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.     

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.     

Superhyperfine structure of the EPR spectra of Ce<Superscript>3+</Superscript> ions in Li<Emphasis Type="Italic">R</Emphasis>F<Subscript>4</Subscript> (<Emphasis Type="Italic">R</Emphasis> = Y,Lu, Tm) double fluorides

The EPR spectra of Ce³⁺ impurity ions in LiYF₄, LiLuF₄, and LiTmF₄ double-fluoride single crystals have been investigated at a frequency of ∼9.3 GHz in the temperature range 5–25 K. The effective g factors of the ground Kramers doublet of the cerium ions in three crystals are close to each other (g _‖ = 2.737, g _⊥ = 1.475 for LiYF₄:Ce³⁺). A superhyperfine structure of the EPR spectrum of Ce³⁺ ions in the LiTmF₄ Van Vleck paramagnet has been observed in the external magnetic field B oriented along the crystallographic axis c (B ‖ c). The superhyperfine structure of the EPR soectra of the Ce³⁺ ions in the LiYF₄ and LiLuF₄ diamagnetic matrices is resolved for B ⊥ c. Possible factors responsible for this pronounced difference in the properties of the systems studied have been discussed.     

Theoretical study of B3O radical isomers and their interconversion pathways

Despite the fact that B₃O is the second simplest B _n O radical after BO, a controversy recently emerged concerning the molecular structure of its global minimum. Two recent theoretical groups predicted the linear quartet BBBO to be the ground isomer. By contrast, another recent theoretical group reported that B₃O has a doublet B₃-ring ground structure. Moreover, larger B _n O clusters usually have low-lying B₃-ring isomers. In order to determine the accurate energetic competition between linear and cyclic structures in both the doublet and quartet, and to understand the detailed isomerism between various isomers, which is vital for understanding the formation mechanism of B₃O, we report the first potential energy surface (PES) study of B₃O at various computational levels, including CCSD(T)/6-311+G(2df), CCSD(T)/aug-cc-pVTZ, CCSD(T)/aug-cc-pVQZ and G3B3 for the single-point energy, as well as B3LYP/6-311+G(d) and QCISD/6-311+G(d) for geometrical optimisation. It is shown that the isomers in the quartet state are all thermodynamically more stable than the corresponding doublet ones, and on both the quartet and doublet PESs, the linear form has the lowest energy. Therefore, our study on both linear and cyclic isomers shows that the linear quartet BBBO ⁴ 01 is definitively the ground isomer. Although being much less stable than the quartet linear BBBO global minimum by >20 kcal mol^?1, five cyclic isomers exist as local minima, with the bi-cyclic structure ⁴ 02 possessing the smallest barrier of around 15 kcal mol^?1. The dissociation energies for direct combination processes B₃ + O, B₂ + BO and B + B₂O are discussed. The present work may be helpful in obtaining a deep understanding of the doping and oxidation process of pure B _n clusters.     

强耦合磁失措自旋冰系统Dy2Ti2O7单晶生长和基本磁性质测量

利用红外光源浮区法生长出大尺寸、高质量的磁失措自旋冰化合物Dy₂Ti₂O₇单晶体.X射线衍射实验证实晶体具有面心立方结构，空间群为Fd3m，晶胞参数a＝1.0112(2) nm，［111］和［400］方向X射线衍射摇摆曲线半高宽分别仅为0.07°和0.05°.直流磁化率与温度关系测量给出晶体的Van Vleck顺磁因子为2.46×10^-5 m³/mol，有效磁矩μ_eff＝10.24(4)μ_B，Cure-Weiss温度Θ_CW＝1.1 K，揭示Dy₂Ti₂O₇具有弱的铁磁性.对磁性起源的综合分析表明，该自旋冰晶体磁性质主要来源于磁偶极相互作用，且相关最近邻长程偶极相互作用能量标度D_nn＝3.00 K. 关键词： 2Ti₂O₇')" href="#">Dy₂Ti₂O₇ 浮区法晶体生长 关联电子系统 自旋冰     

