ZnS:Cr2+中局域晶格结构和自旋单态对零场分裂参量的贡献

在统一配体场耦合图像的基础上,构造了d⁴电子组态过渡金属离子在强场图像下包括所有自旋状态的210×210维完全能量矩阵.通过对角化完全能量矩阵,研究了Cr²⁺掺杂ZnS的局域晶格结构和Jahn-Teller能.理论计算结果与实验值符合非常好.同时,还研究了Cr²⁺掺杂ZnS后体系自旋单态对零场分裂参量的贡献.结果表明:自旋单态对二阶零场分裂参量D的贡献可以忽略,但是对于四阶零场分裂参量a和F的贡献却 关键词： 2+')" href="#">ZnS:Cr²⁺ 统一配体场耦合 自旋单态 Jahn-Teller能     

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.     

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.     

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.     

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.     

Jahn-teller chromium ions in CdF<Subscript>2</Subscript> and CaF<Subscript>2</Subscript> crystals: An EPR spectroscopic study in the frequency range 9.3–300 GHz

The bivalent chromium impurity centers in CdF₂ and CaF₂ crystals are investigated using electron paramagnetic resonance (EPR) in the frequency range 9.3–300 GHz. It is found that Cr²⁺ ions in the lattices of these crystals occupy cation positions and form [CrF₄F₄]^6? clusters whose magnetic properties at low temperatures are characterized by orthorhombic symmetry. The parameters of the electron Zeeman and ligand interactions of the Cr²⁺ ion with four fluorine ions in the nearest environment are determined. The initial splittings in the system of spin energy levels of the cluster are measured.     

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.     

Investigations of the optical band positions,EPR parameters and defect structure for the trigonal Cr3+–Li+ centre in CsMgCl3 crystal

A unified calculation of optical band positions and electron paramagnetic resonance (EPR) (or spin-Hamiltonian) parameters for the trigonal Cr³⁺–Li⁺ centre in CsMgCl₃ crystal is made by using the complete diagonalisation (of energy matrix) method based on the two-spin–orbit-parameter model. In this model, the contributions from the spin–orbit parameter of central dⁿ ion and that of ligand ion are included. From the calculation, the 11 observed optical and EPR data (eight optical band positions and three EPR parameters g_//, g_⊥, D) are reasonably explained with five adjustable parameters and the defect structure of the Cr³⁺–Li⁺ centre (which is consistent with the expectation based on the electrostatic interaction) in CsMgCl₃ is acquired. The results are discussed.     

EPR theoretical study of local lattice structure in ZnS:Cr system

By analyzing the EPR parameters a, D and F of Cr²⁺ ion located at tetrahedral site in ZnS, the local structure around Cr²⁺ in the crystal has been investigated on the basis of the complete energy matrix for a d⁴ configuration in a tetragonal ligand-field within a strong-field-representation. It is shown that there exists an expansion distortion in the local lattice structure. From EPR calculation, the distortion parameters ΔR=0.13 Å and Δθ=1.417° are determined.     

High-frequency tunable EPR spectroscopy of non-Kramers ions in AgGaSe<Subscript>2</Subscript>: Cr,AgGaS<Subscript>2</Subscript>: Cr,and CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>: Cr crystals

Crystals of the chalcopyrite family, AgGaSe₂, AgGaS₂, and CdGa₂S₄, doped with chromium ions have been investigated using high-frequency broad-band EPR spectroscopy in the range 65–530 GHz at T = 4.2 K. It has been revealed that, in the AgGaSe₂ and AgGaS₂ crystals, the Cr²⁺ ions occupy positions with orthorhombic and tetragonal symmetry, whereas the previously investigated CdGaS₄ crystals contain only tetragonal centers. The observed spectra have been described in the framework of the spin-Hamiltonian formalism. Apart from the divalent chromium centers, the EPR lines attributed to non-Kramers ions are observed in the frequency range 300–450 GHz for all the crystals under investigation. The nature of these lines has been discussed.     

Pairwise Interactions of Fe3+ Ions in InBO3 Crystals

Measurements of the electron paramagnetic resonance (EPR) of Fe³⁺ ion pairs in InBO₃ crystals are conducted. Some parts of the procedure of spectrum identification without measuring the temperature dependence of the resonant line intensities have been developed. Experimental curves of the second- and fourth-order axial Hamiltonian constants D _S and (a – F)_S, respectively, of the total spin number S are constructed. The single-ion second-order axial constant D _c is well described by a linear dependence on S. The constant (a – F)_S has a quadratic dependence.     

Lattice dynamics of ZnSe x S1 − x semiconductor crystals

Recently ultrabroadband infrared solid state lasers based on a new vibronic material Cr²⁺:ZnSe _x S_1–x were demonstrated [1–3]. Cr²⁺ ion substitutes the metal ion (tetrahedral sites), the crystal field of the solid solution is responsible for large inhomogeneous broadening of Cr²⁺ electron states. The crystal field can be reconstructed by investigation of lattice dynamics — optical phonon parameters and dielectric function in IR. We paid special attention to investigation of vibrational and infrared spectroscopic properties of ZnSe _x S_{1 ? x} crystals. A very interesting and somewhat unexpected result of these studies was the existence in the crystals of effective S-Se dipoles, which generate an additional deep dynamically charged level in the forbidden gap of the semiconductors. The results of the first-principles calculations of both the phonon structure and the electron localization in ZnSe _x S_1–x crystals as well as acceptor levels in Cr²⁺: ZnSe crystal are discussed.     

