Theoretical studies on the g factors, optical absorption, and their concentration variations for Mo5+ in 40PbO-(10 - x)Y2 O3 -50P2 O5 :xMoO3 glass.

On the basis of the higher order perturbation formulas of g factors for a 4d1 group in tetragonally compressed octahedra, the g factors, optical absorption, local structure, and their concentration dependences of pentavalent molybdenum in 40PbO-(10 - x)Y2 O3 -50P2 O5 :xMoO3 (1 ≤ x ≤ 5 mol%) glass are uniformly investigated. The experimental optical absorption spectra and g factors for Mo5+ at various concentrations x are reasonably regenerated by using the reasonable exponential concentration functions of the cubic field parameter Dq , covalent factor N, and relative tetragonal compression ratio ρ. The tetragonal compression ratio ρ due to the Jahn-Teller effect was found in the range of 3.8% to 4.2%. The decreasing trend of Dq and N and the increasing trend of ρ with concentration can be interpreted as the fact that the variations of MoO3 and Y2 O3 concentrations lead to the modulations of local structure and electron cloud distribution around Mo5+ , associated with the adjustment of the glass network. The concentration dependence of optical basicity is also analyzed for the above glass systems.

Theoretical studies of the concentration dependences of d-d transition band, g factors, and local distortion for V4+ in Li2 O-PbO-B2 O3 -P2 O5 glasses.

In this work, the g factors, d-d transition band, local distortion, and their concentration dependences for impurity V4+ in 20Li2 O-20PbO-45B2 O3 -(15 - x)P2 O5 :V2 O5 (0 ≤ x ≤ 2.5 mol%) glasses are theoretically investigated by using perturbation formulas of g factors for a tetragonally compressed octahedral 3d1 cluster. In the light of the cubic polynomial concentration functions for cubic field parameter Dq , covalency factor N, and relative tetragonal compression ratio ρ, the calculated concentration dependences of d-d transition band and g factors for V4+ show good agreement with the experimental data. With increasing x, N (≈0.7682-0.8165) displays the monotonously increasing trend, whereas ρ (≈6.5-4.2%) and Dq (≈1504.9-1481.1 cm-1 ) exhibit the decreasing tendencies. The above concentration dependences can be ascribed to the modifications of the V4+ -O2- bonding and orbital admixtures around the impurity V4+ due to the effects of V2 O5 doping on the stability of the glass network, the strength of local crystal fields, and the electron cloud distribution.

Investigations on the defect structures and the g factors for the two orthorhombic Ti3+ centers in CaYAlO4.

The defect structures and the g factors for the two orthorhombic Ti(3+) centers (A and B) in CaYAlO(4) are theoretically investigated from the perturbation formulas of the g factors g(xi), g(eta) and g(xi) for a 3d(1) ion in orthorhombically distorted octahedra. The centers may be attributed to Ti(3+) locating on the Al(3+) site associated with one nearest-neighbouring oxygen vacancy (V(O)) along the z (or c) axis and additional next-nearest-neighbouring Ti(4+) replacing the host Al(3+) (Ti(Al), i.e., center A) or Al(3+) vacancy (V(Al), i.e., center B) perpendicular to the c axis, respectively. Due to the electrostatic interactions arising from the local charge mismatch, the central Ti(3+) undergoes a large displacement DeltaZ away from the V(O) in the c axis, while the ligand O(2-) intervening in the Ti(3+) and Ti(Al) (or V(Al)) suffers a small outward (or inward) shift DeltaX in the corresponding c plane related to the center of oxygen octahedron. The theoretical g factors for both centers based on the above displacements are in reasonable agreement with the observed values.

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 studies of lattice distortions around the impurity ions in V2+ doped CdCl2, CdI2 and PbI2.

The lattice distortions around the impurity ions in V(2+) doped CdCl(2), CdI(2) and PbI(2) are theoretically studied from the perturbation formulas of the spin Hamiltonian (SH) parameters zero-field splitting, g factors and the hyperfine structure constants for a 3d(3) ion in trigonal symmetry based on the cluster approach. In these formulas, the contributions from the s-orbitals of the ligands are taken into account. Based on the studies, it is found that the local angles beta (between the impurity-ligand bonding lengths and the C(3) axis) in the impurity centers are smaller than the angles beta(H) in the hosts. The calculated SH parameters based on the above local angles beta show better agreement than those on neglecting of the ligand s-orbital contributions (and those on the host angles beta(H)) with the experimental data.

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.

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.

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.

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 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.

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.

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.

Theoretical studies of the g factors and local structure for the tetragonal Nd3+ center in SrTiO3.

The anisotropic g factors g(//) and g(perpendicular) and the local structure for the tetragonal Nd(3+) center in SrTiO(3) are theoretically studied using the perturbation formulas of the g factors for a 4f(3) ion in tetragonal symmetry. This center is attributed to the impurity Nd(3+) occupying the dodecahedral Sr(2+) site in SrTiO(3), associated with one nearest neighbour interstitial oxygen O(I) along [001] (or C(4)) axis. The impurity Nd(3+) is found to suffer the large displacement (approximately 1.1A) towards the O(I) along the C(4) axis due to their strong interaction. The calculated g factors based on the above impurity axial displacement show reasonable agreement with the experimental results.

Incommensurate phase of a triangular frustrated Heisenberg model studied via Schwinger-boson mean-field theory.

We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J(1) and third-nearest-neighbor interactions J(3) by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J(3) and varying J(1) from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T(2) law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa(2)S(4). From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J(1)≈-3.8755 K and J(3)≈14.0628 K, in order to account for the experimental data.

Simplified diagrammatic expansion for effective operators.

For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams, and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity.

Conservation of connectivity of model-space effective interactions under a class of similarity transformation.

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between Hermitian and non-Hermitian Rayleigh-Schrodinger perturbative effective operators is one of such transformations and hence the connectivity can be deducted from each other.