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The spin Hamiltonian (SH) parameters (i.e. the zero-field splitting parameters (ZFSPs) and g factors) and local structures of the two Cr 3+ centers I and II at room temperature in KCl single crystals are theoretically investigated from the perturbation calculations for a rhombically distorted octahedral 3d 3 cluster. The impurity systems are attributed to the doped Cr(CN) 6 3− groups into KCl replacing the host KCl 6 5 − ones, associated with two nearest neighbor potassium vacancies V K in [011] and [ 0 1 ¯ 1 ¯ ] axes in center I and one nearest neighbor V K along [ 0 1 ¯ 1 ] and another next-nearest neighbor V K along [100] axis in center II, respectively. In center I, the four coplanar and two axial ligands CN − undergo the shifts ∆ R 1 (≈0.0044 nm) away from the V K and ∆ R 2 ′ (≈0.0144 nm) away from the central ion along Z axis, respectively, because of the electrostatic interactions. In center II, the impurity Cr 3+ is found to undergo the shift ∆ R C (≈0.0063 nm) towards the nearest neighbor V K along [ 0 1 ¯ 1 ] axis, while the two ligands in [001] and [ 0 1 ¯ 0 ] axes closest to the V K undergo the shifts ∆ R 1 (≈0.0081 nm) away from the respective V K , and the ligand intervening in the V K and the central ion experiences the shift ∆ R 2 (≈0.0238 nm) away from the V K along [100] axis. The charge-transfer (CT) contributions to g-shifts are found to be opposite in sign and more than half (characterized by the ratios |Δg CT /Δg CF |>50%) in magnitude compared with the CF ones for both centers. The local structures and the microscopic mechanisms of the relevant impurity and ligand shifts are discussed for the two centers. [ABSTRACT FROM AUTHOR]

The local lattice distortions of the various rhombic Ru 3+ centres ( A , A ′, B , B ′, X and X ′) in AgX (X = Cl and Br) are quantitatively investigated from the perturbation calculations of the anisotropic g factors and hyperfine structure constants for a 4d 5 ion in rhombically distorted octahedra. Centre A or A ′ is assigned to the substitutional Ru 3+ on Ag + site associated with one nearest neighbor silver vacancy V Ag in the [1 1 0] axis and one next nearest neighbor V Ag in the [ 1 ¯ 0 0] axis due to charge compensation. Ru 3+ is found to undergo the off-centre displacement 0.022 or 0.017 Å along the [1 1 0] axis, while the halide ligands closest to the V Ag move away from the vacancies by 0.030 or 0.005 Å in AgBr or AgCl, respectively, due to the electrostatic interactions of the V Ag . Centre B or B ′ is ascribed to Ru 3+ associated with each nearest neighbor V Ag in the [1 1 0] and [ 1 ¯ 1 ¯ 0] axes. The two axial ligands experience the displacement 0.036 or 0.015 Å along the Z (or [0 0 1]) axis, and the four planar ligands shift away from the vacancies by about 0.006 or 0.001 Å, respectively. Centre X or X ′ can be described as Ru 3+ associated with one nearest neighbor V Ag and one next nearest neighbor V Ag in the [1 1 0] and [0 0 1] axes, respectively. Ru 3+ may undergo the off-centre displacement 0.019 or 0.015 Å along the [1 1 0] axis, while the ligands closest to the V Ag move away from the V Ag by 0.022 or 0.006 Å. The present studies would be helpful to the investigations on the structures and properties for Ru 3+ in AgX and similar halides. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters ( g factors and hyperfine structure constants) for Cu 2+ in NaF and CsCdF 3 are theoretically studied using the high order perturbation formulas of these parameters for a 3d 9 ion in a tetragonally elongated octahedron. The Cu 2+ centres are found to suffer the relative elongation ratios of about 5.5% and 3.1% for Cu 2+ in NaF and CsCdF 3 , respectively, along the C 4 axis due to the Jahn–Teller effect. The theoretical results of the spin Hamiltonian parameters show good agreement with the experimental data. The larger g anisotropy for Cu 2+ in NaF than CsCdF 3 is attributed to the larger relative tetragonal elongation ratio arising from the longer distance and hence the weaker bonding (or lower force constant) in the former. The significant discrepancies in the hyperfine structure constants for the two systems are analysed in view of their different core polarization constants and the reduction factors H related to the local structures. [ABSTRACT FROM AUTHOR]

