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.     

Theoretical studies on the local structure and spin Hamiltonian parameters for the orthorhombic Cu2+ center in LiNbO3

The local structure and spin Hamiltonian parameters (the g factors and the hyperfine structure constants) for the orthorhombic Cu²⁺ center in LiNbO₃ are theoretically studied from the perturbation formulas of these parameters for a 3d⁹ ion in an orthorhombically elongated octahedron. This center is ascribed to Cu²⁺ occupying the Nb⁵⁺ site in LiNbO₃, associated with one nearest neighbour oxygen vacancy V_O along the Z axis. The planar bond lengths are found to suffer the relative variation of about 0.16 Å by compressing and stretching the Cu²⁺–O^2? bonds along the X and Y axes, respectively, due to the Jahn–Teller effect and the charge mismatching substitution of Nb⁵⁺ by Cu²⁺. Meanwhile, the effectively positive V_O can make the central Cu²⁺ displace away from the V_O along the Z axis by about 0.3 Å. The theoretical spin Hamiltonian parameters based on the above local distortions show good agreement with the experimental data.     

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.     

Theoretical investigations of the spin Hamiltonian parameters and local tetragonal distortions for Cu2+ in crystalline and amorphous TeO2 and GeO2

The spin Hamiltonian parameters (i.e., anisotropic g factors and hyperfine structure constants) and local tetragonal distortions for Cu²⁺ in crystalline and amorphous TeO₂ and GeO₂ are theoretically investigated using the high-order perturbation formulas of these parameters for a tetragonally elongated octahedral 3d⁹ cluster. The impurity Cu²⁺ occupying the octahedral sites are found to experience the relative tetragonal elongation ratios of about 11.4% and 9.5% for crystalline TeO₂ and GeO₂ and 10.8% and 6.6% for amorphous TeO₂ and GeO₂, respectively, along the C₄ axis due to the Jahn–Teller effect. This reveals the larger tetragonal elongation distortions for the Cu²⁺ centres in crystalline than amorphous systems (especially TeO₂). The theoretical spin Hamiltonian parameters show good agreement with the experimental data. The results are discussed.     

Theory studies of the local lattice distortions and the EPR parameters for Cu2+, Mn2+ and Fe3+ centres in ZnWO4

The local lattice distortions and the electron paramagnetic resonance (EPR) parameters (g factors, hyperfine structure constants and zero-field splittings) for Cu²⁺, Mn²⁺ and Fe³⁺ in ZnWO₄ are theoretically studied based on the perturbation calculations for rhombically elongated octahedral 3d⁹ and 3d⁵ complexes. The impurity centres on Zn²⁺ sites undergo the local elongations of 0.01, 0.002 and 0.013 Å along the C₂ axis and the planar bond angle variations of 8.1°, 8.0° and 8.6° for Cu²⁺, Mn²⁺ and Fe³⁺, respectively, due to the Jahn–Teller effect and size and charge mismatch. In contrast to the host Zn²⁺ site with obvious axial elongation (～0.31 Å) and perpendicular (angular) rhombic distortion, all the impurity centres demonstrate more regular octahedral due to the above local lattice distortions. The copper centre exhibits significant Jahn–Teller reductions for the spin-orbit coupling and orbital angular momentum interactions, characterised by the Jahn–Teller reduction factor J (≈0.29 ? 1). The calculated EPR parameters agree well with the experimental results. The local structures of the impurity centres are analysed in view of the corresponding lattice distortions.     

Theoretical studies on the EPR parameters of the interstitial V4+ in rutile

The electron paramagnetic resonance (EPR) parameters g-factors g _i (i=x, y, z) and the hyperfine structure constants A _i for the interstitial V⁴⁺ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically distorted octahedra. On the basis of the studies, the local axial distortion angle Δα′ in the impurity center is found to be about 2° smaller than the host value, characterized as stretching and contraction of the parallel and perpendicular bonding lengths by about 0.28 and 0.14 Å,respectively. This results in the less compressed ligand octahedron because of the Jahn–Teller effect and space effect arising from occupation of the impurity V⁴⁺ at the interstitial site. The theoretical EPR parameters based on the above local structural parameters of this work are in better agreement with the experimental data than those of the previous studies in the absence of the local angular distortion and the ligand orbital contributions. The two experimental optical absorption bands are also reasonably analyzed.     

