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The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants) for Cu in [Cu(ipt)(dap)HO]• nHO (ipt is isophthalic acid, dap-1,3-diaminopropane) are theoretically investigated from the high order perturbation formulas of these parameters for a 3 d ion in a rhombically elongated octahedron. The ligand orbital and spin-orbit coupling contributions are included from the cluster approach because of strong covalency of the system. The nearly axial anisotropies of the g factors and hyperfine structure constants are correlated to the significant elongation distortion of the five-fold coordinated Cu (in a distorted square pyramidal [CuNO] group). Nevertheless, the perpendicular anisotropies arising from the nonequivalent planar ligands are largely concealed by the experimental uncertainties. The theoretical analysis of the EPR behaviours for [Cu(ipt)(dap)HO]• nHO would be helpful to understand the local structures and properties of this and relevant systems. [ABSTRACT FROM AUTHOR]

The anisotropic factors of the deoxygenated YBaCuO (Y123) are theoretically studied using the perturbation formulas of the factors for a tetragonally elongated octahedral cluster. The ligand orbital and spin-orbit coupling contributions are included from the cluster approach in view of covalency. The calculated factors show good agreement with the experimental data. The anisotropy of the factors is analyzed by considering the local tetragonal elongation distortion around this five-fold coordinated site in the deoxygenated Y123 system. [ABSTRACT FROM AUTHOR]

The defect structure and spin Hamiltonian parameters ( factors , and the hyperfine structure constants and ) for the tetragonal in ceramics are theoretically studied from the perturbation formulas of these parameters for a ion in a tetragonally elongated octahedron. The impurity center exhibits the larger relative tetragonal elongation ratio than that of the host site due to the Jahn-Teller effect. The relationship between the anisotropy and the local tetragonal distortion is analyzed. The present studies would be helpful to the understandings of delocalization of the orbitals under tetragonal elongation distortion and its role in superconductivity of oxygen cuprates. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance parameters (i.e., g factor, hyperfine structure constant and superhyperfine parameters) of KMgF3:Cr+ are theoretically investigated from the perturbation formulae of these parameters for an octahedral 3d5 cluster. As for the calculations of g factor and hyperfine structure constant, both the contributions from the crystal-field and charge transfer mechanisms are included based on the cluster approach. The metal to ligand charge transfer contribution to the g-shift Δg (≈ g - 2:0023) is the same (negative) in sign and much larger in magnitude as compared to the crystal-field one. The conventional argument that the charge transfer contributions to zero-field splittings are negligible for 3d5 ions in fluorides is no longer suitable for Δg analysis of KMgF3:Cr+ due to the dominant second-order charge transfer perturbation term. The charge transfer contribution to hyperfine structure constant exhibits the same sign and about 4% of the crystal-field one. The unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively acquired from the relationships with the relevant molecular orbital coefficients using the uniform model. The present treatments are superior to the previous calculations of directly fitting the experimental superhyperfine parameters. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance parameters (i.e., g factor, hyperfine structure constant and superhyperfine parameters) of KMgF3:Cr+ are theoretically investigated from the perturbation formulae of these parameters for an octahedral 3d5 cluster. As for the calculations of g factor and hyperfine structure constant, both the contributions from the crystal-field and charge transfer mechanisms are included based on the cluster approach. The metal to ligand charge transfer contribution to the g-shift Δg (≈ g - 2:0023) is the same (negative) in sign and much larger in magnitude as compared to the crystal-field one. The conventional argument that the charge transfer contributions to zero-field splittings are negligible for 3d5 ions in fluorides is no longer suitable for Δg analysis of KMgF3:Cr+ due to the dominant second-order charge transfer perturbation term. The charge transfer contribution to hyperfine structure constant exhibits the same sign and about 4% of the crystal-field one. The unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively acquired from the relationships with the relevant molecular orbital coefficients using the uniform model. The present treatments are superior to the previous calculations of directly fitting the experimental superhyperfine parameters. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance (EPR) g factors gx, gy and gz of the orthorhombic Cu2+(1) site in fresh PrBa²Cu³O6+x powders are theoretically investigated using the perturbation formulas of the g factors for a 3d9 ion under orthorhombically elongated octahedra. The local orthorhombic distortion around the Cu2+(1) site due to the Jahn-Teller effect is described by the orthorhombic field parameters from the superposition model. The [CuO6]10- complex is found to experience an axial elongation of about 0.04 Å along c axis and the relative bond length variation of about 0.09 Å along a and b axes of the Jahn-Teller nature. The theoretical results of the g factors based on the above local structure are in reasonable agreement with the experimental data. [ABSTRACT FROM AUTHOR]

