EPR g factors and tetragonal distortion for the isoelectronic Ni and Cu centers in the CuGaSe2 crystal

The EPR g factors, g_|| and g_⊥, for the isoelectronic 3d⁹ ions Ni⁺ and Cu²⁺ at the tetragonal Cu⁺ site of the CuGaSe₂ crystal are calculated from the high-order perturbation formulas based on a two-spin-orbit-parameter model. In the model, both the contributions to g factors from the spin-orbit parameter of central 3d⁹ ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ−θ₀, where θ is the angle between the metal-ligand bond and C₄ axis, and θ₀≈54.74° is the same angle in cubic symmetry) of Ni⁺ and Cu²⁺ centers, which are different from the corresponding angle in the host CuGaSe₂ crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g_||−g_⊥ between the isoelectronic Ni⁺ and Cu²⁺ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe₂ crystal.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of V²⁺ ions in trigonal CdCl₂ crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dⁿ ion is considered), both the contributions from the spin-orbit parameter of central dⁿ ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V²⁺ ion due to the introduction of V²⁺ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.     

Research of the g factors,optical band positions and local structure for the tetragonal octahedral (CrO6)7− clusters in glasses

The electron paramagnetic resonance g factors g_//, g_⊥ and also the optical band positions of the tetragonal (CrO₆)^7? octahedral clusters in glasses are calculated from the high-order perturbation formulas (in which the needed crystal-field (CF) energy levels correspond to the optical band positions). The formulas are founded on the two-mechanism model which takes account of both the contribution to g factors from the widely used CF mechanism and that from the frequently neglected charge-transfer (CT) mechanism. The calculated results are in rational agreement with the experimental values, suggesting that the contribution to g factors from CT mechanism should be considered. The local structure of (CrO₆)^7? clusters in glasses is also acquired from the calculation. The results are discussed.     

Theoretical Studies of g Factors and Defect Structures for Cubic, Tetragonal, and Orthorhombic Fe+ Centers in Alkali Halides MX (M=Li,Na;X=F,Cl)

The EPR g factors for cubic, tetragonal and orthorhombic Fe centers in alkali halides MX (M = Li, Na;X = F, Cl) are calculated from second-order perturbation formulas of g factors based on cluster approach for 3d7 ions in three symmetries. From calculations, the g factors of these Fe centers in MX crystals are reasonably explained and the defect structural data for the tetragonal and orthorhombic Fe centers are estimated. The results are discussed.     

Theoretical Studies of g Factors and Defect Structures for Cubic, Tetragonal, and Orthorhombic Fe^＋ Centers in Alkali Halides MX （M=Li, Na; X = F, C1）

The EPR 9 factors for cubic, tetragonal and orthorhombic Fe^＋ centers in alkali halides MX （M= Li, Na; X = F, CI） are calculated from second-order perturbation formulas of g factors based on cluster approach for 3d^7 ions in three symmetries. From calculations, the g factors of these Fe^＋ centers in MX crystals are reasonably explained and the defect structural data for the tetragonal and orthorhombic Fe^＋ centers are estimated. The results are discussed.     

Investigations of the optical band positions,EPR parameters and defect structure for the trigonal Cr3+–Li+ centre in CsMgCl3 crystal

A unified calculation of optical band positions and electron paramagnetic resonance (EPR) (or spin-Hamiltonian) parameters for the trigonal Cr³⁺–Li⁺ centre in CsMgCl₃ crystal is made by using the complete diagonalisation (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, the contributions from the spin–orbit parameter of central dⁿ ion and that of ligand ion are included. From the calculation, the 11 observed optical and EPR data (eight optical band positions and three EPR parameters g_//, g_⊥, D) are reasonably explained with five adjustable parameters and the defect structure of the Cr³⁺–Li⁺ centre (which is consistent with the expectation based on the electrostatic interaction) in CsMgCl₃ is acquired. The results are discussed.     

