掺入Mg2+对CsNiCl3晶体的基态能级、零场分裂参量及Jahn-Teller效应的影响

应用不可约张量理论构造了三角对称晶场中3d²/3d^８态离子的45阶可完全对角化的微扰哈密顿矩阵，在考虑了以前工作中被忽略的自旋-自旋耦合作用的基础上计算了CsNiCl₃晶体和CsNiCl₃:Mg²⁺晶体的基态能级、晶体结构、零场分裂参量和Jahn-Teller效应，研究了掺入Mg²⁺对CsNiCl₃晶体的光谱、零场分裂参量及Jahn-Teller效应的影响和自旋单重态对基态能级的贡献，发现掺杂使得晶体结构产生畸变，从而改变晶体光谱的精细结构和零场分裂参量，不改变Jahn-Teller效应的分裂规律但改变分裂的大小. 关键词： 基态能级 掺杂 零场分裂 自旋-自旋耦合     

BaCrSi4O10与AgGaSe2:Cr2+吸收光谱的精细结构及自旋单态对零场分裂参量的影响

在强场图像中构造了四角对称环境中Cr²⁺离子包括自旋单态在内的完全能量矩阵, 通过对角化能量矩阵方法, 计算得到了BaCrSi₄O₁₀与AgGaSe₂:Cr²⁺吸收光谱的精细结构及自旋单态对零场分裂参量的影响. 从理论上给出了BaCrSi₄O₁₀与AgGaSe₂:Cr²⁺吸收光谱的精细结构及BaCrSi₄O₁₀的零场分裂参量值. 计算结果显示自旋单态对零场分裂参量D的影响完全可忽略, 但对a和F的影响比较大. 这种影响主要来自自旋-轨道耦合导致的自旋五重态与自旋三重态和自旋单态的相互作用, 而自旋轨道耦合的选择定则显示自旋单态并非直接影响五重态而是通过自旋三重态间接地影响基态的五重态. 因此, 为了得到准确的零场分裂参量值, 所有的自旋态都应该考虑.     

掺入Mg2+对CsNiCl3晶体的基态能级、零场分裂参量及Jahn-Teller效应的影响

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵,在考虑了以前工作中被忽略的自旋-自旋耦合作用的基础上计算了CsNiCl3晶体和CsNiCl3:Mg2+晶体的基态能级、晶体结构、零场分裂参量和Jahn-Teller效应,研究了掺入Mg2+对CsNiCl3晶体的光谱、零场分裂参量及Jahn-Teller效应的影响和自旋单重态对基态能级的贡献,发现掺杂使得晶体结构产生畸变,从而改变晶体光谱的精细结构和零场分裂参量,不改变Jahn-Teller效应的分裂规律但改变分裂的大小.     

CsNiCl3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d²/3d⁸态离子的45阶可完全对角化的微扰哈密顿矩阵，研究了CsNiCl₃晶体的光谱精细结构、晶体结构、零场分裂参量、Jahn-Telller效应以及自旋单重态对Ni²⁺离子基态能级的影响，理论与实验相符合.在此基础上，进一步研究了以前工作中被忽略的自旋-自旋耦合作用和Trees修正对CsNiCl₃晶体的光谱精细结构和零场分裂参量的影响，发现有四种机理会影响零场分裂参量：1)自旋-轨道耦合机理，2)自旋-自旋耦合机理；3)自旋-轨道与自旋-自旋联合耦合机理；4)自旋-轨道与Trees修正联合耦合机理，其中自旋-轨道耦合机理是最主要的，其他三种机理也是不可忽略的. 关键词： 基态能级 精细结构 零场分裂 自旋-自旋耦合     

KCdF3:Cr3+晶体EPR零场分裂参量与电荷补偿效应的研究

按照叠加模型与EPR零场分裂参量的三阶微扰理论,建立了KCdF₃:Cr³⁺晶体EPR零场分裂参量与四角对称Cr³⁺-Cd²⁺缺陷中心局域结构之间的定量关系.证实Cd²⁺空位与晶格畸变的存在,我们获得:围绕Cr³⁺离子的六个F^-配体分别向中心Cr³⁺移动Δ₁=0.00294nm,Δ₂=0.0010nm,Δ₃=0.0028nm (参见图2).EPR零场分裂参量与实验一致表明:Cd²⁺空位与晶格畸变的假设是合理的.尽管四角晶场主要来自Cd²⁺空位,但晶格畸变的贡献不可忽略.     

