Theoretical investigation of optical and paramagnetic resonance spectra of [NiF6](4-) clusters with orthorhombic symmetry.

The ground state absorption spectra of [NiF6](4-) clusters with orthorhombic symmetry (Ni(2+) in NiF2 crystal and Ni(2+)-doped ZnF2 crystal, D2h point group) are theoretically calculated and assigned by diagonalization of 45×45 complete energy matrix for 3d(8) configuration and the spin-Hamiltonian (SH) parameters (zero-field splitting D and E, and g factors gx, gy, gz) are studied by use of high-order perturbation method, in the frame of semi-empirical molecular orbital (MO) scheme based on strong crystal field framework. In those energy matrix, all the configuration interactions though the cubic crystal field (CF), the orthorhombic crystal field, the Coulomb interaction are taken into account. The calculated results are in good agreement with the experimental data. The local structure (bond length and bond angle) of [NiF6](4-) clusters are determined, and the results shows that the structure data given by Stout are more plausible than those given by Baur.

Spin-Hamiltonian parameters for the tetragonal Gd(M)3+-F(i)- centers in CaF(2) and SrF(2) crystals.

The spin-Hamiltonian parameters (g factors g(//), g(⊥) and zero-field splittings b(2)(0), b(4)(0), b(4)(4), b(6)(0), b(6)(4)) of the tetragonal Gd(M)(3+)-F(i)(-) centers in CaF(2) and SrF(2) 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 4f(7) ions in crystals.

Theoretical investigations of optical spectra and electron paramagnetic resonance spectra of LiCl:Ni²âº crystals.

The complete energy matrices (45 × 45) including low symmetry ligand field (C(4v)) and Coulomb interactions for 3d(8) ions have been constructed, and the high-order perturbation formulas of spin-Hamiltonian (SH) parameters g factors g(//), g(⊥) and zero-field splitting (ZFS) parameter D for ground state (3)A(2g) of the 3d(8) ions in the tetragonal symmetry environment have been derived. In those formulas both the crystal field (CF) mechanism and the charge transfer (CT) mechanism are taken into account. The complete energy matrices and the high-order perturbation formulas are applied to calculate the energy levels and SH parameters of the Ni(2+) ion in LiCl crystal respectively. The results are in reasonable agreement with the experimental data and indicate that CT mechanism plays important role in the understanding of SH parameters, especially the g factors. All the multiplet energy are assigned theoretically and the local structures of LiCl:Ni(2+) are established.

Research on the optical spectra, g factors and defect structures for two tetragonal Y²+ centers in the irradiated CaF2: Y crystal.

Based on the defect models that the tetragonal Y(2+) (1) center in the irradiated CaF(2): Y crystal is due to Y(2+) at Ca(2+) site associated with a nearest interstitial F(-) ion along C(4) axis and the tetragonal Y(2+) (2) center is Y(2+) at Ca(2+) site where the tetragonal distortion is caused by the static Jahn-Teller effect, the two optical spectral bands and anisotropic g factors for both tetragonal Y(2+) centers are calculated. The calculations are made by using two methods based on the cluster approach, one is the complete diagonalization (of energy matrix) method (CDM) and another is the perturbation theory method (PTM). The calculated results for each Y(2+) center from CDM and PTM coincide and show reasonable agreement with the experimental values. The calculated isotropic g factor for Y(2+) (2) center at higher temperature owing to the dynamical Jahn-Teller effect is also consistent with the observed value. The defect structures (i.e., tetragonal distortion) of the two Y(2+) centers are obtained from the calculation. It appears that both theoretical methods can be applied to explain the optical and EPR data, to study the defect model and to determine the defect structures for d(1) ions in crystals.

Studies of the optical band positions and EPR g factors for Cu(H2O)6(2+) centers in Tutton salt crystals.

