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.     

Investigations of the g factors and hyperfine structure parameters for Er3+ ion in zircon-type compounds

The electron paramagnetic resonance (EPR) g factors g(parallel), g(perpendicular) and hyperfine structure parameters A(parallel), A(perpendicular) of the tetragonal Er3+ centers in zircon-type compounds YXO4 (X = As, P, V), ScVO4 and RSiO4 (R = Zr, Hf, Th) are calculated from the perturbation formulas of EPR parameters for 4f11 ion in tetragonal symmetry. In these formulas, the second-order perturbation contributions are included in addition to the first-order perturbation contributions considered in the previous papers. The crystal-field parameters used in the calculations are obtained by analyzing the optical spectral data from the superposition model. Although the superposition model intrinsic parameters An(R0) used in this paper for Er3+ in various zircon-type compounds are not as scattered as those in the previous paper, the calculated results of both the optical spectra and EPR parameters show better agreement than those in the previous paper with the observed values, suggesting that the above calculation method and parameters are more reasonable. The contributions of the second-order perturbation terms to EPR parameters are also discussed.     

Investigations of the EPR parameters for Sm3+ ions in KY3F10 and LiYF4 crystals

In this paper, we calculate the EPR parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) of rare earth ion Sm3+ in fluoride crystals KY3F10 and LiYF4 from the perturbation formulas of EPR parameters for a 4f5 ion in tetragonal symmetry. In these formulas, the crystal-field J-mixing of the first and second excited-state multiplets 6H(7/2) and 6H(9/2) into the ground state multiplet 6H(5/2), the mixtures among the states with the same J value via spin-orbit coupling interaction and the interactions between the ground Kramers doublet Gammagamma and the same irreducible representation as Gammagamma in other 11 Kramers doublets Gammax within 6HJ (J=5/2, 7/2, 9/2) states via crystal-field and orbital angular momentum (or hyperfine structure) are considered. The calculated results (which are in agreement with the observed values) are discussed.     

Theoretical investigations of the EPR g factors and the local structure for Er3+ in BaWO4

The electron paramagnetic resonance (EPR) parameters g factors g(parallel) and g(perpendicular) as well as the local structure for Er3+ in scheelite-type BaWO4 are theoretically investigated by using the perturbation formulas of the EPR parameters for a 4f11 ion under tetragonal symmetry. In these formulas, the contributions to the EPR parameters arising from the second-order perturbation terms and the admixture of different states are included. It is found that the impurity-ligand bonding angles (or the polar angles) related to the fourfold axis in the tetragonal Er3+ center are about 1.5 degrees smaller than those in pure crystal. The calculated EPR parameters are in agreement with the observed values. The validity of the results is discussed.     

Theoretical investigation of the EPR parameters and local structure for trigonal Yb3+ ion in Bi4Ge3O12 crystal

Bi4Ge3O12 single crystals are of great interest for science research and engineering applications. In this paper, the electron paramagnetic resonance (EPR) g factors g||, gperpendicular of Yb3+ and hyperfine structure constants A||, Aperpendicular of 171Yb3+ and 173Yb3+ isotopes in Bi4Ge3O12 crystal are calculated from the perturbation formulas of these parameters. The crystal-field parameters are obtained from the superposition model and the crystal structure data. The EPR parameters for trigonal Yb3+ centers in Bi4Ge3O12 are reasonably explained by involving the defect structures of impurity Yb3+ centers. Based on the calculations, Yb3+ ion is found not to occupy exactly the host Bi3+ site, but to shift away from the center of oxygen octahedron by a distance DeltaZ approximately 0.317 A along C3 axis. The results are discussed.     

