Studies of the spin-Hamiltonian parameters and defect structures for the tetragonal and cubic Yb3+ centers in AgCl crystal.

The spin-Hamiltonian parameters, g factors and hyperfine structure constants, for the tetragonal and cubic Yb(3+) centers in AgCl crystal are calculated from the complete diagonalization (of energy matrix) method. The calculations are based on the defect models that the tetragonal Yb(3+) center is formed by the substitutional Yb(3+) associated with two nearest Ag(+) vacancy (V(Ag)) along <001> and <001¯> axes (i.e., C(4) axis) owing to charge compensation and in cubic Yb(3+) center the two compensators V(Ag) are remote. From the calculations, the spin-Hamiltonian parameters of both Yb(3+) centers in AgCl are explained reasonably, the signs of hyperfine structure constants A(i)((171)Yb(3+)) and A(i)((173)Yb(3+)) are suggested, the above defect models of both Yb(3+) centers are confirmed and their defect structures are determined.

Studies on the spin-Hamiltonian parameters of CuN(6) clusters and their tetragonal distortions due to Jahn-Teller effect for Cu2+ in trigonal M(1-propyltetrazole)6(BF4)2 (M=Zn, Fe) crystals.

This paper reports the theoretical calculations for the anisotropic and isotropic spin-Hamiltonian parameters (g factors and the hyperfine structure constants) of tetragonal CuN6 octahedral clusters due, respectively, to the static and dynamic Jahn-Teller effects for Cu2+ ion in the trigonal M(=Zn, Fe) sites of M(1-propyltetrazole)6(BF4)2 crystals. The calculations are carried out using the high-order perturbation formulas based on a two-mechanism model, in which besides the contributions to spin-Hamiltonian parameters due to the crystal-field mechanism concerning the crystal-field excited states in the extensively used crystal-field theory, the contributions due to charge-transfer mechanism concerning the charge-transfer excited states (which are neglected in the crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. From the calculations the tetragonal elongations ΔR=R//-R⊥ (where R// and R⊥ denote the Cu-N distances parallel with and perpendicular to the C4 axis) of CuN6 octahedral clusters due to Jahn-Teller effect are obtained. The results are discussed.

Spin-Hamiltonian parameters and angular distortion for the trigonal Nd(3+) center in congruent LiNbO(3).

The 52x52 energy matrix related to the ground multiplet (4)I(9/2) and the first to third excited multiplets (4)I(11/2), (4)I(13/2) and (4)I(15/2) for 4f(3) ions in trigonal crystal field under an external magnetic field is established. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factor g(parallel), g(perpendicular) and hyperfine structure constants (143)A(parallel), (143)A( perpendicular), (145)A(parallel), (145)A( perpendicular)) of the trigonal Nd(3+) center in congruent LiNbO(3) crystal are calculated. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative signs of hyperfine structure constants are suggested and the angular distortion of the trigonal Nd(3+) center in LiNbO(3), which is unable to be determined by EXAFS measurement, is obtained. The results are discussed.

Defect structure and spin-Hamiltonian parameters for the CuCl(6)(4-) cluster in the tetragonal RbCdCl(3):Cu(2+) crystal.

The tetragonal distortion (characterized by R( parallel)-R( perpendicular) where R( parallel) and R( perpendicular) denote the metal-ligand distances parallel with and perpendicular to the tetragonal axis, respectively) for CuCl(6)(4-) cluster in the tetragonal RbCdCl(3):Cu(2+) crystal is studied by calculating its spin-Hamiltonian (SH) parameters (g factors g( parallel), g( perpendicular) and hyperfine structure constants A( parallel), A( perpendicular)). The calculations are performed by using the complete high-order perturbation formulas for 3d(9) ions in tetragonal symmetry based on a two-mechanism model, in which both the widely-used crystal-field (CF) mechanism and the charge-transfer (CT) mechanism (which is omitted in CF theory) are considered. From the calculations, the SH parameters are reasonably explained and the tetragonal distortion R( parallel)-R( perpendicular) approximately 0.14A is obtained. The distortion is much larger than those caused by the cubic-tetragonal transition phase, but is in the same order as those found in many similar CuCl(6)(4-) Jahn-Teller systems. So, the tetragonal distortion (or defect structure) for the CuCl(6)(4-) cluster in RbCdCl(3):Cu(2+) is due mainly to the Jahn-Teller effect. The relative importance of CT mechanism (characterized by Q(CT)/Q(CF), where Q=Deltag(i) or A(i)((2)), i= || or perpendicular are about 12% and 9% for Q=Deltag(i) and A(i)((2)), respectively. It appears that for the exact calculations of SH parameters of CuCl(6)(4-) clusters in crystals, the contributions due to both CF and CT mechanisms should be taken into account.

Spin-Hamiltonian parameters and local structures for Co4+ and Ir4+ impurity centers in the tetragonal phase of SrTiO3.

The calculated results in the recent paper about the spin-Hamiltonian (SH) parameters (g factors g (//), g perpendicular and hyperfine structure constants A(//), A perpendicular) and the local structures of Co4+ and Ir4+ impurity centers in the tetragonal phase of SrTiO3 are doubtful because there are several mistakes in the calculations. So, we restudy the SH parameters and local structures by using the correct methods and parameters. From the studies, for Co4+ and Ir4+ in SrTiO3, the SH parameters are explained rationally, the signs of hyperfine structure constants A(//), A perpendicular are obtained and the suitable and more detailed local structures are given. 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.