The optical band positions and EPR g factors g(i) (i = x, y, z) of Cu(H(2)O)(6)(2+) clusters in pure Tutton salts M(2)Cu(SO(4))(2)·6H(2)O (M = NH(4), Rb) are calculated from the complete diagonalization (of energy matrix) method based on the cluster approach. In the calculation, the superposition model with the structural data is used to obtain the crystal-field parameters. The calculated results are in reasonable agreement with the experimental values, suggesting that the complete diagonalization method and superposition model are effective in the studies of optical and EPR data. The g factors g(i) of Cu(H(2)O)(6)(2+) clusters in Cu(2+)-doped isomorphous diamagnetic Tutton salts M(2)Zn(SO(4))(2)·6H(2)O are also studied from the same method. It is found that the approximately tetragonally compressed Zn(H(2)O)(6)(2+) octahedra in the host crystals change to the approximately tetragonally elongated Cu(H(2)O)(6)(2+) octahedra in the impurity centers. The causes concerning the Jahn-Teller effect are discussed. It appears that in some cases the octahedral environment of an impurity M(I) in crystals differs from that of the replaced host ion, but is close to the one in the isomorphous pure crystals where M(I) is the host ion rather than the impurity ion.

Studies of the spin-Hamiltonian parameters and defect structures for Gd3+ ions in zircon-structure silicates MSiO4 (M=Zr, Hf, Th).

The spin-Hamiltonian parameters (g factors g∥, g⊥ and zero-field splittings b2(0), b4(0), b4(4), b6(0), b6(4)) for 4f7 ion Gd3+ at the tetragonal M4+ site of zircon-structure silicates MSiO4 (M=Zr, Hf, Th) are calculated from a diagonalization (of energy matrix) method. The Hamiltonian concerning this energy matrix contains the free-ion, crystal-field interaction and Zeeman interaction terms and the 56×56 energy matrix is constructed by considering the ground multiplet 8S7/2 and the excited multiplets 6L7/2 (L=P, D, F, G, H, I). The defect structures of Gd3+ centers in the three MSiO4 crystals are yielded from the calculation. The results are discussed.

A theoretical study on the temperature dependence of zero-field splitting for the tetragonal Cr3+ center in MgO crystal.

This paper reports a detailed theoretical calculation of the temperature dependence of zero-field splitting D (characterized by ΔD(T)=D(T)-D(0)) for the tetragonal Cr3+ center in MgO crystal by considering both the static contribution due to the thermal expansion of Cr3+ center and the vibrational contribution caused by electron-phonon (including the acoustic and optical phonons) interaction. The vibrational contribution due to the acoustic phonon is calculated using the long-wave approximation similar to the study on the specific heat of crystals and that due to optical phonon is estimated using the single-phonon model. The calculated results are in reasonable agreement with the experimental values. From the calculation, it is found that the static contribution ΔDstat(T) (which is often regarded as very small and is neglected in the previous papers) is larger than the vibrational contribution ΔDvib(T) and so the reasonable studies of temperature dependence of zero-field splitting should take both the static and the vibrational contributions into account.

A study of the spin-Hamiltonian parameters for the trigonal Sm3+ center in La2Mg3(NO3)(12)·24H2O crystal.

This paper reports a theoretical calculation of spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 147A//, 147A⊥, 149A//, 149A⊥) for 147Sm3+ and 149Sm3+ isotopes in the trigonal La3+ site of La2Mg3(NO3)(12)·24H2O crystal from a diagonalization (of energy matrix) method. In the method, the Hamiltonian concerning the energy matrix includes the Zeeman and hyperfine interaction terms and so there is no perturbation calculation in it. The crystal-field parameters in the energy matrix are calculated using the superposition model, in which the structural data of 12-fold coordinated site rather than those of the incorrect 6-fold coordinated site given in the previous paper are applied. The calculated results are in reasonable agreement with the experimental results. The results are discussed.

Spin-Hamiltonian parameters and defect structure for the rhombic Dy3+ center in AgCl crystal.

Based on the defect model that the rhombic Dy(3+) center in AgCl crystal is formed by substitutional Dy3+ ion associated with two nearest Ag+ vacancies (VAg) along the <110> and <110> axes owing to charge compensation, the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants 161Ai and 163Ai, where i=x, y, z) of this rhombic Dy3+ center are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are attached to the classical Hamiltonian used in the calculation of crystal-field energy levels and a 66×66 energy matrix concerning this Hamiltonian is constructed by taking all the ground-term multiplets 6HJ (J=15/2, 13/2, 11/2, 9/2, 7/2, 5/2) into account. The calculated results (g factors gi and average |A(161Dy3+)| and |A(163Dy3+)|) are in reasonable agreement with the experimental values. From the calculations, the above defect model of rhombic Dy3+ center is confirmed, the defect structure of this Dy3+ center (characterized by the displacement of Cl- ligand caused by VAg) is obtained and the components of hyperfine structure constants Ai(161Dy3+) and Ai(163Dy3+) are predicted. The results are discussed.