EPR, Optical Absorption and Superposition Model Study of Fe3+-Doped Ammonium Dihydrogen Phosphate Single Crystals

X-band electron paramagnetic resonance (EPR) studies are carried out on Fe³⁺ ions doped in ammonium dihydrogen phosphate (ADP) single crystals at room temperature. The crystal field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations. The obtained values of spin Hamiltonian and zero-field parameters of the Fe³⁺ ion in ADP are: g = 1.994 ± 0.002, |D| = (220 ± 5) × 10^?4 cm^?1 and a = (640 ± 5) × 10^?4 cm^?1. On the basis of EPR data, the site symmetry of the Fe³⁺ ion in the crystal is discussed. The Fe³⁺ ion enters the lattice substitutionally replacing the NH₄ ⁺ sites. The optical absorption of the crystal is also studied at room temperature in the wavelength range of 195–925 nm. The energy values of different orbital levels are calculated. The observed bands are assigned as transitions from the ⁶ A _1g (S) ground state to various excited quartet levels of the Fe³⁺ ion in a cubic crystalline field. From the observed band positions, Racah interelectronic repulsion parameters (B and C), cubic crystal field splitting parameter (D _q ) and Trees correction are calculated. There values are: B = 970, C = 1,923, D _q  = 1,380 cm^?1 and α = 90 cm^?1, respectively. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The zero-field splitting (ZFS) parameters are also determined theoretically using B _kq parameters estimated from the superposition model. The values of ZFS parameters thus obtained are |D| = (213 ± 5) × 10^?4 cm^?1 and |E| = (21 ± 5) × 10^?4 cm^?1.     

Theoretical investigations of the spin Hamiltonian parameters for the CoCl(PPh3)3 molecules

The perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and g factor g_// and g_⊥) are established for a 3d⁸ ion in trigonally distorted tetrahedra for the first time. In the theoretical treatments, the contributions from the Jahn–Teller effect, the ligand orbital and spin–orbit coupling interactions and configuration interactions are taken into account from the cluster approach in a uniform way. The above formulas are applied to the studies of the spin Hamiltonian parameters for the three CoCl(PPh₃)₃ molecules, and the experimental electron paramagnetic resonance spectra of all the molecules are satisfactorily explained. The significant compressions of the ligand tetrahedra with mixed chlorine and PPh₃ groups around Co⁺ are analysed for three distinct CoCl(PPh₃)₃ compounds, characterised by the Cl–Co–P bond angles θ larger than the tetrahedral angle of 109.47°. The local trigonal distortions are discussed in view of the Jahn–Teller effect.     

EPR of trivalent iron ions in a LiCaAlF6 crystal

The orientational dependences of the EPR spectra of Fe³⁺-doped LiCaAlF₆ single crystals (space group P31c, Z=2), grown at the Laboratory of Magnetic Radio Spectroscopy at Kazan’ State University, have been investigated in detail. The spectrum is described by a trigonal spin Hamiltonian with the following parameters: B ₂₀=40.072×10⁻⁴ cm⁻¹, B ₄₀=−5.799×10⁻⁴ cm⁻¹, B ₄₃=−4.281×10⁻⁴ cm⁻¹, A _s=24.33±1, A _p=6.13±1, g _∥=g _⊥=2.00217±0.0003. A theoretical calculation of the hyperfine structure parameters shows that they are described quite well when allowance is made for the overlapping of the wave functions of the paramagnetic center and the ligands (F⁻). Fiz. Tverd. Tela (St. Petersburg) 39, 488–490 (March 1997)     

Theoretical explanation of optical absorption spectra and covalent effect of Ni2+ ions in octahedral sites of Ca3Sc2Ge3O12 crystal

