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)     

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.     

掺杂晶体材料ZnGa_2O_4:Fe~(3+)局域结构畸变及其微观自旋哈密顿参量研究

基于Newman的晶场叠模型与微观自旋哈密顿理论,建立了ZnGa2O4:Fe3+晶体材料中磁性离子Fe3+局域结构与其自旋哈密顿(spin-Hamiltonian,SH)参量(包括二阶零场分裂(zero-field splitting,ZFS)参量D,四阶ZFS参量(a-F),Zeeman g因子:g//,g⊥,△g(=g//-g⊥))之间的定量关系.采用以全组态完全对角化方法为理论背景的CFA/MSH(Crystal Filed Analysis/Microscopic Spin Hamiltonian)研究软件,研究了ZnGa2O4:Fe3+材料中磁性离子Fe3+的SH参量与其局域结构的依赖关系.研究表明:对于ZnGa2O4:Fe3+晶体材料,当磁性离子Fe3+的局域结构畸变参数△R=0.0487 nm,△θ=0.192°时,其基态SH参量理论计算结果与实验测量符合很好,进一步表明Fe3+掺入晶体材料后将引起磁性Fe3+离子局域结构的微小畸变,但其仍然保持D3d点群对称局域结构.在此基础上研究分析了SH参量的微观起源,结果表明:ZnGa2O4:Fe3+晶体材料的SH参量主要来源于SO(spin-orbit)磁相互作用机理,来自其他磁相互作用机理(包括SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit),SO-SS-SOO-OO)的贡献比较小.     

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.     

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.     

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)}     

Spin Hamiltonian parameters and structural disorder analysis for Cr ion in YGG crystals

A new crystalline lattice distortion model has been proposed, on the basis of it, the relations between spin Hamiltonian parameters and crystal micro structure have been established. By taking into account slight magnetic interactions, including spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions, the local structure of Cr³⁺ ion in YGG crystal has been studied using complete diagonalization method (CDM). The studies show that the local structure in the YGG:Cr³⁺ crystal is of the compressed trigonal distortion. The ligand oxygen plane moved 0.0138 nm toward Cr³⁺ ion along C₃-axis. Accordingly, the SH parameters in YGG:Cr³⁺ crystal are explained successfully.     

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.     

Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn ions in various hosts exhibiting orthorhombic site symmetry

The intrinsic properties of orthorhombic Hamiltonians, e.g. zero-field splitting (ZFS) ones or crystal-field (CF) ones, embodied in the standardization idea may be utilized to improve reliability and comparability of experimentally determined ZFS (or CF) parameters. These properties have enabled derivation of transformation relations for Hamiltonian parameters expressed in several related axis systems defined earlier by one of us. In this paper the standardization transformations are used to generate alternative physically equivalent yet numerically distinct parameter sets for Mn²⁺ ions in various hosts exhibiting orthorhombic or lower site symmetry. One parameter set out of six alternative sets satisfies the standardization criteria. Importantly, the standardized sets should be used for direct comparisons. Several non-standard ZFS parameter (ZFSP) sets for Mn²⁺ ions in crystals, identified in our literature survey of EMR studies, are here standardized. Thus the ratio of λ=E/D or λ′=B₂²/B₂⁰ is limited to the standard range (0, ±1/3) or (0, ±1), respectively. Our considerations provide useful correlations between the distinct and non-compatible yet physically equivalent ZFS parameter sets reported in literature. All calculated alternative sets are tabularized for ten Mn²⁺ complexes considered. These ZFSP sets may serve for application of the multiple correlated fitting techniques in follow-up EMR studies. Some misinterpretations yielding ambiguous and unreliable results are clarified. The intricate low symmetry aspects are also discussed, whenever applicable. The results of this paper enable more reliable analysis, comparison, and fitting of ZFSP sets from EMR spectra for Mn²⁺ ions in various crystals.     

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g _//, g ⊥ and hyperfine structure constants ⁶³ A _//, ⁶³ A ⊥, ⁶⁵ A _//, ⁶⁵ A ⊥) for Cu²⁺ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d ⁹ ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the ² T ₂ term. It appears that, for exact calculations of SH parameters of d ⁹ ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the ² T ₂ term. The local structures of Cu²⁺ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu²⁺ and GaN : Cu²⁺ are obtained from the calculations. The results are discussed.     

三角对称晶场中6 S(3d5)态离子零场分裂参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶ S(3d⁵)态离子在三角晶场(包括C_3v,D₃,D_3d点群对称晶场)中零场分裂(zero-field splitting, ZFS)参量D和(a-F)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 关键词： 6 S(3d⁵)态离子')" href="#">⁶ S(3d⁵)态离子 零场分裂参量 磁相互作用 完全对角化方法     

EPR and luminescence of Mn2+ in MgF2 single crystals

EPR spectra of Mn²⁺ in MgF₂ crystals grown by the Bridgman technique were measured at 300 and 20 K. Application of the superposition model to the zero field splitting (ZFS) patterns indicates complete absence of dynamic contributions to the ZFS. The luminescence spectra are also in accord with substitutional incorporation of Mn²⁺.     