Studies of the EPR parameters and defect models for three Er3+ impurity centers in ThO2 crystals.

The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants of the ground state, and g factors of the first excited state) of three (one cubic and two trigonal) Er(3+) centers in fluoride-type ThO(2) crystal are studied from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the classical Hamiltonian, and a 52 x 52 energy matrix concerning the ground multiplet (4)I(15/2) and the first to third excited multiplets (4)I(13/2), (4)I(11/2) and (4)I(9/2) is established for a 4f(11) ion in trigonal crystal field and under an external magnetic field. From the studies, the EPR parameters for three Er(3+) centers in ThO(2) are reasonably explained, the defect models for the two trigonal Er(3+) centers suggested in the previous paper are confirmed and the defect structures of the two trigonal centers are obtained. The results are discussed.

Investigation of the spin-Hamiltonian parameters for the trigonal U5+ center in CaF2 crystal.

The spin-Hamiltonian parameters (g factor g(//), g(perpendicular) and hyperfine structure constants A(//), A(perpendicular)) of the trigonal U(5+) center in CaF(2) crystal have been calculated from the complete diagonalization (of energy matrix) method (CDM) for 5f(1) ions in trigonal crystal field and under an external magnetic field. In the calculation, the crystal-field parameters are estimated from the superposition model. From the calculations, these spin-Hamiltonian parameters are reasonably explained, and the defect model (i.e., the trigonal U(5+) center is attributed to U(5+) substituting for Ca(2+) in CaF(2) with six F(-) ions replaced by O(2-) and the other two F(-) sites vacant because of charge compensation) given in the previous paper is confirmed. The results are discussed.

Studies of the spin-Hamiltonian parameters and the Jahn-Teller distortions for tetragonal Cu(H(2)O)(6)(2+) clusters in trigonal A(2)Mg(3)(NO(3))(12).24H(2)O (A=La, Bi) crystals.

The anisotropic and isotropic spin-Hamiltonian parameters (g factors and hyperfine structure constants) of tetragonal Cu(H(2)O)(6)(2+) clusters due, respectively, to the static and dynamic Jahn-Teller effects for Cu(2+) in trigonal A(2)Mg(3)(NO(3))(12).24H(2)O (A=La, Bi) crystals are calculated from the high-order perturbation formulas based on the cluster approach. In the approach, the admixture between the d orbitals of 3d(n) ion and the p orbitals of ligand ion via covalence effect is considered. All of the calculated results are in agreement with the experimental values. The tetragonal elongations (characterized by DeltaR=R(parallel)-R( perpendicular)) of Cu(H(2)O)(6)(2+) cluster due to the Jahn-Teller effect in A(2)Mg(3)(NO(3))(12).24H(2)O crystals are acquired from the calculations. The results are discussed.

Investigations of the optical spectra and EPR g factors for the tetragonal Cu2+ centers in trigonal ZnCO3 crystal.

Two distinctive theoretical methods, the complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM), are employed to calculate the optical band positions and EPR g factors g(||), g(perpendicular) for the tetragonal Cu(2+) centers in trigonal ZnCO(3) crystal. The results from the two methods coincide and are also in good agreement with the experimental values. So both the CDM and PTM are adequate for the investigations of optical and EPR data for d(9) ions in crystals. The tetragonal distortion due to the static Jahn-Teller effect for the tetragonal Cu(2+) centers in trigonal Zn(2+) site of ZnCO(3) is also acquired from the calculations. The results are discussed.

[Studies of the g factor and optical spectra for CaZrO3:Mn4+ crystal].

The complete high-order perturbation formula of g factor for 3d(3) ions in cubic octahedral site was derived. In the formula, both the contribution delta g(CF) to g-shift delta g (= g-g(s), where g(s) = 2.0023) due to crystal-field (CF) mechanism (related to the interactions of CF excited states with the ground state) and that (delta g(CT)) due to charge-transfer (CT) mechanism (related to the interactions of CT excited states with the ground state, which is omitted in crystal-field theory) are included. By using the formula and the parameters obtained from the optical spectra of CaZrO3:Mn4+ crystal, the g factor of CaZrO3:Mn4+ was calculated. The result is consistent with the experimental value. The calculations show that the contribution is opposite in sign and about 62% in magnitude compared with the contribution delta g(CF). It appears that both CF and CT mechanisms should be considered in the calculation of g factor for the high valence 3d(3) (e. g. , Mn4+ and Fe3+) ions in crystals.

