Xian-Fen Hu

Theoretical Investigations of the Knight Shifts and the Hyperfine Structure Constants for the Tetragonal Cu2+ Sites in the Bismuth- and Thallium-Based High-T-c Superconductors

The Knight shifts and hyperfine structure constants for the tetragonal Cu2+ sites in bismuth- and thallium-based high-Tc uperconductors ( Bi1:6Pb0:4Sr2Ca2Cu3O10, TlSr2CaCu2O7-y, and Tl2Ba2CuOy) are theoretically investigated from the high-order perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated octahedra in a unified way. The calculation results show good agreement with the observed values. The significant anisotropies of the Knight shifts are attributed to the local tetragonal elongation distortions of the five-(or six-)coordinated Cu2+ sites in these systems. The present studies would be beneficial to establish a complete physical scheme for unified understandings of electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) spectral behaviours of Cu2+ (or other similar 3d9 ions) in the high-Tc superconductors.

Investigations on the EPR parameters and tetragonal distortions for Cu2+ in alkali lead tetraborate glasses

The electron paramagnetic resonance parameters (g factors and hyperfine structure constants) and local structures are theoretically investigated for Cu2+ in alkali lead tetraborate 90R2B4O7·9PbO·CuO (R = Li, Na and K) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d9 complex. The [CuO6]10− complexes are found to experience the relative tetragonal elongation ratios 18%, 23% and 30% for R = Li, Na and K, respectively, due to the Jahn–Teller effect, much larger than those for similar ARbB4O7 (A = Li, Na and K) glasses. This point is attributed to the lattice expansion (longer A–O bond lengths) with doped PbO, yielding lower force constants and more intense Jahn–Teller elongations in the 90R2B4O7·9PbO·CuO glasses. The increasing tendency (Li > Na > K) of the relative elongation ratio λ, covalency and the ratio Δg///Δg⊥ for g-shifts are systematically analysed in a uniform way.

Theoretical investigations of the spin Hamiltonian parameters and local tetragonal distortions for Cu2+ in crystalline and amorphous TeO2 and GeO2

The spin Hamiltonian parameters (i.e., anisotropic g factors and hyperfine structure constants) and local tetragonal distortions for Cu2+ in crystalline and amorphous TeO2 and GeO2 are theoretically investigated using the high-order perturbation formulas of these parameters for a tetragonally elongated octahedral 3d9 cluster. The impurity Cu2+ occupying the octahedral sites are found to experience the relative tetragonal elongation ratios of about 11.4% and 9.5% for crystalline TeO2 and GeO2 and 10.8% and 6.6% for amorphous TeO2 and GeO2, respectively, along the C4 axis due to the Jahn–Teller effect. This reveals the larger tetragonal elongation distortions for the Cu2+ centres in crystalline than amorphous systems (especially TeO2). The theoretical spin Hamiltonian parameters show good agreement with the experimental data. The results are discussed.

Studies on the spin Hamiltonian parameters for Mn2+ in the ZnS nanocrystals and bulks

The spin Hamiltonian parameters (zero-field splitting D, g factors and hyperfine structure constants) are theoretically studied for Mn2+ in the ZnS nanocrystals and bulks from the perturbation formulae of these quantities for trigonal and cubic tetrahedral 3d5 clusters, respectively. The trigonal Mn2+ centre in the ZnS nanocrystals is attributed to the impurity–ligand bond angle related to the C3 axis about 0.39° larger than that (≈109.47°) of an ideal tetrahedron. Almost the same g factors and hyperfine structure constants for the nanocrystals and bulks can be ascribed to similar crystal-field environments (i.e. comparable cubic field parameters Dq), nearly the same covalency (i.e. the equal covalency factors N) and the Mn2+ 3d–3s orbital admixture (i.e. the identical core polarisation constants κ) in both systems. The ligand orbital and spin–orbit coupling contributions are found to be important and should be included in the electron paramagnetic resonance analysis in view of significant covalency.

Studies of the Local Distortions and the EPR Parameters for Cu2+ in xLi2O-(30–x)Na2O-69·5B2O Glasses

Abstract The local distortions and electron paramagnetic resonance (EPR) parameters for Cu2+ in lithium sodium borate (LNB) glasses xLi2O·(30–x)·Na2O·69.5B2O3 (5≤x≤25 mol%) are theoretically studied at various concentrations x in a consistent way. Owing to the Jahn–Teller effect, the [CuO6]10− clusters are found to experience the significant tetragonal elongations of 16% along C4 axis. Despite the nearly unchanging observed g factors, measured d–d transition band (or cubic field parameter Dq) shows remarkable linear increases with concentration x, whose influences on g‖ and g⊥ are actually cancelled by the linearly increasing covalency factor N and relative elongation ratio η with x. The almost unvarying hyperfine structure constants are attributed to the fact that the influences of the linearly increasing N and the linearly decreasing core polarisation constant κ largely cancel one another. The microscopic mechanisms of the above concentration dependences for these quantities are illustrated from mixed alkali effect (modification of B2O3 network by transforming some BO3 units into BO4 ones with variations in modifier Li2O concentration).

