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.     

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.     

Studies of EPR parameters for Mn5+ -doped Li3PO4 and Li3VO4 crystals

The EPR parameters (zero-field splitting D and g factors g parallel, g perpendicular) of Mn5+ -doped Li3PO4 and Li3VO4 crystals are calculated from the complete high-order perturbation formulas based on a molecular orbital scheme for a 3d2 ion in tetragonal MX4 clusters. These formulas include not only the contribution coming from crystal-field excitations, but also that arising from charge-transfer excitations (which is discarded in crystal field theory). The calculated results are in reasonable agreement with the observed values. The contributions to EPR parameters coming from the charge-transfer excitations are comparable with those arising from the crystal-field excitations. It appears that for a high valence state 3dn ion in crystals, the reasonable explanations of EPR parameters should take the contributions due to both crystal-field and charge-transfer excitations into account.     

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 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.     

g factors and the tetragonal distortion of ligand octahedron for Co2 + in Rb2MgF4 crystal

The calculation formulas of g-factors g(parallel) and g(perpendicular) for 3d7 ion in tetragonal octahedral crystals are established from a cluster approach. In these formulas, the parameters related to covalency effect, configuration interaction and low-symmetry crystal field can be determined from the optical spectra and the structural data of the studied system. Based on these formulas, the structural parameters of ligand octahedra of Co2+ in Rb2MgF4 crystal are obtained by fitting the calculated g(parallel) and g(perpendicular) to the observed values. The result suggests that the CoF6 (and hence MgF6) octahedra in Rb2MgF4:Co2+ are tetragonal compressed. The relationship between the sign of deltag( = g(perpendicular) - g(parallel)) and the sign of distortion (elongated or compressed) of ligand octahedron and the causes of the mistakes of octahedron distortion for Rb2MgF4:Co2+ in the previous papers are discussed.     

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.     

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.     

Local tilting angles tau for Fe+ in Cd2+ site and Fe3+ in Si4+ site of CdSiP2 semiconductor

The EPR parameters (g factors, g(parallel), g(perdendicular) and zero-field splitting D) for Fe+ in Cd2+ site and Fe3+ in Si4+ site of CdSiP2 semiconductor are calculated from the distinct high-order perturbation formulas. From the calculations, the local tetragonal distortions and hence the local tilting angles tau (which are different from the corresponding host values) for both paramagnetic centers are estimated. The results are discussed.     

Investigations of EPR parameters and local lattice distortions for both Co2+ centers in La2Mg3(NO3)12.24H2O crystal

The EPR g factors, g parallel and g perpendicular, of Co2+ and hyperfine structure constants (A parallel, A perpendicular) of 59Co2+ and 60Co2+ isotopes in both trigonal Mg2+ sites of La2Mg3(NO3)12.24H2O crystal are calculated from the high-order perturbation formulas of EPR parameters based on the cluster approach for 3d7 ion. It is found that to explain reasonably all these EPR parameters, the local relaxation effects (particularly, those related to the trigonal distortion angles thetai) in the vicinity of both Co2+ impurities should be considered. The local angles thetai are obtained from the calculations and the results are discussed.     

Theoretical studies of the spin Hamiltonian parameters and the local structures for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3

The spin Hamiltonian parameters (zero-field splitting D, g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3 are studied by using the perturbation formulas of the spin Hamiltonian parameters for 3dn (n=7, 5, 3, 8) ions in trigonal symmetry based on the cluster approach. In these formulas, the contributions to the spin Hamiltonian parameters from the admixture of d orbitals of the central ions with the p orbitals of the ligands and from the trigonal distortion are included and the parameters related to these effects can be obtained from the optical spectra and the local structures of the studied systems. Based on the studies, it is found that the local trigonal distortion angle beta in the M2+ impurity center is unlike that betaH (approximately 51.71 degrees) in the host CsMgCl3. The spin Hamiltonian parameters for these divalent ions in CsMgCl3 are also satisfactorily explained by using the local angle beta. The validity of the results is discussed.     

EPR paramaters and defect structure of the trigonal Ti2+ center in ZnS

The axial Ti2+ center in a nearly wholly cubic ZnS crystal is assigned to the Ti2+ ion on the hexagonal site of wurtzite structure caused by stacking faults. On the ground of the assignment, the EPR parameters (zero-field splitting D, g factor g( parallel) and g-anisotropy Deltag=g( parallel)-g( perpendicular)) of the axial Ti2+ center are calculated from the high-order perturbation formulas based on the cluster approach for the EPR parameters of 3d2 ion in trigonal symmetry. From the calculations, the local atom-position parameter u(loc) (which is different from the corresponding parameter u in the host wurtzite structure) and hence the defect structure of the Ti2+ center are estimated. The results (the calculated EPR parameters and the defect structure) are discussed.     

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.     

Studies of the trigonal field parameters and g factors for magnetic semiconductor NaCrS2

The trigonal field parameters v and v' of magnetic semiconductor NaCrS2 are calculated from the superposition model, and its g factors g parallel and g perpendicular are calculated from the high-order perturbation formulas of 3d3 ions in trigonal symmetry obtained by the one and two spin-orbit coupling parameter models. These calculations are based on the structural data of NaCrS2 crystal. The calculated results suggest that the superposition model is effective to the analyses of the low-symmetry field parameters of 3dn ions in crystals and that the two spin-orbit coupling parameter model (where the contributions from both the spin-orbit coupling parameter of 3dn ion and that of ligand are considered) is preferable to the one spin-orbit coupling parameter model (in which the contribution from only the spin-orbit coupling parameter of 3dn ion is considered) in the explanations of g factors in the cases that ligands have large spin-orbit coupling parameter in 3dn clusters.     

Studies of the g factors and zero-field splitting for the trigonal Ti(2+)(Ga)-S(p) defect center in GaP crystal

The EPR g factors g(parallel), g(perpendicular) and zero-field splitting D suggested to be caused by a donor-acceptor nearest-neighbour pair defect [Ti(Ga)(2+)-Sp] in GaP:Ti(2+) co-doped with sulphur are calculated from the high-order perturbation formulas based on a two spin-orbit coupling parameter model for the EPR parameters of 3d(2) ion in trigonal symmetry. The calculated results are close to the observed values. The suggestion of [Ti(Ga)(2+)-Sp] pair defect in GaP:Ti co-doped with sulphur is also confirmed from this calculation.     

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 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.     

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.     

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.     

Single crystal EPR and optical studies of paramagnetic ions doped zinc potassium phosphate hexahydrate--part II: VO(II)--a case of substitutional site.

Single crystal electron paramagnetic resonance (EPR) studies were carried at room temperature for VO(II) doped zinc potassium phosphate hexahydrate. The results indicate that the paramagnetic impurity has entered the lattice only substitutionally, as confirmed by the single crystal rotations. The spin Hamiltonian parameters calculated from the spectra are g parallel = 1.9356, g perpendicular = 1.9764, A parallel = 200.9 G and A perpendicular = 76.5 G. The optical absorption spectrum exhibits three bands (800, 670 and 340 nm) suggesting the C4v symmetry and the optical parameters evaluated are Dq = 1492, Ds = -3854 and Dt = 186 cm(-1).