The EPR parameters g factors and the superhyperfine parameters for the tetrahedral [FeX4]- clusters in AgX (X = Cl, Br) are theoretically investigated from the perturbation formulas of these parameters for a 3d5 ion under tetrahedra by considering both the crystal-field and charge transfer contributions. The related model parameters are quantitatively determined fromthe cluster approach in a uniformway. The g-shiftΔg (= g-gs, where gs " 2.0023 is the spin only value) from the charge transfer contribution is opposite (positive) in sign and much larger in magnitude as compared with that from the crystal-field one. The importance of the charge transfer contribution increases rapidly with increasing the covalency and the spin-orbit coupling coefficient of the ligand and thus exhibits the order of AgCl < AgBr. The unpaired spin densities of the halogen ns, npσ and npπ orbitals are quantitatively determined from the related molecular orbital coefficients based on the cluster approach. [ABSTRACT FROM AUTHOR]

The 63Cu Knight shifts and g factors for the normal state of YBa2Cu3O7 in tetragonal phase are theoretically studied in a uniform way from the high (fourth-) order perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated octahedral. The calculations are quantitatively correlated with the local structure of the Cu2+(2) site in YBa2Cu3O7. The theoretical results show good agreement with the observed values, and the improvements are achieved by adopting fewer adjustable parameters as compared to the previous works. It is found that the significant anisotropy of the Knight shifts is mainly attributed to the anisotropy of the g factors due to the orbital interactions. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters (g factors g∣∣, g衩 and the hyperfine structure constants A∣∣, A衩) and the local structures for the two tetragonal Cu2+ centers I and II in Ca(OH)2 are theoretically studied from the perturbation formulae of these parameters for a 3d9 ion under tetragonally elongated octahedra. The [Cu(OH)6]4- clusters on the substitutional Ca2+ site are found to suffer the relative elongations by about 0.083 Å and 0.065 Å for centers I and II, respectively, along the C4 axis due to the Jahn-Teller effect. The above tetragonal elongations may entirely depress the original trigonal distortion of the host Ca2+ site in Ca(OH)2. The calculated spin Hamiltonian parameters based on the above Jahn-Teller elongations show good agreement with the experimental results. The EPR spectra and the local structures for the two centers are compared with one another. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters (g factors g∣∣, g衩 and the hyperfine structure constants A∣∣, A衩) and the local structures for the two tetragonal Cu2+ centers I and II in Ca(OH)2 are theoretically studied from the perturbation formulae of these parameters for a 3d9 ion under tetragonally elongated octahedra. The [Cu(OH)6]4- clusters on the substitutional Ca2+ site are found to suffer the relative elongations by about 0.083 Å and 0.065 Å for centers I and II, respectively, along the C4 axis due to the Jahn-Teller effect. The above tetragonal elongations may entirely depress the original trigonal distortion of the host Ca2+ site in Ca(OH)2. The calculated spin Hamiltonian parameters based on the above Jahn-Teller elongations show good agreement with the experimental results. The EPR spectra and the local structures for the two centers are compared with one another. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian (SH) parameters ( g factors g x, g y and g z and the hyperfine structure constants A x, A y and A z) and local structure for the rhombic Rh4+ and Ir4+ centers in TiO2 (rutile) are theoretically studied from the perturbation formulas of these parameters for a low spin ( S = 1/2) d5 ion under rhombically distorted octahedra. In the calculations, the ligand orbital and spin–orbit coupling contributions as well as the influence of the local lattice distortions are taken into account using the cluster approach. The local axial elongation ratios are found to be about 1.7 and 3 times, respectively, larger for the Rh4+ and Ir4+ centers than that (≈0.0075) for the host Ti4+ site in rutile, while the perpendicular distortion angles (≈−0.28° and −0.42°, respectively) are more than one order in magnitude smaller than the host value (≈−9.12°). This means that the impurity centers exhibit further elongations of the oxygen octahedra and much smaller perpendicular rhombic distortions as compared with those of the host Ti4+ site in TiO2. The above local lattice distortions can be mainly ascribed to the substitution of the host Ti4+ by the nd5 impurities, which may induce different physical and chemical properties for the metal–ligand clusters. In addition, the influence of the Jahn–Teller effect on the local structure may not be completely excluded. The calculated SH parameters show reasonable agreement with the observed values. