Theoretical investigation of the spin-Hamiltonian parameters and optical spectra for the doped Cu2+ in ZnCdO nanopowder

The spin-Hamiltonian (SH) parameters (g factors g_||, g_⊥ and hyperfine structure constants A_||, A_⊥) and d–d transitions for ZnCdO:Cu²⁺ are calculated based on the perturbation formulas for a 3d⁹ ion in tetragonally elongated octahedra. Good agreement between the calculated results (four SH parameters and three optical absorption bands) and the experimental results can be obtained. Since the SH parameters are sensitive to the local structure of a paramagnetic impurity center, the tetragonal distortion (characterized by the relative elongation ratio ρ ≈ 3.5% along the C₄ axis) of the impurity center due to the Jahn–Teller effect is also acquired from the calculations. The negative and positive signs of hyperfine structure constants A_|| and A_⊥ for ZnCdO:Cu²⁺, respectively, are also suggested in the discussions.     

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.     

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.     

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 studies of the Spin Hamiltonian parameters and local structures for Cu2+ centers in MNB ternary glasses

ABSTRACT

The spin Hamiltonian parameters (g factors g_|| and g_⊥ and the hyperfine structure constants A_|| and A_⊥) for the doped Cu²⁺ ion (in the form of CuO) in ternary glasses (i.e. xMgO·(30-x)Na₂O·69B₂O₃·CuO, with 5?<?x < 17?mol%) are theoretically investigated based on the high-order perturbation formulas for a tetragonally elongated octahedral 3d⁹ complex. In these formulas, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the spin Hamiltonian parameters with the tetragonal distortion (characterized by relative tetragonal elongation δ along the C₄ axis due to the Jahn–Teller effect) of [CuO₆]^10? cluster. The concentration dependences of the spin Hamiltonian parameters are illustrated by the approximately linear increases of the cubic field parameter D_q and the covalency factor N as well as the relative elongation δ with increasing the MgO concentration x. Based on the calculation, the [CuO₆]^10? clusters in the MNB glasses are found to suffer the relative elongations of about δ (≈ 0.125?Å) along the tetragonal axis due to the Jahn–Teller effect. The theoretical results show good agreement with the experimental data. And the improvement is also achieved in present work with respect to the previous theoretical analysis based on the conventional crystal-field model formulas by including the ligand orbital and spin–orbit coupling contributions.     

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.     

Investigations of the optical spectra and spin-Hamiltonian parameters for the rhombic Yb centers in garnets

Two complete diagonalization (of energy matrix) methods (CDM-I and CDM-II) are used to calculate the six optical spectral band positions and nine spin-Hamiltonian (SH) parameters (g factors g_i and hyperfine structure constants ¹⁷¹A_i, ¹⁷³A_i, where i=x, y, z) for Yb³⁺ ions in the rhombic dodecahedral sites of garnets Y₃Al₅O₁₂, Lu₃Al₅O₁₂ and Y₃Ga₅O₁₂. In CDM-I, the Hamiltonian concerning energy matrix does not contain the Zeeman and hyperfine interaction terms, whereas in CDM-II, it does. So, in CDM-I, the SH parameters are obtained by first-order perturbation method or the equivalence between SH and Zeeman term (or hyperfine interaction term) and in CDM-II, the SH parameters and optical spectral band positions are calculated together. The results obtained from both methods are not only close to each other, but also in reasonable agreement with the observed values. So the second-order perturbation formulas of SH parameters developed recently are incorrect and unnecessary.     

Investigation of the EPR parameters of the rhombic Cu2+ center in (NH4)2Mg(SO4)2·6H2O single crystal

The electron paramagnetic resonance (EPR) parameters (g factors g_x, g_y, g_z and hyperfine structure constants A_x, A_y, A_z) for Cu²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O (DHMS) crystal are theoretically investigated using the high-order perturbation formulas of these parameters. In the calculations, the ligand orbital and spin–orbit coupling for the impurity Cu²⁺ are taken into account; the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the EPR parameters with the local structure of the impurity center. The ligand orbital and the spin–orbit coupling contributions are included on the basis of the cluster approach. Based on the calculation, the theoretical EPR parameters show good agreement with the observed values. The results are discussed.     

Studies of the optical spectra and spin-Hamiltonian parameters for the trivalent ytterbium ions in lithium yttrium fluoride crystals

In this paper, the crystal field (CF) levels and spin-Hamiltonian (SH) parameters (g factors g _∥ and g _⊥ and hyperfine structure constants A _∥ and A _⊥) of the rare-earth ion Yb³⁺ in lithium yttrium fluoride crystals are calculated under D _2d point symmetry assumption. Two main methods are used in the calculation to study the SH parameters: one is the perturbation theory method and the other is the complete diagonalization (energy matrix) method (CDM). Comparing the calculated results with the experimental data, we can see that the CDM is more effective to calculate the SH parameters. In addition, the CF J-mixing of all excited-state multiplets into the ground-state multiplet ²F_7/2 is considered. The validity of the calculated results is discussed.     

Theoretical studies of the spin-Hamiltonian parameters for the orthorhombic Pr4+ centers in Sr2CeO4 crystals

Theoretical studies of spin-Hamiltonian (SH) parameters associated with Pr⁴⁺ in Sr₂CeO₄ single crystals have been made by using the complete diagonalizing energy matrix method (CDM) for the 4f ¹ electronic configuration. The calculated results are in excellent agreement with the experimental data. The negative signs of the anisotropic g _i -factors and hyperfine structure constants A _i (where i = ∥ or ⊥) for the orthorhombic Pr⁴⁺ ion in Sr₂CeO₄ are suggested from the calculations. By comparing the results obtained by the CDM with the experimental data, one finds it is valid to interpret the SH parameters for 4f ¹ ions in crystals. The results are discussed.      