红宝石晶体的基态能级分裂及Jahn-Teller效应

应用不可约张量方法和群的理论构造了三角对称晶场中考虑自旋-轨道相互作用，自旋-自旋相互作用的3d³/3d⁷离子的可完全对角化的120阶微扰哈密顿矩阵，利用该矩阵计算了红宝石晶体的基态能级、零场分裂参量和Jahn-Teller效应，研究了自旋-轨道的自旋二重态对基态能级的贡献，证明其二重态对基态能级的贡献是不可忽略的，理论计算值与实验值相符合.在此基础上，进一步研究了自旋-自旋相互作用对红宝石晶体的光谱精细结构和零场分裂参量的影响，发现自旋-自旋相互作用对零场分裂参量的影响是不可忽略的. 关键词： 基态能级 精细结构 自旋-轨道相互作用 零场分     

GeFe2O4晶体的基态能级和零场分裂参量

GeFe₂O₄是一种单晶化合物，考虑到由3个〈111〉方向之一的一个 轴，从一个中心位置 到另一个中心位置之间，以Fe²⁺离子为中心离子和O^2-为配体构 成了三角（C 3v）对称体系.利用不可约张量理论，建立了3d⁴/3d⁶离子三角（C3 v）对称的晶体场和 自旋相互作用哈密顿矩阵，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 和电子顺磁共振理论公式求出单晶GeFe₂O₄中Fe²⁺离子 的电子顺磁共振零场分 裂参量D和F-a.并研究了自旋三重态对电子顺磁共振（EPR）零场分裂的贡献.结果显示自旋 三重态对基态零场分裂的贡献是较强的，理论计算结果与实验值相符. 关键词： 自旋三重态 晶体场 低自旋态 高自旋态 零场分裂     

Ni2+：CsMgCl3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵,研究了CsNiCl3单晶掺入CsMgCl3晶体后光谱精细结构、晶体结构、零场分裂参量、Jahn-Teller效应以及自旋单重态对Ni2+离子基态能级的影响,理论与实验相符合.研究了自旋-自旋耦合作用和Trees修正对Ni2+:CsMgCl3晶体的光谱精细结构和零场分裂参量的影响,发现有五种机理会影响零场分裂参量:(1)自旋-轨道耦合机理;(2)自旋-自旋耦合机理;(3)自旋-轨道与自旋-自旋联合耦合机理;(4)自旋-轨道与Trees修正联合耦合机理,(5)自旋-自旋作用与Trees联合耦合机理.其中自旋-轨道耦合机理是最主要的,其它几种机理也是不可忽略的.     

ZnAl2O4:Cr3+晶体4A2基态ZFS及其三角晶格畸变研究

用对角化哈密顿矩阵的方法,借助New man晶场叠加模型,研究了ZnAl₂O₄:Cr³⁺晶体的基态零场分裂(ZFS)及其电子光谱,理论结果与实验一致.定量研究表明,掺杂晶体ZnAl₂O₄:Cr³⁺中,络离子(CrO₆)^9-局域结构应有压缩的三角畸变(△θ=3.06°).同时指出,自旋二重态对⁴A₂基态ZFS参量b₂⁰的贡献不可忽略,而对g因子的贡献甚微.     

LaAlO3: Cr3+低温常压下的能谱和顺磁 g 因子的统一解释

利用配位场理论,在强场方案下,建立了包括立方晶场、库仑相互作用、自旋-轨道耦合、低对称场的d³完全能量矩阵,对LaAlO₃：Cr³⁺在低温常压下的能谱进行了拟合,确定了相应的参量,得到了与实验值比较相符的能谱,并利用所得的波函数计算了LaAlO₃：Cr³⁺基态的 g 因子,与实验结果相吻合. 根据所得参量分析了Cr³⁺与配位体之间相互作用的特性.     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.     

Local structure distortion and spin Hamiltonian parameters for Cr3＋-Vzn tetragonal defect centre in Cr3＋ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g_‖, Δg) and the crystal structure parameters for the Cr³⁺—V_Zn tetragonal defect centre in a Cr³⁺:KZnF₃ crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr³⁺—V_Zn tetragonal defect centre in the KZnF_3 crystal are systematically investigated using the complete diagonalization method. It is found that the V_Zn vacancy and the differences in mass, radius and charge between the Cr³⁺ and the Zn²⁺ ions induce the local lattice distortion of the Cr³⁺ centre ions in the KZnF₃ crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F^- ion along [001] and the other five F^- ions move towards the central Cr³⁺ by distances of Δ₁ = 0.0121 nm and Δ₂ = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr³⁺ ions in the Cr³⁺:KZnF₃ crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.     

