(3+) ion in Ba(2)YCl(7) crystal are consistent with those for Nd(3+) in structurally related RbY(2)Cl(7) crystal. This systematic analysis of CF parameters is one of only few such studies encompassing nearly whole series of RE(3+) ions.

Energy levels and crystal field parameters for Nd3+ ions in BaY2F8, LiKYF5, and K2YF5 single crystals.

The available experimental energy levels of Nd(3+) ions doped into single crystals of BaY(2)F(8), LiKYF(5), and K(2)YF(5), which exhibit low site symmetry, are reanalyzed. A combined approach based on the ascent/descent in symmetry (ADS) method, the superposition model (SPM) analysis, and the pseudosymmetry axes method (PAM) is utilized to extract the crystal field (CF) parameters, B(kq), from experimental spectra. Corresponding sets of the free-ion parameters are also fitted. The crystallographic data are used to establish the axis systems most appropriate for approximation of the actual monoclinic C(2) site symmetry to higher orthorhombic D(2) and tetragonal D(4) symmetry used in CF calculations for BaY(2)F(8). Similarly, for triclinic C(1) site symmetry in LiKYF(5) and K(2)YF(5) approximation to monoclinic C(2) and orthorhombic D(2) symmetry for LiKYF(5), whereas the monoclinic C(s) symmetry for K(2)YF(5), are considered. It is shown that the C(2v) approximation used previously for K(2)YF(5):Nd(3+) is not suitable. SPM enables to calculate for the unapproximated and idealized polyhedrons YF(8) in a given ion-host system of the combined coordination factors Sg(k,q) expressed in the modified crystallographic axis system CAS* and approximated symmetry adapted axis systems, respectively. The quantities Sg(k,q) serve as input for PAM calculations for independent determination of the axis system appropriate for higher symmetry approximations. The pseudosymmetry axes represent the axis system that reflects most closely the approximated higher symmetry of the nearest ligands in a paramagnetic complex embodied in the 4th-rank CF parameters. The combined ADS/SPM/PAM approach provides sets of starting CF parameters (CFPs) in well-defined axis systems. Multiple fittings starting from different points in the CF parameter space yield converging solutions, thus increasing the reliability of the final optimized solutions, which may be then considered as the global minima. The present CF analysis, unlike the previous ones, takes into account the low symmetry aspects inherent in the CF Hamiltonian and optical spectra. The improved and more reliable sets of CFPs are generated as well as modified assignments of the CF energy levels are proposed for BaY(2)F(8):Nd(3+). The present considerations enable also clarification of some ambiguous points occurring in previous studies.

Interpretation of multiple solutions and selection of the final crystal field parameter sets for orthorhombic and lower symmetry--case study: Er3+ ions at orthorhombic sites in ErNiAl4.

Existence of multiple solutions for the crystal field (CF) parameter (CFP) sets obtainable from fitting or matching procedures for orthorhombic (as well as monoclinic and triclinic) site symmetry has recently been gaining wider recognition. However, the peculiarities encountered in interpretation of multiple solutions and subsequent selection of the final CFP sets appears not to be properly understood in many cases. In this paper pertinent explanations for the peculiarities in question are provided. As a case study, we carry out analysis of the CFP sets for Er(3+) ions at orthorhombic sites in ErNiAl(4) obtained using theoretical calculations as well as Mössbauer spectroscopy and inelastic neutron scattering data. It turns out that the original and revised CFP sets reported for Er(3+) in ErNiAl(4) require reconsideration in view of these explanations. Clarifications concerning the matching procedure used as well as interpretation of the CFP sets and the assigned axis systems are provided. It appears that the specific constraints involved in matching have generated some incorrect CFP solutions. The crux of the problem is in the intrinsic features of CFP sets for orthorhombic symmetry, which previously were not fully utilized. Consideration of these features enables proper interpretation of multiple solutions as well as discrimination between the physically valid alternative CFP sets, which must be internally correlated, and the additional incorrect solutions generated by inappropriate matching or fitting procedures. Five alternative and correlated CFP sets are calculated for each set obtained for Er(3+) in ErNiAl(4). These considerations provide guidance for reinterpretation of CFP sets reported in literature and may facilitate subsequent fittings. This would enable experimental identification of the alternative CFP sets.

Modeling local structure using crystal field and spin Hamiltonian parameters: the tetragonal Fe(K)(3+)-O(I)(2-) defect center in KTaO(3) crystal.

The local structure and the spin Hamiltonian (SH) parameters, including the zero-field-splitting (ZFS) parameters D and (a+2F/3), and the Zeeman g factors [Formula: see text] and [Formula: see text], are theoretically investigated for the Fe(K)(3+)-O(I)(2-) center in KTaO(3) crystal. The microscopic SH (MSH) parameters are modeled within the framework of the crystal field (CF) theory employing the CF analysis (CFA) package, which also incorporates the MSH modules. Our approach takes into account the spin-orbit interaction as well as the spin-spin and spin-other-orbit interactions omitted in previous studies. The superposition model (SPM) calculations are carried out to provide input CF parameters for the CFA/MSH package. The combined SPM-CFA/MSH approach is used to consider various structural models for the Fe(K)(3+)-O(I)(2-) defect center in KTaO(3). This modeling reveals that the off-center displacement of the Fe(3+) ions, Δ(1)(Fe(3+)), combined with an inward relaxation of the nearest oxygen ligands, Δ(2)(O(2-)), and the existence of the interstitial oxygen O(I)(2-) give rise to a strong tetragonal crystal field. This finding may explain the large ZFS experimentally observed for the Fe(K)(3+)-O(I)(2-) center in KTaO(3). Matching the theoretical MSH predictions with the available structural data as well as electron magnetic resonance (EMR) and optical spectroscopy data enables predicting reasonable ranges of values of Δ(1)(Fe(3+)) and Δ(2)(O(2-)) as well as the possible location of O(I)(2-) ligands around Fe(3+) ions in KTaO(3). The defect structure model obtained using the SPM-CFA/MSH approach reproduces very well the ranges of the experimental SH parameters D, [Formula: see text] and [Formula: see text] and importantly yields not only the correct magnitude of D but also the sign, unlike previous studies. More reliable predictions may be achieved when experimental data on (a+2F/3) and/or crystal field energy levels become available. Comparison of our results with those arising from alternative models existing in the literature indicates considerable advantages of our method and presumably higher reliability of our predictions.