Investigations on the spin Hamiltonian parameters and defect structure for the interstitial Mo centre in TiO2

The spin Hamiltonian parameters, g factors g_i (i = x, y, z) and the hyperfine structure constants A_i for the interstitial Mo⁵⁺ centre in rutile TiO₂ are quantitatively investigated from the perturbation formulas of these parameters for a 4d¹ ion in rhombically compressed octahedra. From the studies, the local compression parameter τ′ (≈0.024) and the rhombic distortion angle δ?′ (≈1.74°) around the impurity Mo⁵⁺ are smaller than the host values (≈0.091 and 3.5°). This means that the oxygen octahedron in the impurity centre has less rhombic distortion than that on the host interstitial site due to the Jahn–Teller effect and occupation of the impurity. The above local lattice distortion of the studied impurity centre is also discussed.     

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.     

Theoretical explanation of absorption spectra and ESR parameters of Cu in shattuckite

The optical absorption spectra and electronic spin resonance parameters (ESR g factors g_‖, g_⊥ and hyperfine structure constants A_‖, A_⊥) for Cu²⁺ in shattuckite crystal are calculated from the two spin–orbital coupling parameters model, high-order perturbation formulas and complete diagonalization (of energy matrix) method (CDM) of 3d⁹ ion in tetragonal symmetry. The calculated results are in good agreement with the observed values. Since the ESR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu²⁺ center in shattuckite crystal is estimated. The results are discussed.     

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X²Π and A²Σ⁺ states of FH⁺, ClH⁺ and BrH⁺. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ _Π, γ _Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq ₀, eQq ₂)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X²Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.     

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.     

Reinvestigation of the second negative (A 2 Π u−X 2 Π g) band system of O 2 +

TheA ² Π _ustate of O₂ ⁺ was earlier established as an inverted state contrary to previous assumptions. The rotational analysis of a few more bands of theA-X system of O₂ ⁺ has now been completed. These studies show that the spin-orbit coupling constantA in theA ² Π _ustate gradually varies with the vibrational quantum numberν and is found to be positive forν⩾6. It has also been observed that the spia-rotation interaction is not negligible in theA ² Π _ustate. The spin splitting constantγ is reported for various vibrational levels of this electronic state.     

Investigation of the local structure of Cu2+ ions doped in alkali lead tetraborate glasses by their electron paramagnetic resonance and optical spectra

The local structure of the Cu²⁺ centers in alkali lead tetraborate glasses was theoretically studied based on the optical spectra data and high-order perturbation formulas of the spin Hamiltonian parameters (electron paramagnetic resonance g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) for a 3d⁹ ion in a tetragonally elongated octahedron. In these formulas, the relative axial elongation of the ligand O^2? octahedron around the Cu²⁺ due to the Jahn–Teller effect is taken into account by considering the contributions to the g factors from the tetragonal distortion which is characterized by the tetragonal crystal-field parameters Ds and Dt. From the calculations, the ligand O^2? octahedral around Cu²⁺ is determined to suffer about 19.2% relative elongation along the C₄ axis of the alkali lead tetraborate glass system, and a negative sign for A_∥ and a positive sign for A_⊥ for these Cu²⁺ centers are suggested in the discussion.     

Structural Assignment of Stilbenethiols and Chalconethiols and Differentiation of Their Isomeric Derivatives by Means of 1H‐ and 13C‐NMR Spectroscopy

Abstract

The ¹H‐ and ¹³C‐NMR spectra of some substituted stilbenes and chalcones were assigned unambiguously on the basis of a combination of homo‐ (COSY) and heteronuclear (HETCOR) two‐dimensional methods, the chemical shifts, as well as spin‐coupling constants. The A_ik empirical parameters of the –O–C(S)–N(CH₃)₂, –S–C(O)–N(CH₃)₂, and –SH group were calculated to help predict the chemical shifts of substituted stilbenes, 4′‐nitrostilbenes, and chalcones. The ¹H‐ and ¹³C‐NMR spectra have been shown to be able to differentiate between the isomers of O‐stilbenyl (4, 5) and S‐stilbenyl N,N‐dimethylthiocarbamates (7, 8) as well as O‐chalconyl (6) and S‐chalconyl N,N‐dimethylthiocarbamates (9).     

Computer simulation of the nonequilibrium critical behavior of disordered two-dimensional Ising systems

We report the results of a computer simulation of the critical relaxation of the magnetization in the two-dimensional Ising model with nonmagnetic impurity atoms frozen at the lattice sites. We assume a square lattice of dimension 400² with spin concentrationsp=1.0, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7. The Monte Carlo and dynamic renormalization group methods are used to determine the dynamical critical indexz as a function ofp: z(p): z(1)=2.24±0.07,z(0.95)=2.24±0.06,z(0.85)=2.38±0.05,z(0.8)=2.51±0.06,z(0.75)=2.66±0.07,z(0.7)=2.88±0.06. It is shown thatz(p) obeys a singular scaling law of the formz=A | ln (p–p _c) |+B withA=0.56±0.07,B=1.62±0.07.Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 83–88, August, 1994.     

Rotational analysis of the 0–9, 0–10 and 0–11 bands of theA 2II u -X 2II g band system of (16O18O)+

High-resolution spectra of the 0–9, 0–10 and 0–11 bands of theA ²II _u —X ²II _g system of (¹⁶O¹⁸O)⁺ ion have been studied for their rotational structure. This study enables a direct determination of the Λ-doubling parameters of theA ²II _u andX ²II _g states. The model of ‘pure precession’ explains, though not entirely, the Λ-doubling of theX ²II _a state as arising out of its interaction with theB ² Σ _g ⁻ state. The Λ-doubling in theA ²II _u state was found insignificant.