Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2 Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the pert1rbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic,tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, Fl2, F44), Zij (Z11, Z12,Z44) and also g factor and hyperfine constant A for MgO:Co2 are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values.The difiiculty in explaining the coeficients Fij and Zij is therefore removed.``     

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.     

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.     

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.     

Theoretical Studies of Electron Paramagnetic Resonance Parameters for Cr4+ Ions in Ca2GeO4 Crystals

The electron paramagnetic resonance (EPR) parameters (zero-field splitting D and g factors g_||, g_⊥) of Cr⁴⁺ ions in Ca₂GeO₄ crystals have been calculated from the complete high-order perturbation formulas of EPR parameters for a 3d² ion in trigonal MX₄ clusters. In these formulas, in addition to the contributions to EPR parameters from the widely used crystal-field (CF) mechanism, the contributions from the charge-transfer (CT) mechanism (which are often neglected) are included. From the calculations, it is found that for the high valence state 3dⁿ ions in crystals, the reasonable explanation of EPR parameters (in particular, the g factors) should take both the CF and CT mechanisms into account.     

ZnS:Co2+和CdTe:Co2+中配体对g因子的贡献

采用双自旋-轨道耦合模型和分子轨道研究了Co²⁺离子在Ⅱ-Ⅵ半磁半导体ZnS和CdTe中的EPR g因子.计算表明,配体Te有大的SO耦合作用和强的共价性,其对g因子有较大的贡献.     

Theoretical analysis of spin-Hamiltonian parameters for the rhombic Cu2+ centres in CuGaSe2 crystals

The spin-Hamiltonian parameters (g factors g_i and hyperfine structure constants A_i, where i = x, y, z) of the rhombic Cu²⁺ centres in the CuGaSe₂ crystal are determined from the high-order perturbation formulae based on the cluster approach (sometimes also called two-spin-orbit parameter model). In the studies, some parameters in the analysis of g factors for the same centre within the tetragonal symmetry approximation in the previous paper are used, and the parameter due to the perturbation of rhombic crystal field caused by a charge compensator at, e.g., [110] direction are considered. As the result of a fitting process, the determined spin-Hamiltonian parameters are in reasonable agreement with the experimental values. The results are discussed.     

Theoretical explanation of spin-Hamiltonian parameters for the rhombic Mo5+ octahedral clusters in molybdenum phosphate glasses

The high-order perturbation formulas based on the two-mechanism model are used to calculate the spin-Hamiltonian parameters (g factors g_i and hyperfine structure constants A_i, where i = x, y, z) of the rhombic Mo⁵⁺ oxygen octahedral clusters in molybdenum phosphate glasses. These formulas consist of the crystal-field mechanism in the extensively applied crystal-field theory and of the charge-transfer mechanism (which is often neglected). In the calculations, only three adjustable parameters are applied and the six calculated spin-Hamiltonian parameters are reasonably coincident with the experimental values. The results are discussed.     

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.     

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.     

Ba2MgGe2O7:Cr4+晶体中荷移激发态对g因子贡献的研究

文章建立了立方四面体3d2络合物g因子的完全高阶微扰公式.在这个公式中,除了与d-d跃迁光谱(晶场激发态)有关的晶场(CF)机制的贡献(包括近年发展的双旋-轨耦合参量模型)外,与电荷转移光谱(荷移激发态)有关的荷移(CT)机制的贡献也被考虑.将这个公式应用于Ba2MgGe2O7:Cr4 晶体平均g因子的计算,发现理论计算值与实验值很好的一致,同时,荷移机制对g移动△g(=g-2.002 3)的贡献△gCT在符号上与晶场机制的贡献△gCF相反,而在大小上约为晶场机制贡献的38%.因此,在对高价态过渡金属离子络合物的g因子计算时应考虑CF机制和CT机制的贡献.     

