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.     

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 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 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.      

Local structure of the trigonal defect center for Cr3+ ions in KMgF3 crystals

Abstract

The zero-field splitting D, the anisotropic g-factors g _∥, Δg(=g _∥ ? g _⊥) and the first excited state splitting Δ(² E) for the trigonal Cr³⁺–V_K center in KMgF₃: Cr³⁺ crystals have been studied from Macfarlane's high-order perturbation formulas. From the studies, the local structure of the trigonal center is obtained. The local lattice distortions (i.e., the displacement directions of the ions in the center) are consistent with the expectation based on the electrostatic interaction.     

Spin Hamiltonian and structural disorder analysis for two high temperature Cr3+ defect centers in α-LiIO3 crystals—low symmetry effects

Complete diagonalization method (CDM) is developed for 3d³ ions in the trigonal type I crystal-fields (CFs). The CDM enables microscopic spin-Hamiltonian (MSH) calculations of the zero-field splitting (ZFS) parameter D and the Zeeman g-factors: g_∥ and g_⊥. CDM/MSH program is used for CF and MSH calculations for the high temperature (HT) Cr³⁺ defect centers (A) and (B) in α-LiIO₃. The contributions to the SH parameters from the single Li⁺ vacancy and the lattice distortions are considered. The calculated SH parameters of the two HT Cr³⁺ centers agree well with the experimental ones. Structural distortions are theoretically predicted with the bond angles α and β for the Cr–O₆ complex in Cr³⁺:α-LiIO₃ greater than those in the host crystal. By incorporating the MSH approach, the comprehensive CF analysis (CFA) package for 3d^N ions at arbitrary symmetry sites is at present extended as a CFA/MSH package to study SH parameters for 3d³ ions at trigonal type I CFs as well as the additional contributions to D, g_∥, and g_⊥ arising from the non-zero distortion angle ϕ at trigonal type II (e.g. C₃) CFs. The new finding for Cr³⁺:α-LiIO₃ is that g_⊥ depends strongly on ϕ, whereas g_∥ and D are rather insensitive to ϕ.     

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.     

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.     

Al and Cu NMR study in UCu5Al

We have studied the microscopic properties of the tetragonal UCu₅Al Kondo compound by ²⁷Al and ^63,65Cu NMR in the paramagnetic state. NMR and susceptibility measurements performed on the powdered sample, but oriented along the applied field, showed χ>χ. Plots of K(T) against χ(T) at temperatures T≥100 K yield the transferred hyperfine fields of +5.9 kOe/μ_B for ²⁷Al nuclei, and +5.3 and −7.0 kOe/μ_B for ⁶⁵Cu nuclei in crystallographically inequivalent Cu(2) and Cu(1) sites, respectively. The Knight shift vs. susceptibility plots for T<100 K exhibit a deviation from the linear behaviour (absolute values of shifts become smaller than expected). We attribute this finding to the crystalline electric field effect in similar way as it was reported for several Ce-based compounds. The random distribution of the Al and Cu(2) atoms in the crystal lattice we consider as a reason of an unusual broadening of the NMR spectra, particularly at low temperatures.     

Theoretical studies of the defect structures and spin Hamiltonian parameters for manganese(II) and nickel(II) doped Zn(en)3(NO3)2 single crystals