Theoretical calculations of spin-Hamiltonian parameters for CsCdX(3):Ni(2+) (X=Cl, Br) crystals from the two-mechanism model

The high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D) for 3d(8) ions in trigonal octahedral sites of crystals are derived considering not only the crystal-field (CF) mechanism, but also the charge-transfer (CT) mechanism (which is neglected in the extensively used CF theory). From these formulas and by considering the suitable impurity-induced local lattice relaxation, the SH parameters of CsCdX(3):Ni(2+) (X=Cl, Br) crystals are calculated. The results are in reasonable agreement with the experimental values. The sign of Q(CT) (Q=Deltag( parallel), Deltag( perpendicular) or D, where the g-shift Deltag(i)=g(i)-g(e), g(e) approximately 2.0023 is the free-electron value) due to CT mechanism is the same as that of the corresponding Q(CF) due to CF mechanism. The relative importance of CT mechanism (characterized by Q(CT)/Q(CF)) increases with the increasing atomic number of ligand X. So, for 3d(n) ion clusters in crystals with heavy element ligand ion (e.g., Br(-)), the reasonable explanations of SH parameters should contain the contributions from both CF and CT mechanisms.     

Theoretical studies of the spin Hamiltonian parameters and local structures for Cs3CoX5 (X = Cl, Br)

The spin Hamiltonian (SH) parameters (zero-field splitting D and anisotropic g factors g(||) and g( perpendicular)) and local structures for Cs(3)CoX(5) (X = Cl, Br) are theoretically studied from the perturbation formulas of the SH parameters for a 3d(7) ion in tetragonally distorted tetrahedra based on the cluster approach. In these formulas, both the contributions from the crystal-field (CF) mechanism and those from the charge-transfer (CT) mechanism are taken into account. It is found that the [CoX(4)](2-) clusters are slightly elongated and the tetragonal distortion angles Deltatheta(=theta-theta(0), where theta(0) equals to approximately 54.74 degrees is the bonding angle related to the C(4)-axis in regular tetrahedra) are about -1.68 degrees and -1.71 degrees for X = Cl and Br, respectively. The calculated SH parameters as well as the effective magnetic moments based on the above angles are in reasonable agreement with the observed values. From the studies, the importance of the contributions to the SH parameters from the CT mechanism increases with increasing the spin-orbit coupling coefficient of the ligand, i.e., Cl(-) < Br(-). The results are compared with those obtained from the conventional crystal-field model in the previous works.     

Investigations of the spin-Hamiltonian parameters for Er3+ at the Th4+ site in ThGeO4

The spin-Hamiltonian (SH) parameters g factors g(parallel), g(perpendicular) and the hyperfine structure parameters A(parallel) and A(perpendicular) for Er3+ at the tetragonally distorted dodecahedral Th4+ site in ThGeO4 are theoretically investigated by using the perturbation formulas of the SH parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the SH parameters from the second-order perturbation terms and the admixture of various energy levels are taken into account. The related crystal-field parameters are calculated from the geometrical relationship of the impurity center and the superposition model. Based on the studies, the lowest Kramers doublet is found to be Gamma7, rather than Gamma6 suggested in the previous work. The calculated SH parameters for Gamma7 doublet in this work are smaller than those obtained for Gamma6 doublet in the previous work and in good agreement with the observed values. The various contributions to the SH parameters are discussed.     

Investigations of the EPR g factors and hyperfine structure constants for two trigonal Co2+ centers in Al2O3 crystals

The EPR g factors gparallel, gperpendicular and the hyperfine structure constants Aparallel, Aperpendicular for two trigonal Co2+ centers (i.e. Co2+(I) center at the substitutional site and Co2+(II) center at the interstitial site) in Al2O3 crystals are calculated from the second-order perturbation formulas based on the cluster approach. In these formulas, the contributions to EPR parameters from both the spin-orbit coupling parameter of central 3dn ion and that of ligand are included. The calculated results are in reasonable agreement with the observed values. Based on the calculations, the defect structures of both Co2+ centers in Al2O3 crystals are obtained and the negative sign of Aparallel for Co2+(I) center is suggested. The results are discussed.     