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.

Zero-field splittings and local tilting angles tauMn2+ for Mn2+ in ZnGeP2 and CdGeP2 crystals.

The electron paramagnetic resonance (EPR) zero-field splittings (ZFSs) D of Mn2+ in ZnGeP2 and CdGeP2 crystals are calculated from both the microscopic spin-orbit coupling mechanism and the empirical superposition model. From the calculations, the ZFS D of ZnGeP2:Mn2+ is reasonably explained by using the local tilting angle tauMn2+ (rather than the corresponding angle tauZn2+ in the host crystal) and the local tilting angle tauMn2+ (which has not been reported) in CdGeP2:Mn2+ is estimated. The intrinsic ZFS parameter b2(R0) approximately -0.052(6)cm(-1) (with R0 approximately 2.43 angstroms) is suggested for Mn2+-P(3-) combination by using the local tilting angles tauMn2+. The value is quite unlike that (approximately 0.4(2)cm(-1)) obtained in the previous paper by combining the crystallographic data of host crystals with the ZFSs for Mn2+ ions in crystals. The reasonableness of these results is 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.

Studies of the defect structure for Mn2+ in KTaO3 crystal from the calculation of EPR zero-field splitting.

There are several mistakes in the recent paper about the theoretical studies of defect structure for Mn(2+) ion at the 12-fold tetrakaidecahedral K+ site in KTaO(3) by calculating the spin Hamiltonian (SH) parameters, so the calculated defect structure (which is smaller than those obtained from the local density approximation (LDA) method, density functional theory in the generalized gradient approximation (GGA) and the dipole moment study (DMS)) is doubtful. Therefore, we restudy the defect structure in this paper by using the reasonable expressions and parameters. The present result is in agreement with those based on LDA, GGA and DMS methods and can be regarded as reasonable. It appears that the reliability of the defect structure of impurity center determined from the calculation of SH parameter depends strongly upon reasonableness of the used expressions and parameters.

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.

Studies of the defect structures of the trigonal Cr3+-Vc centers in fluoroperovskites from EPR and optical spectra.

The EPR parameters (zero-field splitting D and g factors g(parallel), g(perpendicular)) and the first excited state splitting Delta(2E) of the trigonal Cr3+-Vc centers (Vc denotes the cation vacancy in a C3 axis) in Cr3+-doped fluoroperovskites KMgF3, KZnF3, CsCdF3, CsCaF3, RbCdF3 and BaLiF3 are studied from the high-order perturbation formulas. From the studies, the defect structures (characterized by the vacancy-induced displacements Delta x1 of Cr3+ ion and Delta x2 of the three F- ion between Cr3+ and Vc) of these trigonal Cr3+-Vc centers are determined. It is found that the signs of displacements Delta x1 and Delta x2 are consistent with the expectations based on the electrostatic interactions, and the magnitudes of Delta x1 and Delta x2 for Cr3+ in the inverse perovskite BaLiF3 are larger than those for Cr3+ in the classical perovskites. The results are discussed.

EPR parameters and local geometry for Cr3+ and V2+ ions in HfS2 crystals.

From the high-order perturbation formulas of EPR parameters (zero-field splitting D, g factors gparallel, gperpendicular and hyperfine structure constants Aparallel, Aperpendicular) based on the two spin-orbit coupling parameter model for 3d3 ions in trigonal symmetry, the EPR parameters of Cr3+ and V2+ ions in HfS2 crystals are calculated. From the calculations, it is found that the local trigonal distortion angle theta of impurity center in HfS2:Cr3+ is smaller than that in HfS2:V2+. The dominant cause of the small zero-field splitting |D| and g-anisotropy |Deltag|=|gparallel-gperpendicular| in HfS2:Cr3+ (compound to HfS2:V2+) is due to the small local trigonal distortion angle theta rather than to the small impurity-ligand distance R in HfS2:Cr3+.

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.

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.

Studies of the electric-field-induced zero-field splitting for a substitution Mn2+ ion in SrCl2 crystal.

The zero-field splittings induced by the electric-field have been studied theoretically from the formulas, including three important microscopic mechanisms for a substitutional Mn2+ ion in SrCl2 crystal. From the studies, it is found that the zero-field splitting can be attributed primarily to the electric-field-induced displacement of Mn2+ ion along the electric-field direction and the magnitudes of the displacements at various strengths of electric-field are obtained. The results are comparable with those obtained from the potential-energy curve of Mn2+ center.

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.

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.

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.

Studies of electron paramagnetic resonance parameters and defect structures for Ti2+ and V3+ ions in CdS crystals.

By applying the high-order perturbation formulas based on the cluster approach for the EPR parameters of 3d2 ions in trigonal symmetry, the zero-field splitting D, g factors gparallel, gperpendicular, and hyperfine structure constants Aparallel, Aperpendicular for Ti2+ and V3+ ions in CdS crystals are studied. From the studies, the defect structures of these paramagnetic impurity centers are obtained and the EPR parameters are also explained reasonably.