Theoretical studies on the SH parameters and local distortion structure of KCl:Ag crystal

Complete diagonalization of the energy matrix and high order perturbation formulae of spin-Hamiltonian (SH) parameters possessing D_4h symmetry for the 4d⁹ ion based on the crystal- and ligand-field theory in tetragonal symmetry are expressed and applied to the study of local distortion structure of the KCl:Ag²⁺ crystal. The calculated results agree well with experimental findings. Both complete diagonalization of energy matrix and high order perturbation approach are appropriate for the investigations of SH parameters of 4d⁹ ions in tetragonal crystals. Tetragonal distortion due to the Jahn-Teller effect for the tetragonal Ag²⁺ center at the K⁺ site of KCl crystal is also acquired from the calculations.     

Zero-field splitting and local structure for V<Superscript>2+</Superscript> ions in CsMg<Emphasis Type="Italic">X</Emphasis><Subscript>3</Subscript> (<Emphasis Type="Italic">X</Emphasis>=Cl,Br, I) crystals

The zero-field splitting and local structure for V²⁺ ions in CsMgX ₃ (X =Cl, Br, I) crystals are theoretically investigated using complete diagonalization method (CDM) for a 3d ³ ion in trigonal symmetry. Spin-spin (SS) and spin-other-orbit (SOO) interactions are taken into account in addition to the general spin-orbit (SO) interaction. On this basis, using ligand ion displacement model, we find that the ligand ions move away from C ₃-axis, and therefore the local angles in the V²⁺ centres are larger than the angles in the hosts. The results show good agreement with the observed values.     

Al2O3:V3+晶体局域结构及其自旋哈密顿参量研究

提出了解释掺杂离子局域结构畸变的配体平面移动模型，建立了此模型下晶体微观结构与自旋哈密顿参量之间的定量关系.在考虑自旋与自旋、自旋与另一电子轨道和轨道与轨道作用等微小磁相互作用的基础上，采用全组态完全对角化方法，对Al₂O₃晶体中V³⁺的局域结构和自旋哈密顿参量进行了系统的研究.结果表明，V³⁺掺入Al₂O₃晶体后，上下配体氧平面间距离增大了0.0060 nm.从而成功地解释了Al₂O₃:V³⁺晶体的自旋哈密顿参量.在此基础上，研究了三角晶场下3d²离子自旋哈密顿参量的微观起源.研究发现，自旋三重态对自旋哈密顿参量的贡献是主要的，微小磁相互作用对自旋哈密顿参量的贡献只与自旋三重态有关.     

晶体材料中3d2态离子自旋哈密顿参量的微观起源

采用了中间场耦合图像，考虑了以前研究中被忽略的SS (spin-spin)磁相互作用以及SOO (spin-other-orbit)磁相互作用，利用完全对角化方法，研究了3d₂态离子在三角对称 (C_3v, D₃, D_3d)晶体中自旋哈密顿(SH)参量的微观起源.发现自旋哈密顿参量 (包括零场分裂参量D和g因子g∥,g⊥)来自四种耦合机理：（1）SO (spin-orbit)耦合机理; (2) SS耦合机理；（3）SOO 关键词： 自旋哈密顿参量 2态离子')" href="#">3d₂态离子 三角对称晶场 SS与SOO作用 SO-SS-SOO联合作用机理     

YAG∶Cr3+ 晶体精细光谱结构研究

采用不同的晶体畸变模型，利用CDM(complete diagonalization method)方法对YAG∶Cr3+ 晶体的EPR参量进行了系统研究.通过计算结果对晶格畸变模型进行了分析.结果表明,在三角对称下，对杂质离子电荷与中心离子电荷相等的情况，不适合用杂质离子沿C3轴位移的模型来研究晶体的局域结构，而且由于基态和第一激发态的零场分裂都对局域结构微变非常敏感，因此仅由基态零场分裂来确定晶格局域结构是不可靠的.同时结果表明，Cr3+ 离子进入YAG晶体后，产生了Δθ=1.88°的三角畸变.从而成功统一地解释了YAG∶Cr3+ 晶体的EPR参量和精细光谱结构.     

氟钙钛矿AMF3:Fe3+晶体中Fe3+离子的零场分裂参量及晶格缺陷研究

对氟钙钛矿晶体AMF₃：Fe³⁺（A=K，Rb，Cs；M=Zn，Cd）四角对称占位的零场分裂（ZFS）进行分析，证实了晶格缺陷及畸变的存在．对ZFS参量随晶格畸变参量的变化关系进行了详细研究，考虑了缺陷及缺陷引起的晶格畸变两者的贡献，得出几种氟钙钛矿晶体的晶格畸变参量 关键词：     

Luminescence of Mn ions in Tb3Al5O12 garnet

The paper is dedicated to investigation of the Mn²⁺ luminescence in Tb₃Al₅O₁₂ (TbAG) garnet, as well as the processes of excitation energy transfer between host cations (Tb³⁺ ions) and activators (Mn²⁺ and Mn²⁺-Ce³⁺ pair ions) in single crystalline films of TbAG:Mn and TbAG:Mn,Ce garnets which can be considered as promising luminescent materials for conversion of LED's radiation. Due to the effective energy transfer between TbAG host and activator, Mn²⁺ ions in TbAG possess the bright orange luminescence in the bands peaked at 595 nm with a lifetime of 0.64 ms which are caused by the ⁴T₁→⁶A₁ radiative transitions. The simultaneous process of energy transfer is realized in TbAG:Mn,Ce: (i) from Tb³⁺ to Mn²⁺ ions; (ii) from Tb³⁺ cations to Ce³⁺ ions and then partly to Mn²⁺ ions through Tb³⁺ ion sublattice and Ce-Mn dipole-dipole interaction.