Energy Spectrum and g Factor of MgO:Cr3+ and Their Pressure-Induced Shifts

The unified calculation of the whole energy spectrum and g factor of the ground state for MgO:Cr³⁺ at normal pressure and their pressure-induced shifts has been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d³ energy matrix in a regular octahedral field. All the calculated results are in very good agreement with a lot of experimental data. For the first time, by using the wavefunctions obtained by diagonalization of the complete energy matrix, the pressure-induced shifts of g factor have satisfactorily been calculated and explained by microscopic theory. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters have been calculated. The distinct differences in magnitude and/or sign of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels and g factor have provided important criteria for the correctness of the calculations and assignments of the energy spectrum and wavefunctions, and it is quite necessary and important to carry out the unified calculation of the whole energy spectrum and g factor at normal pressure and their pressure-induced shifts.     

Unified Calculations of the Energy and EPR Spectra and Their Pressure-Induced Shifts of Ruby

By taking into account the effect of variation in angular wavefunction, reconsidering the expressions of spin-orbit coupling parameters, diagonalizing the complete d³ energy matrix in a trigonally distorted cubic-field and using the wavefunctions from it, the unified calculations of the energy spectrum and EPR spectrum for ruby and their pressure-induced shifts have been carried out. All the calculated results are in very good agreement with a lot of experimental data. The estimation by making use of superposition model has also demonstrated the high sensitivity of trigonal-field parameters to angular variation. The distinct differences in magnitude and/or sign of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels and g factors have provided important criteria for the correctness of calculations and assignments of the energy spectrum and wavefunctions.     

Microscopic—Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：V^2＋

A great improvement on a previous work (PHYS.Rev.B48 (1993) 14067) has been made.By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d^3 electronic configuration,the values of all the parameters in the expressions of thermal shift(TS) and thermal broadening (TB) from EPI for the ground level,R level and R line of MgO:V^2 have microscopically been evaluated;and then,both the TS and TB of R line and various contributions to them have uniformly been calculated.The results are in very good agreement with the experimental data.It is found that all the three terms of TS from EPI are red shifts;the term of the contribution to TS from thermal expansion is blue shift.The Raman term is the largest,and the other terms are also important for TS.The R-line TS of MgO:V^2 comes from the first-order term of EPI.The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:V^2 .For calculations of both the TS and TB,it is very important to take into account all the admixtures of wavefunctions.     

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.     

Co2+离子在MgF2和ZnF2晶体中的各向异性g因子的理论研究

利用基于基团模型的3d⁷离子在斜方对称中的高阶微扰公式计算了MgF₂和ZnF₂晶体中Co²⁺杂质中心的各向异性g因子g_x，g_y和g_z. 在计算中，考虑了共价效应， 组态相互作用和斜方晶体场的贡献；而且与此相关的参量可由所研究的晶体的光谱和结构数据得到. 计算结果与实验符合较好.     

Substitutional site of Co2+ ion in RbMgF3 crystal

The spin-Hamiltonian (SH) parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for Co²⁺ ions at the trigonal Mg²⁺ (I) and Mg²⁺ (II) sites of RbMgF₃ crystal are calculated from the second-order perturbation formulas based on the cluster approach for 3d⁷ ions in trigonal symmetry. From the calculations, it is found that the calculated SH parameters for Co²⁺ ion at the Mg²⁺ (I) site are in poor agreement with, but those for Co²⁺ at the Mg²⁺ (II) site are close to, the experimental values. Therefore, we suggest that Co²⁺ in RbMgF₃ crystal substitutes for Mg²⁺ (II) ion. The results are discussed.     

KAl(MoO4)2晶体中掺杂Cr3+的能谱和g因子的理论计算*

采用强场方案和三角基，通过对角化三角畸变的立方晶场下的d3 完全能量矩阵，计算出了KAl(MoO4)2:Cr3+ 的能谱和波函数。使用对角化完全能量矩阵所获得的波函数，进一步计算了KAl(MoO4)2:Cr3+ 的基态g 因子。计算结果与光谱，EPR谱实验数据很好地符合。研究表明,利用对角化完全能量矩阵获得的波函数对 g 因子所作的计算为整个理论计算及波函数的归属提供了重要判据,充分体现了将能谱和g 因子作统一计算的重要性和必要性.