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian (SH) parameters ( g factors g x, g y and g z and the hyperfine structure constants A x, A y and A z) and local structure for the rhombic Rh4+ and Ir4+ centers in TiO2 (rutile) are theoretically studied from the perturbation formulas of these parameters for a low spin ( S = 1/2) d5 ion under rhombically distorted octahedra. In the calculations, the ligand orbital and spin–orbit coupling contributions as well as the influence of the local lattice distortions are taken into account using the cluster approach. The local axial elongation ratios are found to be about 1.7 and 3 times, respectively, larger for the Rh4+ and Ir4+ centers than that (≈0.0075) for the host Ti4+ site in rutile, while the perpendicular distortion angles (≈−0.28° and −0.42°, respectively) are more than one order in magnitude smaller than the host value (≈−9.12°). This means that the impurity centers exhibit further elongations of the oxygen octahedra and much smaller perpendicular rhombic distortions as compared with those of the host Ti4+ site in TiO2. The above local lattice distortions can be mainly ascribed to the substitution of the host Ti4+ by the nd5 impurities, which may induce different physical and chemical properties for the metal–ligand clusters. In addition, the influence of the Jahn–Teller effect on the local structure may not be completely excluded. The calculated SH parameters show reasonable agreement with the observed values. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance (EPR) parameters (the g factors, hyperfine structure constants and the superhyperfine parameters) for the tetragonal Ir2+ centre in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 5d7 ion in tetragonally elongated octahedra. This impurity centre is attributed to the substitutional [IrCl6]4− cluster on host Na+ site, associated with the 4% relative elongation along the C4-axis due to the Jahn-Teller effect. Despite the ionicity of host NaCl, the [IrCl6]4− cluster still exhibits moderate covalency and then the ligand orbital and spin-orbit coupling contributions should be taken into account. In addition, the theoretical EPR parameters based on the Jahn-Teller elongation show good agreement with the observed values. [ABSTRACT FROM AUTHOR]

The g factors and the ligand superhyperfine parameters A′ and B′ for Ni3+ in KMgF3, CsCaF3 and RbCaF3 are theoretically studied from the formulas of these parameters for a 3d7 ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor ρ related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF3:Ni3+ are satisfactorily interpreted from the different impurity{ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition. [ABSTRACT FROM AUTHOR]

The g factors and the ligand superhyperfine parameters A′ and B′ for Ni3+ in KMgF3, CsCaF3 and RbCaF3 are theoretically studied from the formulas of these parameters for a 3d7 ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor ρ related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF3:Ni3+ are satisfactorily interpreted from the different impurity{ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition. [ABSTRACT FROM AUTHOR]

The EPR g factors gi (i = x; y; z) for the interstitial Ti3+ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically compressed octahedra. The ligand octahedron in the impurity center is found to be less compressed than that on the host interstitial site due to the Jahn—Teller effect. The local compression parameter (≈0.026) and the rhombic distortion angle δɸ′(≈0.7°) around the impurity Ti3+ are smaller than the host values (≈0.091 and 3.5°). The theoretical g factors based on the above local structural parameters are in good agreement with the experimental data. In addition, the g factors for a tetragonal interstitial Ti3+ center are also reasonably interpreted. [ABSTRACT FROM AUTHOR]