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.     

Investigations of the local lattice distortions and the EPR parameters for the orthorhombic Pt3+ center in YAG

The local lattice distortions and the EPR parameters (anisotropic g factors and the hyperfine structure constants) for the orthorhombic Pt³⁺ center in YAG are theoretically investigated from the perturbation formulas of these parameters for a 5d⁷ ion in an orthorhombically elongated octahedron. The [ PtO₆] ^9- cluster on Al³⁺ site is found to experience the axial elongation of about 0.01 Å along Z axis, and the planar impurity-ligand bond lengths suffer the relative variation of about 0.11 Å? along X and Y axes due to the Jahn-Teller effect. As a result, the above local lattice distortions produce significant orthorhombic deformation, whereas the original slight trigonal distortion of the host [ AlO₆] ^9- octahedron is entirely depressed by the Jahn-Teller effect. The calculated EPR parameters based on the above lattice distortions show good agreement with the experimental data, and the local structure of the impurity center is also discussed.     

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants ⁶⁵A_// and ⁶⁵A_⊥) for the tetragonal Cu²⁺ centres in trigonal Zn(BrO₃)·6H₂O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d⁹ ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO₃)·6H₂O: Cu²⁺ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R_// ? R _⊥, where R_// and R _⊥ represent the metal-ligand distances parallel with and perpendicular to the C₄ axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.     

Theoretical investigations of the local structure and the g factors for the tetragonal Ru3+ center in PbTiO3

The local structure and the g factors for the tetragonal Ru³⁺ center in PbTiO₃ are theoretically studied from the perturbation formulas of the g factors for a 4d⁵ ion in tetragonally distorted octahedra. From the studies, the distance between the impurity Ru³⁺ and the center of the oxygen octahedron is found to be about 0.283 Å, which is smaller than that (≈0.3 Å) for the host Ti⁴⁺ site. It appears that the impurity may not occupy exactly the host Ti⁴⁺ site but suffer a slight inward shift toward the center of the oxygen octahedron. The calculated g factors based on the above local structure show good agreement with the experimental values.     

Spin-Hamiltonian Parameters and Defect Structure of the Copper (2+) Center in Lithium Borate

The spin-Hamiltonian parameters (the anisotropic g factors g _|| and g _⊥ and the hyperfine structure constants A _|| and A _⊥) for the impurity Cu²⁺ in Li₂B₄O₇ are theoretically investigated using the high-order perturbation formulas of these parameters for a 3d ⁹ ion in tetragonally elongated octahedra. In the calculation formulas, the tetragonal field parameters D_s and D_t are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative axial elongation of about 0.21 Å for the tetragonal Cu²⁺ center was found.     

Electron spin resonance study of a CuIr2S4 single crystal

A spinel sulphide CuIr₂S₄ single crystal, which exhibits an orbitally induced Peierls phase transition at ～230?K, is investigated by electron spin resonance (ESR) spectroscopy. The phase transition is clearly manifested on the ESR spectra. It is suggested that the ESR signals are produced by a few non-dimerized Ir⁴⁺ ions. Moreover, an extra ESR spectrum appears at low temperature in addition to the paramagnetic ESR signals of Ir⁴⁺ ions, which is suggested to be caused by the Jahn–Teller effect of the non-dimerized Ir⁴⁺ ions. From the ESR results, it is found that the Jahn–Teller splitting energy ΔE _JT is much smaller than the spin-dimerization gap.     