Defect model and EPR parameters for the tetragonal Yb3+ center in KTaO3 crystal.

The defect model of the tetragonal Yb3+ (at K+ site) center in KTaO3 crystal is suggested, i.e., Yb3+ ion does not occupy the ideal K+ site, but is displaced by an amount DeltaZ along one of 100 axes because of the much smaller ionic radius of Yb3+ compared with that of the replaced K+. Based on the defect model, the EPR parameters (g factors g(parallel), g(perpendicular) and hyperfine structure constants 171A parallel, 171A perpendicular, 173A parallel, 173A perpendicular) are calculated by diagonalizing the 14 x 14 complete energy matrix. The calculated values are in agreement with the observed values and the off-center displacement DeltaZ (approximately 0.2 angstroms) is estimated from the calculations. These results are discussed.

Theoretical investigations of the EPR parameters for Cr3+ and Mn4+ ions in PbTiO3 crystals.

The complete high-order perturbation formulas of EPR parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D), containing the crystal-field (CF) mechanism and charge-transfer (CT) mechanism (the latter is omitted in crystal-field theory which is often used to study the EPR parameters), are established from a cluster approach for 3d3 ions in tetragonal octahedral sites. According to the calculations based on these formulas, the EPR parameters g( parallel), g( perpendicular) and zero-field splitting D for Cr3+ and Mn4+ ions in PbTiO3 crystals are explained reasonably. The calculations show that (i) the sign of g-shift Deltag(i)(CT) (=g(i)-g(s), where g(s)=2.0023 is free-electron value and i= parallel and perpendicular) in CT mechanism is opposite to, but that of D(CT) is the same as, the corresponding signs in the CF mechanism and (ii) the relative importance of CT mechanism for the high valence state 3d3 ion (e.g., Mn4+) is large and so the contributions to EPR parameters from CT mechanism should be taken into account. The different sign of splitting D and the different defect structure for Cr3+ and Mn4+ impurity centers in PbTiO3 crystals are also suggested from the calculations. The results are discussed.

[Investigation of optical and EPR spectra of ZnO : V3+ crystal].

In the present paper, the 45 X 45 energy matrix of the 3d2 ions in trigonal symmetry with the strong-field-coupling mechanism is established. The forty-five optical energy levels and five EPR parameters (including the zero-field splitting D, g factors g//, g perpendicular and hyperfine structure constants A//, A perpendicular) of ZnO : V3+ cryst are calculated from the diagonalization of this complete energy matrix. The calculated results are in agreement with the observed values. Based on the calculation, it was found that the local structure of V3+ impurity center is different from the corresponding structure in the host crystal, i. e., the V3+ ion in ZnO does not occupy the exact Zn2+ site, but is displaced by DeltaZ approximately 0.003 nm along the c3 axis. The reasonableness of these results is discussed.

Theoretical calculation of EPR g factors for Ni(3+) ion at the interstitial site of SnO(2) crystal.

The EPR g factors g(x), g(y) and g(z) for Ni(3+) ion at the interstitial site in the rutile-type SnO(2) crystal are calculated from the second-order perturbation formulas of g factors based on the cluster approach for 3d(7) ion in rhombic symmetry. The calculated results are in agreement with the experimental values. The local lattice distortion induced by the impurity Ni(3+) at the interstitial site of SnO(2) is also estimated from the calculations. These results are discussed.

Investigations of the EPR zero-field splitting and the defect structure for Mn(2+) and Fe(3+) ions in anatase crystals.

The EPR zero-field splittings D of Mn(2+) and Fe(3+) ions in anatase crystals at room and low temperatures are calculated from the high-order perturbation formula of zero-field splitting D for 3d(5) ions in tetragonal symmetry based on the dominant spin-orbit coupling mechanism. The calculated results are consistent with the observed values. From the calculations, Mn(2+) and Fe(3+) ions are suggested to substitute for Ti(4+) ions in anatase (in the previous paper, Mn(2+) ion was suggested at an interstitial site rather than substitutional site) and the defect structures (characterized mainly by the local oxygen parameter u) for both tetragonal Mn(2+) and Fe(3+) impurity centers are estimated. The different zero-field splitting at room and low temperatures are due mainly to the change of local oxygen parameter u with the temperature. These results are discussed.