四角对称晶场中3d3离子零场分裂理论研究

分别采用完全对角化方法和微扰方法讨论了微小磁相互作用对四角对称下基态⁴B₁态和第一激发态²E 态零场分裂的影响. 结果表明,⁴B₁态零场分裂与微小磁相互作用参量成线性关系,²E 态零场分裂主要由二重态决定,磁相互作用和四角晶场对²E 态零场分裂的贡献相比较,四角晶场的作用是主要的.     

ZnSiF66H2O:Fe2+晶体光谱结构的杨-特勒效应和电子顺磁共振g因子

研究了过渡金属络合物ZnSiF66H2O∶Fe2 晶体光谱结构的杨特勒效应和电子顺磁共振g因子。由单晶的中子衍射方法得到ZnSiF66H2O∶Fe2 的晶体结构,这种结构可以用SiF62-和Zn(H2O) ∶Fe2 两个离子来描述。而局域三角对称的Zn(H2O) ∶Fe2 离子反映了这种晶体的主要光谱性质。利用不可约张量的理论构成了晶体场和自旋轨道相互作用哈密顿矩阵和电子顺磁共振理论公式,求出了晶体ZnSiF66H2O∶Fe2 中Fe2 离子的电子顺磁共振零场分裂参量(D,F-a)及g因子,并研究了低自旋3L态对电子顺磁共振零场分裂参量的贡献是不能忽略的,而对g因子的贡献是非常小的,并理论计算了它的晶体结构,证实了杨特勒效应的存在,理论计算的结果与实验值是相符的。     

ZnSiF66H2O∶Fe2+晶体光谱结构的杨特勒效应和电子顺磁共振g因子

研究了过渡金属络合物ZnSiF66H2O∶Fe2+晶体光谱结构的杨特勒效应和电子顺磁共振g因子。由单晶的中子衍射方法得到ZnSiF66H2O∶Fe2+的晶体结构,这种结构可以用SiF2-6和Zn(H2O)++∶Fe2+两个离子来描述。而局域三角对称的Zn(H2O)++∶Fe2+离子反映了这种晶体的主要光谱性质。利用不可约张量的理论构成了晶体场和自旋轨道相互作用哈密顿矩阵和电子顺磁共振理论公式,求出了晶体ZnSiF66H2O∶Fe2+中Fe2+离子的电子顺磁共振零场分裂参量(D,F-a)及g因子,并研究了低自旋3L态对电子顺磁共振零场分裂参量的贡献是不能忽略的,而对g因子的贡献是非常小的,并理论计算了它的晶体结构,证实了杨特勒效应的存在,理论计算的结果与实验值是相符的。     

FeSiF66H2O晶体的基态能级和零场分裂参量

由单晶的中子衍射方法得到FeS_iF₆6H₂O的晶体结构,这种晶体结构可以用S_iF^6-和Fe(H₂O)⁺⁺两个离子来描述,而局域三角对称的Fe(H₂O)⁺⁺离子反映了这种晶体的主要光谱性质利用不可约张量的理论,构成了晶体场和自旋轨道相互作用哈密顿完全对角化矩阵因此,由完全对角化的晶体场和自旋轨道相互作用哈密顿矩阵和电子顺磁共振的理论公式来求出晶体FeS_iF₆6H₂O中Fe²⁺离子的电子顺磁共振零场分裂参量D和Fa并研究了低自旋³L态对电子顺磁共振(EPR)零场分裂参量的贡献结果显示低自旋³L态对电子顺磁共振的零场分裂参量的贡献是较强的理论计算的结果与实验值是相符的.     