Theoretical evaluation of the electron paramagnetic resonance spin Hamiltonian parameters for the impurity displacements for Fe3+ and Ru3+ in corundum

The impurity displacements for Fe³⁺ and Ru³⁺ in corundum (Al₂O₃) are theoretically studied using the perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and anisotropic g factors) for a 3d⁵ (with high spin S = 5/2) and a 4d⁵ (with low spin S = 1/2) ion in trigonal symmetry, respectively. According to the investigations, the nd⁵ (n = 3 and 4) impurity ions may not locate at the ideal Al³⁺ site but undergo axial displacements by about 0.132 Å and 0.170 Å for Fe³⁺ and Ru³⁺, respectively, away from the center of the ligand octahedron along the C₃ axis. The calculated spin Hamiltonian parameters based on the above axial displacements show good agreement with the observed values. The validity of the results is discussed.     

Investigations on the local structure and the spin-Hamiltonian parameters for the tetragonal Cu<Superscript>2+</Superscript> centre in ZnGeF<Subscript>6</Subscript>⋅6H<Subscript>2</Subscript>O crystal

The spin-Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) and the local structure for the tetragonal Cu²⁺ centre in trigonal ZnGeF₆?6H₂O crystal are theoretically studied using the perturbation formulae of these parameters for a 3 d⁹ ion in tetragonally elongated octahedra. In the calculations, the contributions to the spin-Hamiltonian parameters from ligand orbital and spin-orbit coupling are included on the basis of the cluster approach in view of moderate covalency of the studied systems, and the required crystal-field parameters are obtained using the superposition model and the local structures of the studied [Cu(H₂O)₆] ²⁺ cluster. According to the calculations, the ligand octahedra around Cu²⁺ suffer relative elongation τ (≈ 0.085 Å) along the [0 0 1] (or C₄) axis for the tetragonal Cu²⁺ centres in ZnGeF₆?6H₂O crystal, due to the Jahn–Teller effect. The calculated results show good agreement with the experimental data.     

Theoretical investigations on the g factors and local structures for Cu2+ in the ZnX (X= O,S and Se) nanocrystals

ABSTRACT

The g factors and local structures for Cu²⁺ in the ZnX (X = O, S and Se) nanocrystals at room temperature are theoretically investigated by the perturbation calculations for a tetragonally distorted tetrahedral 3d⁹ cluster in a consistent way, and the isotropic g factor is predicted for the ZnS:Cu²⁺ nanocrystals at room temperature. The bond angles θ between the four equivalent Cu²⁺?X^2? bonds and the C₄ axis are found to be about 1.26°, 1.24° and 1.07°, respectively, larger in the ZnO, ZnS and ZnSe nanocrystals than that (θ₀ ≈ 54.74°) for an ideal tetrahedron, inducing tetragonally compressed tetrahedra. The declining tendency (ZnO > ZnS > ZnSe) of the tetragonal angular distortion Δθ (= θ ? θ₀) can be ascribed to the decreasing strength of the dynamic Jahn–Teller effect via the vibration interactions of the [CuX₄]^6? groups due to the weakening Cu²⁺?X^2? bonding. The isotropic g factors are attributable to the appropriate Δθ due to the dynamic Jahn–Teller effect and the internal stress. The slightly increasing (ZnO < ZnS < ZnSe) g factors can be illustrated by the declining cubic field parameter Dq, angular distortion Δθ and covalency factor N of the systems.     

Investigations of the spin-Hamiltonian parameters,optical absorption bands,and local structure for the tetragonal Cu2+ center in Cu2+-doped ZnCdO nanopowder

The spin-Hamiltonian (or EPR) parameters of tetragonal Cu²⁺ octahedral centers in ZnCdO nanopowders are calculated from the high-order perturbation formulas based on the cluster approach. In these formulas, the contributions to spin-Hamiltonian parameters due to the admixture between the d orbitals of dⁿ ion and the p orbitals of ligand ions via covalence effect are considered. The crystal field parameters are calculated from the superposition model and so the optical absorption bands (related to the crystal field energy levels) and local structure of Cu²⁺ octahedral centers in ZnCdO nanopowder are also studied. The calculated spin-Hamiltonian parameters and optical absorption bands are in reasonable agreement with the experimental values. The tetragonal elongation ΔR (=R_//−R_⊥) of Cu²⁺ octahedron in ZnCdO nanopowder due to Jahn–Teller effect is acquired from the calculations. The results are discussed.     