Theoretical studies on the optical spectra and EPR parameters for trigonal Yb3+ center in CsCdBr3 crystal

In this paper, the crystal-field energy levels, the EPR g factors g//, g(perpendicular) of Yb3+ and hyperfine structure constants A//, A(perpendicular) of 171Yb3+ and 173Yb3+ isotopes in CsCdBr3 crystal are calculated from the crystal-field theory. The calculated results (seven energy levels and six EPR parameters) are in reasonable agreement with the observed values. In the calculation, we find that Yb3+ ion does not occupy the exact Cd2+ site, but is shifted from the center of bromine octahedron by a distance (Delta)Z approximately 0.184 angstroms along C3 axis. The results are discussed.     

Gyromagnetic factor of Cr4+ ions in forsterite

The average value of g factor (i.e., g ) of Cr4+ ions in forsterite (Mg2SiO4) is calculated with the cubic symmetry approximation from the complete high-order perturbation formula of g factor for 3d2 ion in cubic tetrahedral cluster. In the formula, the contribution to g factor from the charge-transfer mechanism (which is neglected in the crystal-field theory) is considered in addition to that from the widely used crystal-field mechanism. From the calculations, the reasonable observed value of g is suggested (note: the experimental values of g by various authors are scattered) and the important contribution of charge-transfer mechanism to g factor can be found.     

EPR g factors of trigonal Dy(3+) center in ThO(2) crystal

The perturbation formulas of EPR g factors g(parallel) and g( perpendicular ) for the lowest Kramers doublet of 6H(15/2) of a 4f(9) ion in trigonal symmetry are established in this paper. In these formulas, besides the contribution due to the interaction within the lowest 6H(15/2) manifolds considered in the previous papers, the contributions due to the J-mixing among the 6H(15/2), 6H(13/2) (first excited state) and 6H(11/2) (second excited state) via crystal-field interaction, the admixtures among the states with the same J value via spin-orbit coupling interaction and those between the lowest Kramers doublet Gammagamma and other Kramers doublets Gamma(X) within the states 6H(J) (J=15/2,13/2,11/2) via crystal-field and orbital angular momentum interactions are included. From these formulas, the g factors g(parallel) and g( perpendicular ) for the trigonal Dy(3+) center in ThO(2) crystal are calculated. The results are discussed.     

三角对称晶场中 4 A2(3d3 )态离子EPR参量的SS和SOO机制

A CDM/ EPR program has been developed using Visual Basic 6. 0. The spin-spin（SS）and spin-otherorbit（SOO）interactions omitted in published works have also been included in the Hamiltonian. The CDM/EPR program can study not only the EPR parameters but also the CF energy levels and wavefunctions for 4A2 （3d3）states ions in crystals. Utilizing the CDM/ EPR program,the EPR parameters and fine spectra for Ruby and Emerald have been investigated. The theoretical results are in good agreement with the experimental findings. The contributions to the EPR parameters and fine spectra arising from SS and SOO interactions have been studied. The investigation shows:① The EPR parameters are mainly induced by SO coupling interaction;② The contribution to the zerofield-splitting（ZFS）arising from SS interaction is appreciable and cannot be omitted,whereas the contributions to the ZFS parameter D arising from SOO interaction are smaller;③ The contribution to the Zeeman g-factors and spectra arising from SS and SOO interactions is slight.     

Investigations of the optical and EPR spectra for VO2+ in LiKSO4 crystals

The optical spectra and EPR spectra (characterized by the spin-Hamiltonian parameters g(//), g(perpendicular), A(//) and A(perpendicular)) for the molecular ion VO2+ in LiKSO4 crystals are calculated from two microscopic theory methods, one of which is the complete diagonalization (of energy matrix) method (CDM) and the other is the perturbation theory method (PTM). The calculated three optical absorption bands and four spin-Hamiltonian parameters from the two methods are not only close to each other, but also in reasonable agreement with the experimental values. It appears that both theoretical methods are effective in the explanation of optical and EPR spectra for 3d1 ions in crystals. The negative signs of hyperfine structure constants A(//) and A(perpendicular) for VO2+ in LiKSO4 crystals are also suggested from the calculations.     