Theoretical investigations of 63Cu2+ orbital Knight shifts for YBa2Cu4O8

The temperature-independent orbital Knight shifts for the orthorhombic 63Cu2+(1) site in YBa2Cu4O8 (Y124) are investigated by utilizing the high order perturbation formulae of these parameters for a 3d9 ion situated into orthorhombically elongated octahedra. The calculation results are in good agreement with the experimental data. The moderate quasi-axial anisotropies of the Knight shifts are ascribed to the elongation distortion of the four-fold coordinated Cu2+(1) site. The g factors are also theoretically calculated in a uniform way for further experimental verification.

Studies on the Local Angular Distortion and Spin Hamiltonian Parameters for the Trigonal Co2+ Center in MgCl2

Abstract The local angular distortion and spin Hamiltonian parameters (g factors g||, g⊥ and the hyperfine structure constants) for the trigonal Co2+ center in MgCl2 are theoretically studied by diagonalizing the 6×6 energy matrix of ground 4T1 state for a trigonally distorted octahedral 3d7 cluster. Based on the cluster approach, the contributions from the admixtures of various J (= 1/2;3/2;5/2) states and the ligand orbital and spin-orbit coupling interactions are taken into account in a uniform way. The local impurity-ligand bond angle in the Co2+ center is found to be about 3.44° larger than the host metal-ligand bond angle in the pure crystal due to substitution of smaller Mg2+ by bigger Co2+, inducing a further compressed ligand octahedron. The calculated spin Hamiltonian parameters using the above local angular distortion are in good agreement with the experimental data. The present studies on the local structure and the spin Hamiltonian parameters for Co2+ in MgCl2 are tentatively extended to a more general case by comparing the relevant impurity behaviours for Co2+ in various trigonal environments.

Theoretical studies of 63Cu2+ orbital Knight shifts of HgBa2Ca2Cu3O8+δ

The orbital Knight shifts and g factors for the tetragonal 63Cu2+ site in HgBa2Ca2Cu3O8+δ at 133 and 115 K are theoretically investigated based on the high-order perturbation formulae of these quantities for a 3d9 ion situated into tetragonally elongated octahedra. The theoretical results reveal good agreement with the observed values. The significant anisotropies of the Knight shifts are illustrated as the considerable local tetragonal elongation distortions of the five-coordinated Cu2+ sites. The results at different temperatures are also discussed in view of the local structure of the Cu2+ sites.The orbital Knight shifts and g factors for the tetragonal 63Cu2+ site in HgBa2Ca2Cu3O8+δ at 133 and 115 K are theoretically investigated based on the high-order perturbation formulae of these quantities for a 3d9 ion situated into tetragonally elongated octahedra. The theoretical results reveal good agreement with the observed values. The significant anisotropies of the Knight shifts are illustrated as the considerable local tetragonal elongation distortions of the five-coordinated Cu2+ sites. The results at different temperatures are also discussed in view of the local structure of the Cu2+ sites.

Theoretical studies of the spin Hamiltonian parameters and local structures for Ag 2+ in AgCl and KCl crystals

The spin Hamiltonian parameters (g factors, hyperfine structure constants and superhyperfine parameters) and local structures for Ag2+ centers in AgCl and KCl crystals are theoretically studied using the high-order perturbation formulas for a tetragonally elongated 4d9 cluster. The impurity centers undergo relative elongations (≈0.05 Å and 0.23 Å for Ag2+ in AgCl and KCl, respectively) along the C4 axis owing to the Jahn–Teller effect. All the calculated spin Hamiltonian parameters show good agreement with the experimental data, and the ligand contributions to the spin Hamiltonian parameters are important and should be taken into account. The unpaired spin densities in the superhyperfine parameters are determined from molecular orbital coefficients based on the cluster approach, instead of being taken as the adjustable parameters in the previous treatments. Increasing tetragonal elongation from AgCl to KCl is attributed to a decrease in chemical bonding (or lower force constant) with increasing Ag2+–Cl distance.

Studies on the g -factors of the copper(II)–oxygen compounds

The g factors for Cu2+ in meta-zeunerite (Cu(UO2)2(AsO4)2·3H2O), kroehnkite (Na2Cu(SO4)2·2H2O), copper benzoate (Cu(PhCO2)2·3H2O) and diaboleite (Pb2Cu(OH)4Cl2) of the tetragonal phase are uniformly treated by high order perturbation formulas for 3d9 ions in tetragonally elongated octahedra. The calculation results are in good agreement with the observed values and systematically analyzed in view of the local structures around Cu2+. The g anisotropies Δg (= g‖−g⊥) are largely ascribed to the local tetragonal elongations of the Cu2+ sites, characterized by the relative elongation ratios (R‖−R⊥)/R̅ ≈ 19%, 21%, 27% and 30% for metazeunertie, kroehnkite, copper benzoate and diaboletie, respectively. The anomalous valley (minimum) of relative g anisotropy for copper benzoate is attributed to the modification of the Cu2+ electronic states due to the phenyl ring. The ligand orbital contributions are found to be significant due to covalency, and should be taken into account. The present study would be helpful to the unified investigations of structures and properties of the copper oxygen compounds.