The temperature-independent orbital Knight shifts for the orthorhombic site in (Y124) are investigated by utilizing the high order perturbation formulae of these parameters for a ion situated into orthorhombically elongated octahedra. The calculation results are in good agreement with the experimental data. The moderate quasi-axial anisotropies of the Knight shifts are ascribed to the elongation distortion of the four-fold coordinated Cu site. The factors are also theoretically calculated in a uniform way for further experimental verification. [ABSTRACT FROM AUTHOR]

The Knight shifts for the tetragonal site in are theoretically studied from the high order perturbation formulas of the Knight shifts for a tetragonally elongated octahedral cluster. The significant anisotropy of the Knight shifts is attributable to the obvious tetragonal elongation distortion of the site. The anisotropic factors of this system are uniformly analyzed, and the calculation results and the local structure of the copper site are also discussed. [ABSTRACT FROM AUTHOR]

The anisotropic factors are theoretically studied for the sites in and from the perturbation formulas of the factors for a ion in tetragonally elongated octahedra. The local low symmetrical (tetragonal) distortions of the five-fold coordinated sites are quantitatively correlated to the electron paramagnetic resonance (EPR) analysis in terms of the tetragonal field parameters based on the superposition model, and the ligand contributions are included in view of obvious covalency. The possibility of the above EPR signals arising from may be excluded for both systems. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters ( factors and hyperfine structure constants) of the five-fold coordinated Cu(2) site in superconductors are investigated from the high order perturbation formulas of these parameters for a ion in tetragonally elongated octahedron. The observed anisotropies and are ascribed to the ground state for under octahedral tetragonal elongation distortion. The comparable magnitudes of the parallel and perpendicular hyperfine structure constants may be illustrated by the small core polarization constant and the reduction factor . The ligand orbital and spin-orbit coupling contributions are found to be important due to significant covalency and should be considered in the calculations. [ABSTRACT FROM AUTHOR]

The local lattice distortions and the electron paramagnetic resonance (EPR) parameters (anisotropic g factors and the hyperfine structure constants) for the two Pt centers in ZnWO are theoretically investigated by utilizing the perturbation formulas of these parameters for a 5 d ion under rhombically elongated and compressed octahedra. The elongated (and compressed) centers are ascribed to the [PtO] clusters on Zn site suffering the axial elongation of 0.01 Å (and compression of 0.02 Å) along Z axis and the planar bond angle variations of 7.4° (and 7.8°), respectively, due to the Jahn-Teller effect. The above local lattice deformations may considerably cancel the original large axial elongation (~0.31 Å) and perpendicular rhombic angular distortion of the host [ZnO] cluster and yield more regular [PtO] clusters in the impurity centers. The calculated EPR parameters based on the above lattice deformations show good agreement with the experimental data, and the local structures of the impurity centers are discussed. [ABSTRACT FROM AUTHOR]

The anisotropic g factors and local structure for the rhombic Fe + center in NaF are theoretically studied using the perturbation formulas of the g factors for a rhombically distorted octahedral 3d 7 cluster. The impurity Fe + is found not to occupy exactly the host Na + site in NaF but to experience the off-center displacement of about 0.28 Å along [1 1 0] axis due to size mismatch substitution. The calculated g factors based on the above impurity displacement show reasonable agreement with the experimental data. The local structure of the Fe + center is discussed. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian parameters (zero-field splittings D, g factors g and g) for V in the alum compounds are theoretically studied using the perturbation formulas for these parameters for a 3d ion in the trigonally distorted octahedra. The contributions from the dynamical Jahn-Teller effect, the configuration interactions and the ligand orbital and spin-orbit coupling interactions are considered from the cluster approach in a uniform way. The angles in the deformed octahedra around V ions are increased by 1.1°-2.7°, as compared with those ones for the host. The theoretical spin Hamiltonian parameters based on the above angular variations and the related effects show good agreement with the experimental data, which reveal that these effects (especially the Jahn-Teller effect) can bring forward significant influences on the spin Hamiltonian parameters, and should be taken into account in electron paramagnetic resonance (EPR) analysis. The contributions from the configuration interactions and the ligand orbital and spin-orbit coupling interactions are quantitatively involved from the cluster approach in a uniform way. The results are discussed. [ABSTRACT FROM AUTHOR]