Investigations on the electron paramagnetic resonance parameters for Mn2+ in the ABF3 fluoroperovskites

The electron paramagnetic resonance (EPR) parameters (g factor, the hyperfine structure constant A and the superhyperfine parameters A' and B') for Mn(2+) in the fluoroperovskites ABF(3) (A=K and Cs; B=Zn, Mg, Cd and Ca) are theoretically investigated from the perturbation formulas of these parameters for a 3d(5) ion under ideal octahedra. In the above treatments, not only the crystal-field mechanism but also the charge transfer mechanism is considered uniformly on the basis of the cluster approach. The theoretical EPR parameters are in good agreement with the experimental data. The charge transfer contribution to the g-shift Δg (≈g-g(s), where g(s)≈2.0023 is the spin-only value) is opposite (positive) in sign and comparable in magnitude to the crystal-field one. Nevertheless, the charge transfer contribution to the hyperfine structure constant shows the same sign and about 10% that of the crystal-field one. So, the conventional argument that the charge transfer contributions to the zero-field splittings are negligible for 3d(5) ions under low symmetrically distorted fluorine octahedra is proved no longer valid for the Δg analysis of ABF(3):Mn(2+) in view of the dominant second-order charge transfer perturbation terms. The unpaired spin densities of the fluorine 2s, 2p σ and 2p π orbitals are determined from the quantitative dependences upon the related molecular orbital coefficients, rather than obtained by fitting the observed superhyperfine parameters in the previous works.     

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.     

EPR parameters and defect structures for the Co2+ ions in LiNbO3 and LiTaO3 crystals

The electron paramagnetic resonance (EPR) parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for Co2+ ions in LiNbO3 and LiTaO3 crystals are calculated from the second-order perturbation formulas based on the cluster approach for 3d7 ions in trigonal octahedral clusters. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative sign of A parallel for Co2+ in the two crystals and the more exact and rational values of A parallel for Co2+ in LiTaO3 are suggested. The defect structures (characterized by the Co2+ displacement DeltaZ along C3 axis and the O(2-) displacement DeltaX in an oxygen triangle towards the center of the triangle) for the Co2+ centers in both crystals are estimated. The results are discussed.     

EPR parameters and impurity structures for Cr3+ ions in KSc(MoO4)2, RbIn(MoO4)2 and RbSc(MoO4)2 crystals

The calculations of EPR parameters (g factors g||, g(perpendicular) and zero-field splitting D) related to the impurity structures have been made from the high-order perturbation formulas for Cr(3+) ions in trigonal KSc(MoO(4))(2), RbIn(MoO(4))(2) and RbSc(MoO(4))(2) crystals. It is found that the MO(6) octahedra in these crystals change from the trigonal elongation in the pure crystals to the trigonal compression in the impurity centers. The results are discussed.     

Investigations of the optical spectra and EPR parameters in CaWO4:Yb3+

In this paper, we calculate the optical spectra data (crystal-field energy levels), the electron paramagnetic resonance (EPR) g factors gparallel, gperpendicular of Yb3+ and hyperfine structure constants Aparallel, Aperpendicular of 171Yb3+ and 173Yb3+ isotopes in CaWO4 crystal in a unified way from the crystal-field theory. All the calculated results are in good agreement with the experimental values. The signs of Aparallel and Aperpendicular for both isotopes 171Yb3+ and 173Yb3+ are suggested.     

Investigations of zero-field splitting (ZFS) and local distortion parameters of ZnAl2S4:Mn2+ by theoretical analysis

Fourth-order perturbation formula on the basis of the dominant spin-orbit coupling mechanism is employed to investigate the local environment around Mn2+ centers in ZnAl2S4 single crystals. The zero-field splitting (ZFS) parameter D is calculated for the Mn2+ ions at the Al3+ site with local symmetry D3d using the different orbital reduction factors. Both the contributions of the lattice distortions to the crystal-field (CF) parameters and the D are examined by means of different cases. The comparison between the calculated results in this study and the previous experimental and theoretical values reveals a good agreement and reasonable distortion parameters for Mn2+ ions at Al3+ sites.