Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Cr ions in Y2Ti2O7 crystal

The optical band positions and spin-Hamiltonian parameters (g factors g_g_? and zero-field splitting D) for the trigonal Cr³⁺ centers in Y₂Ti₂O₇ crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central dⁿ ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ center is suggested.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.     

Studies of EPR g factors of the isoelectronic 3d series Cr, Mn and Fe in SrTiO3 crystals

The g-shifts Δg(=g−g_s, where g_s≈2.0023 is the free-ion value) of the isoelectronic 3d³ series Cr³⁺, Mn⁴⁺ and Fe⁵⁺ in SrTiO₃ crystals are calculated from the high-order perturbation formula based on the cluster approach for 3d³ ion in cubic octahedral site. The formula includes not only the contribution from the crystal-field (CF) mechanism, but also that from the charge-transfer (CT) mechanism (which is omitted in the CF theory). From the calculations, it is found that the contribution Δg_CT from the CT mechanism in sign is contrary to the corresponding Δg_CF from the CF mechanism and the relative importance of CT mechanism (characterized by |Δg_CT/Δg_CF|) increases with the increasing valence state (and hence the atomic number) of 3d³ ion. The positive g-shift Δg of SrTiO₃:Fe⁵⁺ is due mainly to the contribution of CT mechanism. So, for the explanations of g factors of the high valence state 3dⁿ ions (e.g. Mn⁴⁺ and Fe⁵⁺) in crystals, the contributions from both CF and CT mechanisms should be taken into account.     

Theoretical explanation of the g factor for Cr in Y2SiO5 crystal

The g factor of Cr⁴⁺ in Y₂SiO₅ crystal is calculated from a completed high-order perturbation formula, in which not only the conventional contribution to the g-shift Δg(=g−g_e) from the crystal-field mechanism, but also the contribution from the charge-transfer mechanism (which is neglected in the crystal-field theory) are considered. The calculated result shows good agreement with the observed value. It is found that the calculated Δg due to the charge-transfer mechanism is opposite in sign and about 38% in magnitude, compared with that due to the crystal-field mechanism. So, in the studies of the g factor for a 3dⁿ ion having high valence state in crystals, the contribution due to the charge-transfer mechanism should be taken into account.     

EPR parameters and defect structures of the off-center Ti ion on the Sr site in neutron-irradiated SrTiO3 crystal

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti³⁺ center in cubic phase and the rhombic Ti³⁺ center in tetragonal phase in the neutron-irradiated SrTiO₃ crystals are calculated from the third-order perturbation formulas of EPR parameters for d¹ ions. These low-symmetry Ti³⁺ centers in both phases of SrTiO₃ are due to the Ti³⁺ ion at “off center” on the Sr²⁺ site. From the calculation, the defect models (including the direction and magnitude of the Ti³⁺ off-center displacement) of the two Ti³⁺ centers in SrTiO₃ are estimated and the EPR parameters of both Ti³⁺ centers are reasonably explained on the basis of the defect models. The results are discussed.     

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr ions at tetragonal charge-compensation defect CrF5O site in Cr: KMgF3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g_‖ and g_⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF₅O defect center in Cr³⁺:KMgF₃ crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O²⁻ for F⁻ and its induced lattice relaxation Δ₁(O²⁻) combined with an inward relaxation of the nearest five fluorine Δ₂(F⁻) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O²⁻ moves towards the central ion Cr³⁺ by Δ₁(O²⁻)=0.172R₀ and the five F⁻ ions towards the central ion Cr³⁺ by Δ₂(F⁻)=0.022R₀. Our approach takes into account the spin-orbit (SO) interaction as well as the spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.     

Crystal field and microscopic spin Hamiltonians approach including spin-spin and spin-other-orbit interactions for d and d ions at low symmetry C3 symmetry sites: V in Al2O3