The EPR g factors gi (i = x; y; z) for the interstitial Ti3+ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d¹ ion in rhombically compressed octahedra. The ligand octahedron in the impurity center is found to be less compressed than that on the host interstitial site due to the Jahn—Teller effect. The local compression parameter (≈0.026) and the rhombic distortion angle δɸ′(≈0.7°) around the impurity Ti3+ are smaller than the host values (≈0.091 and 3.5°). The theoretical g factors based on the above local structural parameters are in good agreement with the experimental data. In addition, the g factors for a tetragonal interstitial Ti3+ center are also reasonably interpreted. [ABSTRACT FROM AUTHOR]

The EPR g factors g// and g⊥ for the six-coordinated Cu2+(1) site in YBa2Cu3O6+x are theoretically investigated from the perturbation formulas for a 3d9 ion in tetragonally elongated octahedra. The related tetragonal crystal-field parameters Ds and Dt are determined from the superposition model and the structural data for the Cu2+(1) site, by considering the effective elongation of the oxygen octahedron due to the Jahn-Teller effect of the Cu2+ cluster. Based on the calculations, the effective elongation (≈ 15%) of the ligand octahedron is obtained for the signals at 100K. As for the EPR signals at room temperature, the elongation declines to merely 4%, corresponding to the smaller anisotropy Δg (=g// - g⊥). The theoretical results for the g factors are in good agreement with the observed values, and the local tetragonal distortion due to the Jahn-Teller effect is discussed. [ABSTRACT FROM AUTHOR]

The EPR g factors g// and g⊥ for the six-coordinated Cu2+(1) site in YBa2Cu3O6+x are theoretically investigated from the perturbation formulas for a 3d9 ion in tetragonally elongated octahedra. The related tetragonal crystal-field parameters Ds and Dt are determined from the superposition model and the structural data for the Cu2+(1) site, by considering the effective elongation of the oxygen octahedron due to the Jahn-Teller effect of the Cu2+ cluster. Based on the calculations, the effective elongation (≈ 15%) of the ligand octahedron is obtained for the signals at 100K. As for the EPR signals at room temperature, the elongation declines to merely 4%, corresponding to the smaller anisotropy Δg (=g// - g⊥). The theoretical results for the g factors are in good agreement with the observed values, and the local tetragonal distortion due to the Jahn-Teller effect is discussed. [ABSTRACT FROM AUTHOR]

The superhyperfine parameters A′ and B′ for Cr3+ ions in K2NaGaF6, K2NaCrF6, KMgF3 and CsCdF3 are theoretically studied from the cluster approach. In the present treatments, the orbital admixture coefficients and the unpaired spin densities in 2s, $$ 2{\text{p}}_{\sigma } $$ and $$ 2{\text{p}}_{\pi } $$ 2 fluorine orbitals are obtained in a uniform way. The experimental A′ and B′ are reasonably explained, and the unpaired spin densities for the 2s, 2pσ and 2pπ orbitals of the ligand F− are also compared with those in the previous works. [ABSTRACT FROM AUTHOR]