The optical absorption spectra (d-d transition bands) and covalent effect of Ni²⁺ ions in octahedral sites of Ca₃Sc₂Ge₃O₁₂ crystal have been investigated by the full energy matrix based on the two spin–orbit coupling parameters model. The bond length of octahedral site is R_i?=?2.19 Å, which can be determined by the cubic crystal-field parameter and optical spectral data. The lattice distortion of the Ni²⁺ center in Ca₃Sc₂Ge₃O₁₂ crystal is also obtained from the calculations. In addition, the result has shown that the covalent effect of Ni²⁺ ion in the octahedral site of Ga₃Sc₂Ge₃O₁₂ is obvious and cannot be ignored. The calculated d-d transition bands agree well with that of the experimental findings, suggesting that the present methods can explain reasonably the optical spectral data and covalent effect of 3d⁸ ions in octahedral lattices.     

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)     

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.     

Spin–orbit coupling in biradicals. 5. Zero-field splitting in triplet dimethylnitrenium,dimethylphosphenium and dimethylarsenium cations

The spin dipole–spin dipole and spin–orbit coupling contributions to the zero-field splitting parameters D and E of [CH₃–N–CH₃]⁺, [CH₃–P–CH₃]⁺, and [CH₃–As–CH₃]⁺ have been calculated from CASSCF(14,14)/cc-pVTZ wave functions and the Breit–Pauli Hamiltonian at T₁ B3LYP/cc-pVTZ optimized geometries. The spin–orbit coupling contributions represent a minor correction for the dimethylnitrenium cation, which has a triplet ground state. They dominate the spin–spin terms by an order of magnitude in the dimethylphosphenium cation and by more than two orders of magnitude in the dimethylarsenium cation, both of which have a singlet ground state. The properties of all these biradicaloids follow expectations based on the simple algebraic 2-in-2 model of biradical structure.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

Alternation of the spin–orbit coupling in the 2Π ground state of HC n S (n = 1–12) radicals

First-order calculations of spin–orbit constants, dipole moments and carbon–sulphur distances have been performed for HC _n S (n = 1–12) radicals in the ²Π electronic ground state. It is found that these molecular properties alternate with even or odd numbers of carbon atoms in the chains and the spin–orbit constant A _SO is around ?300 cm^?1 for n even and about +120 cm^?1 for n odd throughout the series. This agrees with the experimentally determined value of about ?270 cm^?1 for HC₂S, but the theoretically predicted A _SO values are much larger than the values given for HC₃S and HC₄S from a fit of their millimeter-wave spectra. Values that were too low were also assumed in the analysis of the rotational spectra of n = 4–8.     

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.     

NdNi2Ge2化合物的结构和电磁输运性质

利用非自耗真空电弧熔炼法制备了NdNi₂Ge₂化合物样品,采用X射线粉末衍射技术和Rietveld全谱拟合分析方法测定了其晶体结构. 结果显示该化合物的空间群为I4/mmm,点阵参数为:a=4.120(1),c=9.835(0),Z=2,Nd原子占据2a晶位,Ni原子占据4d晶位,Ge原子占据4e晶位. NdNi₂Ge₂化合物呈现顺磁性,应用居里-外斯定律拟合计算得到居里-外斯常数为25.8,居里-外斯温度为6.24 K. 有效势磁矩为3.69μ_B,这与理论计算Nd³⁺的磁矩相符,表明磁矩主要源于Nd³⁺. 电阻率变化范围为0.3 Ω ·μm^-1-1 Ω ·μm,电阻曲线拟合显示NdNi₂Ge₂呈半金属性. 关键词： 2Ge₂')" href="#">NdNi₂Ge₂ Rietveld结构精修 电磁输运     

Study on the local structure and EPR spectroscopy of compressed CuX4 (X = N,S, Cl and Br) tetrahedral cluster