A new module has been developed within the CFA/MSH computer package, which is applicable for d² and d⁸ ions at sites of trigonal symmetry type I (C_3v,D₃,D_3d) and type II (C₃,C_3i), including the ‘imaginary’ CF term. For the first time the spin-spin (SS) and spin-other-orbit (SOO) interactions have also been included in the Hamiltonian. This module enables to study the contributions to the energy levels and the spin Hamiltonian parameters, i.e. zero-field splitting D and g-factors: g_∥ and g_⊥. The contributions arising from the spin-orbit (SO), SS, and SOO interaction as well as those due to the low symmetry CF effects induced by the distortion angle ?, which describes the difference between C₃ and C_3v symmetry, can be studied. As an application of the new module, calculations have been carried out for V³⁺(3d²) ions in α-Al₂O₃ crystal, taking into account for the first time the SS and SOO interactions, and the low symmetry CF effects. The results show that (i) the contributions from the SS and SOO interactions to the energy levels are larger for free V³⁺ ions than those for V³⁺ ions in α-Al₂O₃ crystal, (ii) both the contributions to the SH parameters and the energy levels arising from the SOO interaction are larger than those arising from the SS interaction, (iii) the contributions due to the low symmetry CF effects induced by the distortion angle ? are in general significant, (iv) D and g_⊥ are sensitive to the distortion angle ?, whereas g_∥ is insensitive to ?, and (v) the influence of the lattice distortions on the spectroscopic properties of V³⁺ ion in α-Al₂O₃ is pronounced. It appears important for similar ion-crystal cases to consider the lattice distortions in detailed calculations, which take into account the relevant contributions from the SO, SS and SOO interactions. A good agreement between the theoretical and experimental results has been obtained.     

轴对称晶场中d3离子激发态对4A2基态自旋哈密顿参量的影响

采用完全对角化方法，讨论了三角对称和四角对称下d³离子自旋二重态和自旋四重态对基态⁴A₂(⁴F)自旋哈密顿(SH)参量(包括零场分裂(ZFS)和g因子)的影响机理. 并对影响基态SH参量的四种机理(SO机理，SS机理，SOO机理和SO-SS-SOO联合机理)进行了分析. 结果表明，自旋二重态与四重态对d³离子基态零场分裂都具有重要贡献；而基态g因子主要由四重态决定，二重态对g因子贡献很小. 此外，发现SS机理和SOO机理对基态EPR参量的贡献主要由四重态决定，二重态的影响很小.     

四角对称晶场中4B1(3d3)态离子的磁相互作用及其自旋哈密顿参量研究

基于完全对角化方法，研究了⁴B₁(3d³)态 离子在四角对称晶场中的磁相互作用，分析了自旋哈密顿参量(b⁰₂, g_∥, g_⊥ , Δg)的微观起源.结果表明 ：在被考虑的大部分晶场区域，人们通常考虑的SO(spin-orbit)磁相互作用的贡献最为重要 ；然而，对于零场分裂参量b⁰₂而言，来自其他机理(包 括SS(spin-orbit)，SOO(sp in-other-orbit)，SO-SS-SOO)的贡献在大部分晶场区域超过了20％；在部分晶场区域，其 他机理的贡献甚至超过SO机理的贡献.详细地分析了Macfarlane 零场分裂参量b^{0₂ 近似三阶微扰理论的收敛性，结果表明：该理论在大部分晶场区域收敛性较差.讨论了3d3}态离子第一激发态²E_g分裂的微观起源.并利用 群论方法解 释了在C_4v和C_3v对称晶场中²E_{g< /sub>态分裂的不同机理. 关键词： 4B1(3d³)态离子')" href="#">⁴B1(3d³)态离子 磁相互作用 自旋哈密 顿参量 完全对角化方法(CDM) 微扰理论方法(PTM)}     

Investigations of the optical and EPR spectra for (NiX6) (X=Cl, Br, I) clusters

In this paper, the formulae of optical spectral levels and electron paramagnetic resonance (EPR) spectra in trigonal symmetry of 3d⁸ ions are established on the basis of strong field mechanism and a two spin-coupling (SO) parameters model. Unlike the classical crystal-field approach which has only taken the SO coupling of the central metal ions into account, the contribution of the SO coupling of the ligand ions to the optical and EPR spectra has been included in these formulae. When the optical and EPR spectra of the strong covalent crystals are calculated, the reasonable results can be obtained if the two SO parameters model has been put into action. As an application, the optical and EPR spectra of the (NiX₆)⁴⁻ clusters in CsMgX₃:Ni²⁺ (X=Cl, Br, I) crystals have been studied by the complete diagonalization (of energy matrix) method (CDM). The calculated results agree well with experimental findings. From the investigations, a more valid method to calculate the optical and EPR spectra for 3d⁸ ions clusters is provided.     