The spin Hamiltonian parameters (g factors, hyperfine structure constants and zero-field splittings D and E) and local structures for Mn²⁺ and Ni²⁺ in [Zn(en)₃](NO₃)₂ single crystal are theoretically investigated from the perturbation calculations for trigonally distorted 3d⁵ and trigonally (or orthorhombically) distorted 3d⁸ cluster. The trigonal Mn²⁺ and Ni²⁺ centres are found to undergo the moderate angular variations Δβ of 4.5° and 5.2°, respectively, related to host Zn²⁺ site due to size mismatch. The orthorhombic Ni²⁺ centre shows the relative axial elongation ratio ρ (≈ 2.5%) and the relative perpendicular bond length variation ratio τ (≈0.2%). For Mn²⁺ centre, the contributions to g-shifts Δg_CT (or hyperfine structure constants A_CT and zero-field splitting D_CT) from charge-transfer (CT) mechanism are opposite in sign and five times (or 5% and 8%) in magnitude compared with those from crystal-field (CF) mechanism. For the trigonal Ni²⁺ centre, Δg_CT (or D_CT) are the same (or opposite) in sign and 17% (or 2%) in magnitude related to those from CF mechanism. For the orthorhombic Ni²⁺ centre, Δg_CT and E_CT (or D_CT) are same (or opposite) in sign and 16% and 48% (or 442%) in magnitude with respect to those from the CF mechanism. The signs and magnitudes of the trigonal distortion angles δβ (≈ ?0.3 and 0.4°) related to an ideal octahedron and the local angular variations Δβ related to the host bond angle are suitably illustrated by those of the axial distortion degree (ADD) and the angular variation degree (AVD) of the systems, respectively.     

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.     

Theoretical Studies of the Electron Paramagnetic Resonance and Optical Spectral Data for Vanadium(IV) Ion in Yttrium Aluminum Garnet Crystal

Four spin-Hamiltonian parameters (g factors g _// and g _⊥ and hyperfine structure constants A _// and A _⊥) and two optical spectral band positions for vanadium(IV) (V⁴⁺) ion in the tetrahedral Al³⁺ site of yttrium aluminum garnet (Y₃Al₅O₁₂) crystals are calculated from the (third-order) perturbation theory method (PTM) and complete diagonalization (of energy matrix) method (CDM). Both methods are based on the cluster approach. The calculated results from both methods coincide and reasonably agree with the experimental values. The defect structure of V⁴⁺ center (which is different from the corresponding structure in the host crystal) in Y₃Al₅O₁₂ crystal is also obtained from the calculation.     

Investigating the impurity structure for Fe3+ ions doped into rutile titanium dioxide single crystal

The local environment around Fe³⁺ centers in rutile TiO₂ crystals is studied by employing fourth-order perturbation theory formula based on the dominant spin–orbit coupling mechanism. The zero-field splitting parameters (ZFSPs) D and E and crystal field parameters are modeled for the Fe³⁺ ions not only at the substitution Ti⁴⁺ site, but also at the interstitial site with local symmetry D_2h. In order to acquire the best agreement between the calculated ZFSPs and those measured by electron magnetic resonance, the model parameters are adjusted on the basis of several approaches. This enables us to determine the feasible values of the structural distortions resulting from dopant Fe³⁺ ions. Consequently, it is confirmed that Fe³⁺ ions substitute for Ti⁴⁺ sites in rutile TiO₂ crystals.     

Magnetic-field-controlled polarized luminescence of Y3Al5O12-Tb and Y3Al5O12-Ho garnets

The circularly polarized luminescence spectra of Y₃Al₅O₁₂-Tb and Y₃Al₅O₁₂-Ho garnets are analyzed in the wavelength ranges of the ⁵ D ₄ → ⁷ F ₅ transition in the Tb³⁺ ion and the ⁵ S ₂ → ⁵ I ₈ transition in the Ho³⁺ ion. It is found that the intensities of the orthogonal circularly polarized components of the series of luminescence lines attributed to the studied garnets differ substantially. The results obtained are interpreted in terms of the mixing of the Tb³⁺ and Ho³⁺ electronic states in an external magnetic field.     