Abstract: The local structure and spin Hamiltonian parameters (zero-field splitting and g factors) for Ti2+ in MgCl2 are theoretically studied using the perturbation formulas of these parameters for a 3d2 ion under trigonally distorted octahedra. The contributions from the dynamical Jahn–Teller effect, the configuration interactions and the ligand orbital and spin–orbit coupling interactions are quantitatively involved based on the cluster approach in a uniform way. The chlorine polyhedron around the impurity Ti2+ is found to transform from a slightly compressed octahedron in pure MgCl2 to a slightly elongated one, characterized by the local angular decrease of 0.3° related to the host bond angle 54.78° due to the Jahn–Teller effect. The calculated spin Hamiltonian parameters based on the above trigonal elongation show good agreement with the experimental data. The results are discussed. [Copyright &y& Elsevier]

Abstract: The spin Hamiltonian parameters (zero-field splitting D, g factor and hyperfine structure constant) and the local structures for MgO:V3+, CaO:V3+ and CaO:Ti2+ are theoretically investigated from the perturbation formulas of these parameters for 3d2 ions under tetragonally distorted octahedra. The contributions from the dynamical Jahn–Teller effect, the configuration interactions and the ligand orbital and spin–orbit coupling interactions are quantitatively taken into account based on the cluster approach in a uniform way. The ligand octahedra are found to suffer the relative elongations of about 1.5%, 4.4% and 4.6% for MgO:V3+, CaO:V3+ and CaO:Ti2+, respectively, along the C4 axis due to the dynamical Jahn–Teller effect. The calculated spin Hamiltonian parameters based on the above local tetragonal elongations show reasonable agreement with the experimental data for all the systems. The results are discussed. [Copyright &y& Elsevier]

Abstract: 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 VO along the Z axis. The planar bond lengths are found to suffer the relative variation of about 0.16Å by compressing and stretching the Cu2+–O2− 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 VO can make the central Cu2+ displace away from the VO along the Z axis by about 0.3Å. The theoretical spin Hamiltonian parameters based on the above local distortions show good agreement with the experimental data. [Copyright &y& Elsevier]

Abstract: The spin Hamiltonian parameters (the g factors and the hyperfine structure constants) and the local structures for the orthorhombic [CuX4(H2O)2]2− clusters in NH4X (X=Cl, Br) are theoretically investigated from the perturbation formulas of these parameters for a 3d9 ion in orthorhombically compressed octahedra. The related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way. The studied defect centers are attributed to the impurity Cu2+ occupying the interstitial site associated with two adjacent water molecules along the [100] (or C 2) axis. The ligand octahedra are found to suffer the relative planar bond length variations of about 0.19 and 0.20Å along X and Y axes for X=Cl and Br, respectively, due to the Jahn–Teller effect. The calculated spin Hamiltonian parameters based on the above local structures show reasonable agreement with the observed values for both the centers. The validity of the results is also discussed. [ABSTRACT FROM AUTHOR]