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.     

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.     

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.     

Theoretical study of spin-singlet contributions to zero-field splitting of a 3d6 ion in a trigonal ligand field and applications to Fe2+ in FeSiF6 · 6H2O and FeCO3

The complete energy matrix (210 × 210) for d⁶(d⁴) configuration ions in a trigonal ligand field is constructed. The energy levels and zero-field splitting parameters in ferrous fluosilicate and ferrous carbonate are studied. The contributions of spin singlets to zero-field splitting parameters in a trigonal ligand field are investigated for the first time. The calculation results indicate that the spin-singlet contribution to second-order zero-field splitting parameter D is negligible, but the contributions to fourth-order zero-field splitting parameter a ? F cannot be neglected. Moreover, it is found that the stronger the trigonal ligand field, the larger are the spin-singlet contributions to the zero-field splitting parameters.     

Effect of local structure on electron paramagnetic resonance spectra for trigonal [Cr(H2O)6]3+coordination complex in the sulfate alums series: a ligand field theory study

A simple theoretical method is introduced for studying the interrelation between electronic and molecular structures.By diagonalizing the 120 × 120 complete energy matrices,the relationships between zero-field splitting(ZFS) parameter D and local distortion parameter △θ for Cr 3+ ions doped,separately,in α-and β-alums are investigated.Our results indicate that there exists an approximately linear relationship between D and △θ in a temperature range 4.2-297 K and the signs of D and △θ are opposite to each other.Moreover,in order to understand the contribution of spin-orbit coupling coefficient ζ to ZFS parameter D,the relation between D and ζ is also discussed.     

Investigation of local lattice structure around Cr3+ ions at the trigonal and tetragonal sites in RbCdF3: Cr3+ crystal

The local lattice structure and EPR, optical spectra for Cr³⁺ doped in RbCdF₃ crystal have been studied by diagonalizing the complete energy matrices. The results show that the local structure of the Cr³⁺ ions in RbCdF₃ exhibits a compressed distortion at the trigonal and tetragonal sites. The compressed distortion can be ascribed to the fact that the radius of Cr³⁺ ion is smaller than that of Cd²⁺ ion, and therefore Cr³⁺ ion will draw the fluorin ligands inwards. The variational ranges of the local structural parameters for Cr³⁺ doped in RbCdF₃ crystal R =?1.9491 Å ～?1.9814 Å, θ?= 55.234° ～?55.286° at the trigonal site and R ₁ =?1.8617 Å ～?1.8928 Å, R ₂ =?1.9527 Å ～?1.9851 Å at tetragonal site are obtained respectively, and the EPR and optical spectra agree well with the experimental results.     

Theoretical study of the dependence of EPR spectra on local structure for octahedral Cr3+ centres in oxides and fluorides series

A theoretical method for investigating the inter-relation between the EPR parameters and local structure has been established on the basis of the complete energy matrices for 3d³ configuration ions in both the trigonal and tetragonal ligand fields. By means of this method, the local structure of the octahedral Cr³⁺ centres in double molybdates series and spinels series as well as the perovskite-type fluorides series has been studied systematically. Furthermore, the dependence of the EPR zero-field splitting parameter D on the local structure parameters in both trigonal and tetragonal ligand-fields has been revealed, simultaneously. The inter-relation between the EPR parameters D and Δg(g _// ??g _⊥) is also elucidated.     

Tb ions in presence of ZnS:Mn nanocrystals immobilized on silica: Energy transfer ZnS→Tb and coordination state of Mn ions

Three-component luminescent material consisting of silica xerogel as a support with immobilized ZnS:Mn²⁺ nanocrystals and Tb³⁺ ions was compared with such two-component materials as the silica support with ZnS:Mn²⁺ as well as the support with Tb³⁺. In each case the nanocrystals and the lanthanide ions were immobilized at silica surface by impregnation procedure. Size of the ZnS quantum dots doped with Mn²⁺ were estimated by Scherrer method from the X-ray diffraction (XRD) pattern. The materials have been characterized by EPR and optical spectroscopy techniques. EPR spectra allow to distinguish two different Mn²⁺ sites: the first is assigned to isolated Mn²⁺ substitutionally and incorporated into cubic ZnS lattice and the second is ascribed to the Mn²⁺ situated near the nanocrystal surface. From the optical spectra we have found that in the three-component material, energy transfer from excited ZnS:Mn²⁺ nanocrystals to Tb³⁺ ions takes place. The different mechanisms of such transfer are discussed.