The local structure and the g factors ( g x, g y, and g z) of the Cu2+ site in Y2BaCuO5 are theoretically studied using the perturbation formulas of the g factors for a 3d9 ion in orthorhombically elongated octahedra. The orthorhombic field parameters in these formulas are determined from the superposition model and the local geometry of the system. From the calculations, the oxygen octahedron is found to undergo the local elongation Δ Z (≈0.05 Å) along c-axis and the relative bond length variation Δ X (≈0.1 Å) along a- and b-axes, respectively. The calculated g factors based on the above local structure are in good agreement with the experimental data. The relationships between the anisotropies of the g factors and the low symmetrical (orthorhombic) distortions of the Cu2+ site in Y2BaCuO5 are discussed. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters (the anisotropic g factors g ∥ and g ⊥ and the hyperfine structure constants) for the Cu2+ sites in PrBa2Cu3O6+ x and Pr0.5Er0.5Ba2Cu3O6+ x are theoretically investigated using the high order perturbation formulas of these parameters for a 3d9 ion in tetragonally elongated octahedra. In these formulas, the tetragonal field parameters are determined from the superposition model and the local structures of the Cu2+ sites. The theoretical spin Hamiltonian parameters are in good agreement with the observed values for both systems, and the results show improvements as compared with those based on various adjustable covalency coefficients in the previous work. The larger hyperfine structure constants for PrBa2Cu3O6+ x than those for Pr0.5Er0.5Ba2Cu3O6+ x can be attributed to the weaker covalency due to the relatively longer Cu2+– $\mathrm{O}^{\bar{2}}$ bonds in the former. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors g x, g y, g z, and the hyperfine structure constants A x, A y, and A z) of the two orthorhombic Er3+ centers in Bi2Sr2 YCu2O8 are theoretically studied from the perturbation formulas of these parameters for a 4f11 ion in orthorhombic symmetry. In these formulas, the contributions due to the admixtures of various states are taken into account, and the orthorhombic field parameters are determined from the superposition model and the local geometry of Bi3+ site in Bi2Sr2 YCu2O8. The calculated EPR parameters show reasonable agreement with the observed values. The anisotropy g z> g x( g y) for the g factors may be attributed to the compression of the ligand octahedra in the Er3+ centers. [ABSTRACT FROM AUTHOR]

The local structure and the g factors ( g x, g y, and g z) of the Cu2+ site in Y2BaCuO5 are theoretically studied using the perturbation formulas of the g factors for a 3d9 ion in orthorhombically elongated octahedra. The orthorhombic field parameters in these formulas are determined from the superposition model and the local geometry of the system. From the calculations, the oxygen octahedron is found to undergo the local elongation Δ Z (≈0.05 Å) along c-axis and the relative bond length variation Δ X (≈0.1 Å) along a- and b-axes, respectively. The calculated g factors based on the above local structure are in good agreement with the experimental data. The relationships between the anisotropies of the g factors and the low symmetrical (orthorhombic) distortions of the Cu2+ site in Y2BaCuO5 are discussed. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters (the anisotropic g factors g ∥ and g ⊥ and the hyperfine structure constants) for the Cu2+ sites in PrBa2Cu3O6+ x and Pr0.5Er0.5Ba2Cu3O6+ x are theoretically investigated using the high order perturbation formulas of these parameters for a 3d9 ion in tetragonally elongated octahedra. In these formulas, the tetragonal field parameters are determined from the superposition model and the local structures of the Cu2+ sites. The theoretical spin Hamiltonian parameters are in good agreement with the observed values for both systems, and the results show improvements as compared with those based on various adjustable covalency coefficients in the previous work. The larger hyperfine structure constants for PrBa2Cu3O6+ x than those for Pr0.5Er0.5Ba2Cu3O6+ x can be attributed to the weaker covalency due to the relatively longer Cu2+– $\mathrm{O}^{\bar{2}}$ bonds in the former. [ABSTRACT FROM AUTHOR]

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors g x, g y, g z, and the hyperfine structure constants A x, A y, and A z) of the two orthorhombic Er3+ centers in Bi2Sr2 YCu2O8 are theoretically studied from the perturbation formulas of these parameters for a 4f11 ion in orthorhombic symmetry. In these formulas, the contributions due to the admixtures of various states are taken into account, and the orthorhombic field parameters are determined from the superposition model and the local geometry of Bi3+ site in Bi2Sr2 YCu2O8. The calculated EPR parameters show reasonable agreement with the observed values. The anisotropy g z> g x( g y) for the g factors may be attributed to the compression of the ligand octahedra in the Er3+ centers. [ABSTRACT FROM AUTHOR]