Vibrational Spectra and Structure of Potassium Alum Kal(SO4)2·12[(H2O) x (D2O)1−x ]

The IR spectra and polarization Raman spectra of Kal(SO₄)₂·12(H₂O) and Kal(SO₄)₂·12[H₂O)_0.3(D₂O)_0.7] crystals at 93 K and room temperature have been obtained experimentally. The vibrational spectra of structural elements of potassium alum — the complexes [Al(H₂O)₆ ³⁺ and [Al(D₂O)₆]³⁺ — have been calculated. The vibrational spectra have been interpreted based on the calculation and factor-group analysis data. The spectral data obtained point to the fact that, in the crystals considered, the sulfate ions are partially disordered and there exist two crystallographically different types of water molecules.     

Radiation-Induced Paramagnetic Centers in the Glasses Of CaO-Ga2O3-GeO2 System

The X-band (v ? 9.4 GHz) ESR spectra of the UV-, X-, and γ-irradiated glasses of CaO-Ga₂O₃-GeO₂ system with compositions similar to Ca₃Ga₂Ge₃O₁₂, Ca₃Ga₂Ge₄O₁₄, and Ca₃Ga₂O₆ crystals have been investigated at 300 and 77 K. It was shown that X- and γ-irradiation of the Ge-contained glasses induce simultaneously electron and hole paramagnetic centers, stable at room temperature. The UV-irradiation of Ge-contained glasses leads to the generation of stable centers of electron type, whereas the X- and γ-irradiation of glasses with Ca₃Ga₂O₆ composition induces stable hole centers, exclusively. The electron centers are assigned to E′ (Ge) centers with different local environments. ESR spectrum of hole centers is ascribed to O^? centers, localized on non-bridging oxygen of the glass network. The E′ (Ge) and O^? centers show high thermal stability in the CaO-Ga₂O₃-GeO₂ glass network. The obtained ESR spectra are described by spin Hamiltonian with g-factor of axial and rhombic symmetry for the E′ (Ge) and O^? centers, respectively. The nature, electron structure and some formation peculiarities of the radiation defects in CaO-Ga₂O₃-GeO₂ glasses are discussed in comparison with other glasses as well as Ca₃Ga₂Ge₃O₁₂ and Ca₃Ga₂Ge₄O₁₄ crystals.     

Calculations of the optical and EPR spectral data for Cr3+ ion in Y3Ga5O12 crystal from the complete diagonalisation method

The complete diagonalisation (of energy matrix) method is applied in this paper to calculate together the optical and electron paramagnetic resonance (EPR) spectral data for Cr³⁺ ion at the trigonal Ga³⁺ site of Y₃Ga₅O₁₂ crystal. The method is founded on the two-spin-orbit-parameter model where in addition to the contributions from the spin-orbit parameter of central dⁿ ion (i.e., one-spin-orbit-parameter model) in the traditional crystal field theory, those from the spin-orbit parameter of ligand ion via covalence effect is also considered. The calculated results propose that by using only four adjustable parameters, the 12 observed spectral data (nine optical band positions and three EPR parameters g_//, g_⊥ and D) in Y₃Ga₅O₁₂: Cr³⁺ are reasonably explained. The impurity-induced local lattice distortion of Cr³⁺ in Y₃Ga₅O₁₂ crystal is also estimated through the calculations. The results are discussed.     

Al and Si MAS NMR investigations of cordierite glass, μ- and α-cordierite

²⁷Al and ²⁹Si Magic-Angle Spinning NMR results are reported for conventionally prepared glass of cordierite stoichiometry (2MgO · 2Al₂O₃ · 5SiO₂), the metastable high-quartz solid solution (μ-cordierite) and the high-temperature polymorph of cordierite (α-cordierite). Both, ²⁷Al two-dimensional (2D) quadrupole nutation experiments and ²⁷Al satellite transition spectroscopy (SATRAS) have been applied to identify two different tetrahedrally-coordinated aluminium sites (AlO₄). SATRAS has been used to extract the quadrupole interaction parameters and their distribution, the isotropic chemical shifts and the relative populations of the different Al sites. Both, the ²⁷Al and ²⁹Si NMR results, lead to the conclusion that a perfect Si/Al disorder does not exist in these investigated cordierite samples.