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     

Energy Spectra,g Factors and Their Pressure—induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ Ⅱ：Pressure Effects on Ground_State g Factor and Splittings of t2^32E and t2^34A2 of Sr

By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3:Cr^3 and its pressure-induced shift have been microscopically calculated.Only by taking the local strains around Cr^3 in SrTiO3:Cr^3 (which are about twice the bulk ones)and corresponding P-χ dependence,can we obtain a good agreement etween the calculated result of pressure-induced shift of ground-state g factor and the experimental one.The physical origins of this pressure-induced shift have been explained.It is found that the change of Dq^-1 with pressure makes main contribution to the pressure-induced shift of ground-state g factor of SrTiO3:Cr^3 .By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal pressure,the relevant matrix elements and accordingly strain-induced splittings of t2^32E and t2^34A2 of SrTiO3:Cr^3 have been calculated.The important results of Yc.Zc,Pc and Qc have also been evaluated.It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and /or Coulomb interaction and /or Kramers degeneracy that make the strain-induced splittings of the levels nonzero.It is found that there are nonvanishing matrix elements of operators T2ξ between wavefuncgtions with positive Ms and those with negative Ms′ and those with negative ms′,which have important effects on the strain-induced splittings of the levels.     

Ni~(2+):LiNbO_3的光学吸收谱和EPR的研究

应用三角晶场中d2 (d8)电子组态的包括静电相互作用和自旋 轨道耦合相互作用的强场能量矩阵 ,采用完全对角化方法 ,精确地计算了具有C3V 对称的Ni2 +:LiNbO3 的光学吸收谱和EPR谱。理论结果与实验值符合得很好     

Microscopic Analysis of 5d States Splitting and Charge Transfer Energies Dependence on Interionic Distance in Alkaline Earth Fluorides Doped with Light Trivalent Lanthanides

A first principles fully relativistic analysis (K. Ogasawara et al., Phys. Rev. B 2001, 64, 115413) of the dependence of 5d orbitals splitting (10Dq) and charge transfer (CT) energies on interionic distance has been performed for light lanthanides (Ce³⁺, Pr³⁺, Nd³⁺) in CaF₂, SrF₂, BaF₂ crystals. The salient feature of the method is that four‐component molecular orbitals (MO) composed of atomic wave functions are used as the basis set. Without any fitting parameter, the power dependencies for 10Dq and linear dependencies for the CT energies on the distance between rare‐earth (RE) ions and ligands were obtained. A comparison with experimental values is discussed.     

On the relations between the crystal field parameter notations in the “Wybourne” notation and the conventional ones for 3d ions in axial symmetry crystal field

The correlations of the various crystal field (CF) notations existing in the literature for 3d^N ions in axial symmetry crystal field have been investigated. The confusions among these CF notations have been clarified. The correlations of the various CF notations are summarized in Table 1, which is very useful in the investigations of 3d^N ions in crystal material.     

掺入Ni2+和V3+对α-Al2O3晶体光谱精细结构、晶体局域结构和零场分裂参量的影响

应用晶体场理论和不可约张量算符方法构造了3d2/3d8态离子在C3v对称晶场中包含自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用四种微观磁效应的45阶可完全对角化的能量哈密顿矩阵.利用该矩阵,计算了V³⁺∶α-Al₂O₃和Ni²⁺∶α-Al₂O₃晶体的光谱精细结构、晶体局域结构和零场分裂参量,研究了掺入两种互补态离子Ni²⁺和V³⁺对同种晶体的光谱精细结构、晶体局域结构和零场分裂参量的影响,理论计算值和实验值相符.研究发现：掺杂没有改变晶体的光谱精细结构和能级分裂条数,但改变了能级间距|掺杂也没有改变晶体的对称性,但使晶体局域结构发生了一定程度的畸变| Ni²⁺∶α-Al₂O₃晶体局域结构的伸长畸变量大于V³⁺∶α-Al₂O₃晶体,键角的变化量小于V³⁺∶α-Al₂O₃晶体.     

Theoretical Calculations of Strain—Induced Splittings and／or Shifts of t2^32E and t2^34A2 Levels for MgO：Cr^3＋