Theoretical investigations of the spin Hamiltonian parameters for the tetragonal [Rh(CN)4Cl2] complex in KCl

The spin Hamiltonian parameters (g factors, hyperfine structure constants and superhyperfine parameters) for the tetragonal [Rh(CN)₄Cl₂]⁴⁻ complex in KCl are theoretically investigated from the perturbation formulas of these parameters for a 4d⁷ ion in a tetragonally elongated octahedron. This center can be assigned to the substitutional Rh²⁺ on host K⁺ site reduced from Rh³⁺ by capturing one electron during the electron irradiation, associated with the two axial ligands CN⁻ replaced by two Cl⁻. The crystal-fields of the two axial Cl⁻ are weaker than those of the four planar CN⁻, yielding the tetragonal elongation distortion. This system belongs to the case of low spin (S = 1/2) under strong crystal-fields, different from that of high spin (S = 3/2) under weak and intermediate crystal-fields (e.g., 3d⁷ ions such as Fe⁺ and Co²⁺ in conventional chlorides). The calculated spin Hamiltonian parameters show good agreement with the experimental data. The above [Rh(CN)₄Cl₂]⁴⁻ complex due to the different axial and perpendicular ligands is unlike the tetragonally elongated [RhCl₆]⁴⁻ complex due to the Jahn–Teller effect in the similar NaCl:Rh²⁺ crystals.     

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.     

Theoretical studies of the spin Hamiltonian parameters and local structures for WO3 doped Zn3(PO4)2ZnO nanopowders

The spin Hamiltonian parameters (SHPs) and the local structures for impurity W⁵⁺ in the Zn₃(PO₄)₂ZnO nanopowders doped with WO₃ under different concentrations are theoretically investigated using the perturbation calculations of these parameters. The exponential functions of the related quantities (cubic field parameter Dq, covalency factor N, relative tetragonal compression ratio τ and core polarisation constant κ) of concentration x with totally four adjustable coefficients a, b, c and d are adopted to fit the concentration dependences of the experimental d-d transition bands and SHPs. The impurity W⁵⁺ centres demonstrate moderate tetragonal compression ratios τ (～3.1%) due to the Jahn–Teller effect. With the increase of WO₃ concentration, Dq and N show moderately decreasing rules, while τ and κ exhibit slightly and moderately increasing tendencies with x, respectively. The mechanisms of the above concentration dependences of these quantities are analysed from the modifications of the local crystal-field strength and electron cloud density around the impurity W⁵⁺ with the variation of x. Present theoretical studies would be useful to the exploration of the structural properties and optical applications for WO₃ doped Zn₃(PO₄)₂ZnO nanopowders.     

Theoretical studies on the SH parameters and local distortion structure of KCl:Ag crystal

Complete diagonalization of the energy matrix and high order perturbation formulae of spin-Hamiltonian (SH) parameters possessing D_4h symmetry for the 4d⁹ ion based on the crystal- and ligand-field theory in tetragonal symmetry are expressed and applied to the study of local distortion structure of the KCl:Ag²⁺ crystal. The calculated results agree well with experimental findings. Both complete diagonalization of energy matrix and high order perturbation approach are appropriate for the investigations of SH parameters of 4d⁹ ions in tetragonal crystals. Tetragonal distortion due to the Jahn-Teller effect for the tetragonal Ag²⁺ center at the K⁺ site of KCl crystal is also acquired from the calculations.