EPR and NMR in powders of doped and undoped IV-VI crystals.

The results of the extensive investigations of the variation of the EPR and NMR spectra of active centers due to the existence of the native defects generated by disorder in the IV-VI semiconductor matrices are presented. Both undoped and doped with Gd impurity powder samples of different grain sizes, made from Pb(1-x)Sn(x)Te crystals with the composition in the range 0 < or = x < or = 0.2 were studied. Impurity Gd ions were used as the paramagnetic EPR probe, whereas the 207 Pb nuclei as the NMR probe. The following aspects have been ascertained. (i) Grinding of the initial single crystals into powders leads to an additional component line appearing in the NMR spectra of the 207 Pb nuclei and also to a significant increase in the intensity of EPR spectra of the impurity Gd ions. (ii) Both the Gd EPR spectra as well as the 207 Pb NMR spectra undergo modifications due to isothermal annealing, whereas the character of these modifications is determined by both the temperature and duration of the thermal treatment applied. (iii) Some characteristic correlation between the variation of the EPR spectra of impurity Gd ions and that of the NMR spectra of 207 Pb nuclei, which results from the annealing of the samples, has been observed. Experimental results are interpreted based on the prevailing models of the behavior of the doped impurities and the native defects in the lead and tin telluride crystals.

Low-symmetry spin hamiltonian and crystal field tensors analysis: Fe(3+) in natrolite.

Electron paramagnetic resonance study of a natural single crystal of natrolite was carried out at the frequency nu=36.772 GHz at room temperature. The angular dependence of the four symmetry-related spectra of Fe(3+) in the three crystallographic planes was fitted to a spin Hamiltonian (S=5/2) of symmetry C(i). The rank 4 crystal field tensors at tetrahedral sites were calculated using the point-charge model to determine the principal axes orientations of their cubic and trigonal components. The analysis of zero-field splitting tensors and comparison with crystal field ones suggests that Fe(3+) substitutes for Al(3+) with no significant distortion of the coordination tetrahedron in natrolite. Comparison of data for several natural and synthetic crystals reveals that the 4-rank zero-field splitting tensor invariants for Fe(3+) at the tetrahedral oxygen-coordinated sites are distinguishably smaller than those for Fe(3+) at octahedral sites. Such comparative analysis may help to determine the substitutional sites in other crystals.

The extended version of the computer package CST for conversions, standardization and transformations of the spin Hamiltonian and the crystal-field Hamiltonian.

The computer package CST (Conversions, Standardization and Transformations) is useful for general manipulations of the zero-field splitting (ZFS) and crystal field (CF) parameters for various systems, especially for transition ions at orthorhombic and lower symmetry sites in crystals. The ZFS parameters are extensively used in the EMR and related spectroscopic and magnetic studies (e.g. magnetic susceptibility, magnetic anisotropy, Mössbauer spectroscopy), whereas the CF parameters in optical absorption spectroscopy, inelastic neutron scattering, and infrared spectroscopy. An extended version of the CST package developed recently is presented in this paper. The standardization, including the standardization errors, for the five possible non-standard ranges of the 'rhombicity' parameter for monoclinic and triclinic symmetry in the local axis system has been worked out. The handling of the border points in the standardization module has been improved. The rotational invariants used before only for the transformations of the CF parameters have been incorporated into the standardization module for the CF and ZFS parameters expressed in any of the major tensor operator notations. The input option in the Euler angles has been added into the transformation module, and the newest physical constants in the unit conversions module have been adopted. Specific applications of the CST package for the CF and ZFS parameters will be presented elsewhere.

Crossing of low-lying electronic levels of high-spin ferrous ion in deoxyhemoglobin and deoxymyoglobin.

The electronic structure of high-spin S = 2 ferrous ion in deoxy forms of hemoglobin and myoglobin is considered in terms of spin Hamiltonian formalism. Spin Hamiltonian parameters of the second order B0(2)(D), B2(2)(E) and, for the first time in the available literature, of fourth order B0(4), B2(4) and B4(4), are calculated for the rhombic symmetry case of Fe2+. The Hamiltonian matrix is diagonalized for several sets of Bq(k) parameters compatible with other experimental data. The low-lying Fe2+ levels exhibit crossings in a high magnetic field, applied along the z-axis perpendicular to the heme plane. The cross-over values of the magnetic field are determined to be Hc1 = 46 kOe and Hc2 = 168 kOe for D = 5.2, E = 0.6 cm-1 (close to the magnetic data of Nakano, N., Otsuka, J. and Tasaki, A. (1972) Biochim. Biophys. Acta 278, 355-371) and with B0(4) = 0.037, B2(4) = 0.005, B4(4) = 0.013 cm-1 and gz = 2.028. Experimental techniques for measurement of the crossing effects are discussed.