Under various uniaxial stresses, both strains with low symmetry and isotropic strains of crystals take place. The former gives the strain-induced low-symmetry crystal fields and accordingly splittings of levels; the latter gives the isotropic parts of strain-induced crystal fields and accordingly shifts of levels. By using the wavefunctions obtained from the diagonalization of the complete d^3$ energy matrix in a regular octahedral field, the relevant matrix elements and accordingly strain-induced splittings and/or shifts of t₂³²E and t₂³⁴A₂ for MgO:Cr³⁺ have been calculated. Their physical origins have been thoroughly analyzed and revealed. It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and/or Coulomb interaction and/or Kramers degeneracy that make strain-induced splittings of levels nonzero. In contrast with this, strain-induced shifts come mainly from the zero-order approximate wavefunctions. It is found that there are nonvanishing matrix elements of operators T₂ξ, T₂η and T₂ζ between wavefunctions with positive M_s and those with negative M_s', which have important effects on strain-induced splittings of levels. The shifts of t₂³²E under both hydrostatic pressure and uniaxial pressure have been uniformly calculated. The important results of Y_c, Z_c, P_c, Q_c and 〈t₂|| C(A₁)|| t₂〉have been evaluated.     

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.     

Ionization of Atoms and the Thomas-Fermi Model for the Electric Field in Crystal Planar Channels

The electric field in the crystal planar channels is studied by the Thomas Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numericalsolution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles ofchannelling protons in them are shown. Reasonable agreements with the experimental data are obtained. The resultsshow that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channelelectric field with the contribution of all atoms and the atomic ionization being taken into account is practical.     

Spectroscopic properties of Fe ions at tetragonal sites—Crystal field effects and microscopic modeling of spin Hamiltonian parameters for Fe (S=2) ions in K2FeF4 and K2ZnF4

Magnetic and spectroscopic properties of the planar antiferromagnet K₂FeF₄ are determined by the Fe²⁺ ions at tetragonal sites. The two-dimensional easy-plane anisotropy exhibited by K₂FeF₄ is due to the zero field splitting (ZFS) terms arising from the orbital singlet ground state of Fe²⁺ ions with the spin S=2. To provide insight into the single-ion magnetic anisotropy of K₂FeF₄, the crystal field theory and the microscopic spin Hamiltonian (MSH) approach based on the tensor method is adopted. Survey of available experimental data on the crystal field energy levels and free-ion parameters for Fe²⁺ ions in K₂FeF₄ and related compounds is carried out to provide input for microscopic modeling of the ZFS parameters and the Zeeman electronic ones. The ZFS parameters are expressed in the extended Stevens notation and include contributions up to the fourth-order using as perturbation the spin-orbit and electronic spin-spin couplings within the tetragonal crystal field states of the ground ⁵D multiplet. Modeling of the ZFS parameters and the Zeeman electronic ones is carried out. Variation of these parameters is studied taking into account reasonable ranges of the microscopic ones, i.e. the spin-orbit and spin-spin coupling constants, and the energy level splittings, suitable for Fe²⁺ ions in K₂FeF₄ and Fe²⁺:K₂ZnF₄. Conversions between the ZFS parameters in the extended Stevens notation and the conventional ones are considered to enable comparison with the data of others. Comparative analysis of the MSH formulas derived earlier and our more complete ones indicates the importance of terms omitted earlier as well as the fourth-order ZFS parameters and the spin-spin coupling related contributions. The results may be useful also for Fe²⁺ ions at axial symmetry sites in related systems, i.e. Fe:K₂MnF₄, Rb₂Co_1−xFe_xF₄, Fe²⁺:Rb₂CrCl₄, and Fe²⁺:Rb₂ZnCl₄.     

Zero-field splitting of <Superscript>4</Superscript><Emphasis Type="Italic">T</Emphasis><Subscript>2</Subscript> term for 3d<Superscript>3</Superscript> ions in tetragonal symmetry

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ⁴ T ₂ state for 3d³ ions at tetragonal symmetry has been studied. The convergence of the approximation perturbation formula of ⁴ T ₂ state for 3d³ ions at tetragonal symmetry has been investigated, and the contributions to zero-field splitting arising from magnetic interaction and tetragonal crystal field are discussed. It is found that there exists combined mechanism between magnetic interactions and tetragonal crystal field.      

Method for fitting crystal field parameters and the energy level fitting for Yb3+ in crystal Sc2O3

<正>A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given,based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt,Newton method, and so on,can be used to solve crystal field parameters by fitting to experimental energy levels.With the numerical eigenvalue derivative,a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described.This method is used to compute the crystal parameters of Yb~(3+) in Sc_2O_3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method.By fitting on the parameters of a simple overlap model of crystal field,the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.