Local structure distortion and spin Hamiltonian parameters of oxide-diluted magnetic semiconductor Mn-doped ZnO

The local structure distortion, the spin Hamiltonian (SH) parameters, and the electric fine structure of the ground state for Mn²⁺(3d⁵) ion in ZnO crystals are systematically investigated, where spin--spin (SS), spin--other--orbit (SOO) and orbit--orbit (OO) magnetic interactions, besides the well-known spin--orbit (SO) coupling, are taken into account for the first time, by using the complete diagonalization method. The theoretical results of the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g_// and g_⊥, and the energy differences of the ground state: \delta₁ and \delta₂ for Mn²⁺ in Mn²⁺: ZnO are in good agreement with experimental measurements when the three O^2- ions below the Mn²⁺ ion rotate by 1.085^o away from the [111]-axis. Hence, the local structure distortion effect plays an important role in explaining the spectroscopic properties of Mn²⁺ ions in Mn²⁺: ZnO crystals. It is found for Mn²⁺ ions in Mn²⁺: ZnO crystals that although the SO mechanism is the most important one, the contributions to the SH parameters, made by other four mechanisms, i.e. SS, SOO, OO, and SO～SS～SOO～OO mechanisms, are significant and should not be omitted, especially for calculating ZFS parameter D.     

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.     

Crystal field analysis of the absorption spectra and electron-phonon interaction in Ca3Sc2Ge3O12:Ni

Exchange charge model of crystal field [B.Z. Malkin, in: A.A. Kaplyanskii, B.M. Macfarlane (Eds.), Spectroscopy of Solids Containing Rare-earth Ions, North-Holland, Amsterdam, 1987, pp. 33-50.] was used to analyze the energy level schemes of Ni²⁺ ion at both possible positions (octahedral and tetrahedral) in Ca₃Sc₂Ge₃O₁₂. The crystal field parameters were calculated from the crystal structure data; the crystal field Hamiltonian was diagonalised in the complete basis consisting of 25 wave functions of all LS terms of the Ni²⁺ ion. Results of calculations are in a good agreement with experimental data. From the experimental spectra available in the literature, the Huang-Rhys parameter S=3.5 and effective phonon energy were evaluated for the octahedral Ni²⁺ ion.     

Investigations of EPR Parameters of MgTiO3:Cr3+, SrTiO3:Cr3+, and SrTiO3:Mn4+ Crystals

Complete high-order perturbation formulas are established based on charge-transfer (CT) and crystal-field (CF) mechanisms. The electron paramagnetic resonance (EPR) g-factors of MgTiO₃:Cr³⁺, SrTiO₃:Cr³⁺, and SrTiO₃:Mn⁴⁺ crystals are calculated from the formulas. The calculations of the EPR g-factors agree well with the experimental values. The contribution rate of the CT mechanism to EPR parameters increases with increasing valence state of the 3d ⁿ ions in the crystals. For the higher-valence state 3d ³ Mn⁴⁺ ion in the crystals, the elucidation of the EPR parameters rationally involves both CF and CT mechanisms.     

EPR theoretical study of local lattice structure in Al2O3:Fe system

By analyzing the EPR spectrum of transition-metal ion Fe³⁺ in Al₂O₃:Fe³⁺ system, the local lattice structure around impurity Fe³⁺ ion in the crystal has been studied by means of the diagonalization of the energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for a d⁵ configuration ion in a trigonal ligand-field. Both the second-order and fourth-order EPR parameters D and (a−F) are taken simultaneously in the structural investigation. The results indicate that the two three-edge-pyramids elongated obviously along C₃ axis. The two distortion angles Δθ₁=−1.1±0.1°,Δθ₂=−1.8° as well as the two Fe-O bond lengths R₁=2.016 A, R₂=1.907 A are determined, respectively.     

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.     

Ni2+—6X-络合物g因子的双自旋—轨道耦合系数模型

本文提出一个计算Ni²⁺—6X^-络合物g因子的双自旋-轨道耦合系数模型,并用以计算NaCl:Ni²⁺和NaBr:Ni²⁺的g因子。计算中采用了一种半经验方法来确定分子轨道系数。结果表明,对Br^-或I^-这类具有大的自旋-轨道耦合系数的配体离子,配体自旋-轨道耦合作用对g因子的贡献不可忽略。这表明,对某些共价晶体,g因子的计算必须用双自旋-轨道耦合系数模型的理论公式而不能用只包括 关键词：     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Theoretical explanation of g factors for Ti ions in LiNbO3 and LiTaO3 crystals

The EPR g factors g_// and g_⊥ for Ti³⁺ ions at the trigonal octahedral Li⁺ sites of LiNbO₃ and LiTaO₃ crystals are calculated from the third-order perturbation formulas of g factors for 3d¹ ion in trigonal symmetry. In the calculations, the crystal-field parameters are obtained from the structural data by using the superposition model. The calculated values are in reasonable agreement with the observed values. The results are discussed.