The spin Hamiltonian parameters g and A for copper(II) in CuX₄ (X = N, S, Cl and Br) tetrahedrons are theoretically investigated within a uniform model by utilizing the perturbation method and cluster approach for 3d⁹ ions suffering D_2d symmetry in view of host structures and angular distortions in terms of a single parameter β. For all the studied polymers, the isotropy of g tensors g_av and the hyperfine structure constant component A_‖ are found, respectively, to undergo an increasing and decreasing trend with the enlarging average X–Cu–X angle β, while the obtained cubic crystal field parameter D_q and isotropic Fermi contact constant κ are experiencing a declining and growing tendency with the rising Cu–X bond length, respectively. The critical angle β_c is concluded locating in the range of 109.471°–120° in which the g-isotropy value would reach the maximum, while the hyperfine structure factor might vanish that needs to be verified in future X-ray and EPR experiments. This work would be beneficial to the establishment of complete EPR and structure diagram for CuX₄ complexes and the synthesis of new compounds possessing novel physical and chemical properties.     

Review of Spin–Orbit Coupled Semimetal SrIrO3 in Thin Film Form

Spin–orbit coupling, locking the momentum of an electron to its spin, has been shown essential for giving rise to many novel physical behaviors. SrIrO₃ is a typical metallic member of the strong spin–orbit coupling iridate family. Its orthorhombic phase has been confirmed as a paramagnetic semimetal resulted from the interplay among spin–orbit coupling, electron correlation, and crystal field, and was theoretically predicted to host versatile topological phases. This article reviews the current knowledge on the preparation and the tunable properties of orthorhombic SrIrO₃ films. Experiments have demonstrated that orthorhombic SrIrO₃ can be successfully synthesized as films under substrate lattice constraint without high pressure, and the films frequently display metal-insulator transition due to disorder and weak-antilocalization owing to spin-orbit coupling. The properties of orthorhombic SrIrO₃ film are sensitive to the rotation and tilting of the IrO₆ octahedral, and consequently can be significantly tuned through strain engineering. Simultaneously, thickness-dependent size effect is also remarkable in SrIrO₃ films. The accumulated research on SrIrO₃ films suggests an urgent demand for research on superlattices constructed with orthorhombic SrIrO₃, to better understand the mechanism of the electron structure evolution, and thus the relevant magnetic states and topological phases in orthorhombic SrIrO₃ and its family.     

Spin inversion in trigonal centers of CaF2:Dy3+

Abstract

Magnetic circular dichroism in the 4431 Å absorption line of the oxygen compensated CaF₂:Dy³⁺ crystal has been used to measure transient phenomena in the Kramers doublet ground level ⁶H_15/2 of the Dy³⁺ ion during magnetic field reversal. After inverting the field with a rate 10 T·s^?1 <dB/dt < 400 T·s^?1 a considerable spin inversion with the final electron spin polarization P_F was achieved while P_F=-0.86±0.03 relaxed to less than 0.05 when dB/dT < 10^?2 T·s^?1.     

EPR of Gd3+ in single crystal colquiriite and analysis of the spin Hamiltonian tensorsB 4 andB 6

In single crystal colquiriite LiCaAlF₆ doped with Gd³⁺ ions two EPR spectra of the Gd³⁺ ions with the Laue site-symmetry groups C_i and C_3i were observed. The spectrum angular dependence for trigonal Gd³⁺ centre was investigated in detail and corresponding spin Hamiltonian parameters were fitted. From analysis of the spin Hamiltonian tensorsB ₄ andB ₆ it was established that Gd³⁺ with the Laue group C_3i substitutes at Ca²⁺ site with the excess charge compensation by an ion located along the threefold axis from this site. The transformation formulas for a sixth-rank irreducible Hermitian tensor under coordinate rotation are tabulated in an explicit form. By using the EPR data for Gd³⁺ substituted in a variety of host crystals, the fourth-rank and sixth-rank tensors of Gd³⁺ spin Hamiltonians were tabulated and correlated with structures of the coordination polyhedra at substitution sites. The results suppose a predominance of quadratic crystal field contributions into the spin Hamiltonian tensorB ₄ of Gd³⁺.