Theoretical Calculations of g Factors and Hyperfine Structure Constants for Co2+ inCd2+(I) and Cd2+(II) Sites of CsCdCl3 Crystal

The g factors g‖,g⊥ and hyperfine structure constants A‖,A⊥ for two trigonal Co2+ centers (i.e.,Co2+ in Cd2+ (I) and Cd2+ (II) sites) in CsCdCl3:Co2+ crystals are calculated from the high-order perturbation formulas based on the cluster approach.In the calculation,the contributionsfrom covalency effect and configuration interaction effect are considered and the parameters related to both effects are obtained from the optical spectrum and the structure data of the studied system.The results are in good agreement with the observed values.     

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants ⁶⁵A_// and ⁶⁵A_⊥) for the tetragonal Cu²⁺ centres in trigonal Zn(BrO₃)·6H₂O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d⁹ ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO₃)·6H₂O: Cu²⁺ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R_// ? R _⊥, where R_// and R _⊥ represent the metal-ligand distances parallel with and perpendicular to the C₄ axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.     

Calculations of the optical and EPR spectral data for Cr3+ ion in Y3Ga5O12 crystal from the complete diagonalisation method

The complete diagonalisation (of energy matrix) method is applied in this paper to calculate together the optical and electron paramagnetic resonance (EPR) spectral data for Cr³⁺ ion at the trigonal Ga³⁺ site of Y₃Ga₅O₁₂ crystal. The method is founded on the two-spin-orbit-parameter model where in addition to the contributions from the spin-orbit parameter of central dⁿ ion (i.e., one-spin-orbit-parameter model) in the traditional crystal field theory, those from the spin-orbit parameter of ligand ion via covalence effect is also considered. The calculated results propose that by using only four adjustable parameters, the 12 observed spectral data (nine optical band positions and three EPR parameters g_//, g_⊥ and D) in Y₃Ga₅O₁₂: Cr³⁺ are reasonably explained. The impurity-induced local lattice distortion of Cr³⁺ in Y₃Ga₅O₁₂ crystal is also estimated through the calculations. The results are discussed.     

Investigation of the EPR parameters of the rhombic Cu2+ center in (NH4)2Mg(SO4)2·6H2O single crystal

The electron paramagnetic resonance (EPR) parameters (g factors g_x, g_y, g_z and hyperfine structure constants A_x, A_y, A_z) for Cu²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O (DHMS) crystal are theoretically investigated using the high-order perturbation formulas of these parameters. In the calculations, the ligand orbital and spin–orbit coupling for the impurity Cu²⁺ are taken into account; the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the EPR parameters with the local structure of the impurity center. The ligand orbital and the spin–orbit coupling contributions are included on the basis of the cluster approach. Based on the calculation, the theoretical EPR parameters show good agreement with the observed values. The results are discussed.     

Investigation of the EPR g factors and defect structure for the Cu-VNa center in the X-irradiated NaCl: Cu crystal

The g factors of a tetragonally-compressed Cu²⁺ center in NaCl: Cu⁺ crystal X-irradiated at room temperature are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, the contribution to g factors from both crystal-field (CF) and charge-transfer (CT) mechanisms are included. The calculations are based on the defect model that the tetragonally-compressed Cu²⁺center is assigned to the Cu²⁺ ion (which is caused by Cu⁺ ion (at the Na⁺ site) irradiated by X-ray) associated with a nearest Na⁺ ion vacancy V_Na along C₄ axis due to charge compensation. From the calculations, the g factors g_|| and g_⊥ are explained and the defect structure (charactering by the displacement ΔZ of the Cl⁻ ion intervening in Cu²⁺ and V_Na) of the Cu²⁺ (or Cu²⁺-V_Na) center is obtained. The results are discussed.     

Theoretical Calculations of g Factors and Hyperfine Structure Constants for Co^2＋ in Cd^2＋（I） and Cd^2＋（Ⅱ） Sites of CsCdCl3 Crystal

The g factors g||,g⊥ and hyperfine structure constants A||,A⊥ for two trigonal Co^2 centers (i.e.,Co^2 in Cd^2 (I) and Cd^2 (Ⅱ) sites) in CsCdCl3:Co^2 crystals are calculated from the high-order perturbation formulas based on the cluster approach.In the calculation,the contributions from covalency effect and configuration interaction effect are considered and the parameters related to both effects are obtained from the optical spectrum and the structure data of the studied system.The results are in good agreement with the observed values.