Trigonal Distortions of the Cr<Superscript>3+</Superscript> Octahedral Centers in Cr<Superscript>3+</Superscript>-Doped ABO<Subscript>3</Subscript> (A = Sc,In, Lu) Crystals Obtained by Analyzing EPR Data

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of the trigonal Cr³⁺ centers in Cr³⁺-doped ABO₃ (A = Sc, In, Lu) borate crystals are computed from both the complete diagonalization (of energy matrix) method and also the perturbation method based on the two-spin–orbit-parameter model, where the contributions to spin-Hamiltonian parameters due to both the spin–orbit parameter of central d ⁿ ion and that of ligands via covalence effect are considered. The calculated results are compatible with those available in experiments. The defect structures of the trigonal (CrO₆)^9? octahedral centers are also evaluated from the calculations. It is found that the trigonal (MO₆)^9? octahedra change from the elongation in the host crystals to the compression in the impurity centers because of the large size and nature mismatch substitution in these Cr³⁺-doped ABO₃ crystals. The results are discussed.     

Superposition model in electron magnetic resonance spectroscopy – a primer for experimentalists with illustrative applications and literature database

We review applications of the superposition model (SPM) in EMR area, which enables semi-empirical modeling of zero-field splitting (ZFS) parameters (ZFSPs) for transition ions in crystals by separation of geometrical and physical information. Nomenclature used for ZFS and crystal field (CF) Hamiltonians is presented to expose common framework underlying two independent implementations: SPM/ZFS and SPM/CF, which require distinct model parameters. SPM/ZFSP applications in EMR area for S-state 3d⁵ (4f⁷) ions and 3d^N ions with orbital singlet ground state are reviewed. SPM/ZFS methodology for ML_n complexes [central metal (M) ion surrounded by n ligands (L)] with specific symmetry is presented. SPM-related computer packages combined with other methods, role of axis systems in SPM analysis, and structural models for several ion-host systems, are discussed. Extensive survey of SPM/ZFS applications is provided to elucidate usefulness of SPM modeling for interpretation of ZFSPs. This review is geared for EMR practitioners interested in practical utilization of SPM/ZFS (or SPM/CFP) analysis. Database of SPM/ZFS references is compiled for studies of single molecule magnets and single ion magnets based on transition ions. Due to its comprehensiveness, suitable sets of model parameters required for practical utilization SPM/ZFS may be easily located using source references as pointers.     

Studies on the local structures and the spin Hamiltonian parameters for Fe3+ in CdX (X = S,Se, Te)

The improved perturbation formulas of the spin Hamiltonian parameters (zero-field splitting D and g factors) for a 3d⁵ ion in trigonally distorted tetrahedra are constructed from the cluster approach by including both the crystal-field and charge-transfer contributions. These formulas are applied to the studies of the local structures and the electron paramagnetic resonance (EPR) spectra for Fe³⁺ in CdX (X = S, Se, Te). The impurity Fe³⁺ is found not to occupy exactly the host Cd²⁺ sites but to experience the small outward shifts 0.014 and 0.006 Å away from the ligand triangles along the C₃ axis in CdS and CdSe, respectively. The charge-transfer contributions to the spin Hamiltonian parameters are important and increase significantly with increasing atomic number of the ligand (i.e., S^2? < Se^2? < Te^2?) arising from the decreases of charge-transfer energy levels and the increases of ligand spin–orbit coupling coefficients. The results are discussed.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Cr ions in Y2Ti2O7 crystal

The optical band positions and spin-Hamiltonian parameters (g factors g_g_? and zero-field splitting D) for the trigonal Cr³⁺ centers in Y₂Ti₂O₇ crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central dⁿ ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ center is suggested.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript> ions in ABO<Subscript>3</Subscript> (A = Sc,Lu, In) diamagnetic crystals

A magnetic resonance method is applied to the investigation of a number of isostructural diamagnetic compounds ABO₃ (A = Sc, Lu, In) with small additions of Cr³⁺ ions (S = 3/2) sufficient to observe single-ion spectra. It is shown that the resonance spectra for isolated Cr³⁺ ions can be described to a good accuracy by the ordinary axial spin Hamiltonian for 3d ions in octahedral oxygen environment. The parameters of the spin Hamiltonian are determined. It is established that Cr³⁺ ions in these crystals are characterized by easy-axis-type anisotropy.     

Photoelectric Properties of p-GaSe/n-CdGa2S4 Heterostructures

Single crystals of the ternary compound CdGa₂S₄ have been grown from the melt by the Bridgman–Stockbarger method and their composition, structure, and electrophysical properties have been determined. From the crystals obtained, p-GaSe/n-CdGa₂S₄ heterostructures have been generated for the first time and their photoelectric properties in natural and linearly polarized light have been investigated. We determine the main parameters of the heterostructures and show that they can be used in photoprocessors of optical radiation.