The g factors and the superhyperfine parameters for the tetragonal Pd3+ centers in AgX (X = Cl, Br) are theoretically investigated from the perturbation formulas of these parameters for a 4d7 ion in tetragonally elongated octahedra In the calculations, the related molecular orbital coefficients and the unpaired spin densities of the ligands are determined quantitatively from the cluster approach in a uniform way. Both centers originate from substitutional Pd3+ on Ag+ site in AgX, with no charge compensator (silver vacancy) nearby. The [PdX6]3- clusters suffer a relative elongation of 0.01 Å, (or 0.06 Å) along [1 0 0] (or C4) axis for X = Cl (or Br) due to the Jahn-Teller effect The calculated g factors and the superhyperfine parameters based on the above Jahn-Teller elongations show good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The local structures and electron paramagnetic resonance (EPR) parameters (the g factors, the hyperfine structure constants and the superhyperfine parameters) for various Rh2+ centers in AgCl are theoretically studied using the perturbation formulas of these parameters for a 4d7 ion in tetragonally and orthorhombically distorted octahedra. These defects include the tetragonally and orthorhombically elongated centers at low temperatures (labeled as TL and OL) and the tetragonally compressed center at high temperature (labeled as TH). The centers TL and OL are attributed to the substitutional Rh2+ on Ag+ site, associated with none and one next nearest neighbour cation vacancy VAg along [100] (or X) axis, respectively. The ligand octahedron in the orthorhombic center OL is found to suffer the relative elongation ΔZ OL ≈0.079Å along [001] (or Z) axis due to the Jahn–Teller effect, and the intervening ligand Cl− in the VAg and the Rh2+ may experience the inward displacement ΔX ≈0.008Å towards the central Rh2+. In the center TL, the uncompensated [RhCl6]4− cluster is found to suffer the relative elongation ΔZ TL ≈0.116Å along [001] axis due to the Jahn–Teller effect. As for the center TH, one VAg occurs in the next nearest neighbour site along [001] axis, which may compel the intervening Cl− in the VAg and the Rh2+ to shift towards the central Rh2+ by an amount ΔZ H ≈0.112Å. In the calculations of the superhyperfine parameters, the related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The theoretical EPR parameters based on the above local structures show good agreement with the experimental data for all the centers. [Copyright &y& Elsevier]

Abstract: The anisotropic g factors g ∥ and g ⊥ and the planar F− superhyperfine parameters A ∥ and A ⊥ in the tetragonal impurity Ni+ I, II and III centers (as well as the axial F− superhyperfine parameters and in I center) on the substitutional Ca2+ site in RbCaF3 are theoretically investigated in a uniform way using the perturbation formulas of these parameters for a 3d9 ion in tetragonally elongated octahedra. In the calculations, the ligand unpaired spin densities are determined quantitatively from the related molecular orbital coefficients based on the cluster approach. These defects are attributed to the substitutional Ni+ associated with none, one and two axial nearest neighbour F− vacancies for I, II and III centers, respectively. Ni+ I center is found to suffer the relative elongation (≈5%) along the [001] (or C 4) axis due to the Jahn–Teller effect, while the tetragonal elongation distortions are mainly ascribed to the axial vacancies in II and III centers. The local structures of the various impurity centers are discussed. [Copyright &y& Elsevier]

The local structures and the spin Hamiltonian parameters (zero-field splittings D and E and the anisotropic g factors gx, gy and gz) for the rhombic Ni2+ centers in AgX (X = Cl, Br) are theoretically studied from the perturbation formulas of these parameters for a 3d8 ion under rhombically distorted octahedra. In these formulas, the ligand p- and s-orbital and spin-orbit coupling contributions are included on the basis of the cluster approach. The rhombic centers are attributed to the impurity Ni2+ associated with one nearest-neighbor silver vacancy VAg along the [110] direction as charge compensation. Based on the calculations, Ni2+ is found to suffer an off-center displacement 0.092 Å (or 0.335 Å) for AgCl (or AgBr) towards the VAg along the [110] axis, while the ligands closest to the VAg undergo a small shift 0.065 Å (or 0.006 Å) away from (or towards) the VAg. The theoretical spin Hamiltonian parameters based on the above defect structures show good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The spin Hamiltonian parameters (the g factors and the hyperfine structure constants) and local structure for ZnO:Cu2+ are theoretically studied from the perturbation formulas of these parameters for a 3d9 ion under trigonally distorted tetrahedra. The ligand orbital and spin–orbit coupling contributions are taken into account from the cluster approach due to the significant covalency of the [CuO4]6− cluster. According to the investigations, the impurity Cu2+ is suggested not to locate on the ideal Zn2+ site in ZnO but to undergo a slight outward displacement (≈0.01Å) away from the ligand triangle along C3 axis. The calculated spin Hamiltonian parameters are in good agreement with the observed values. The validity of the above impurity displacement is also discussed. [Copyright &y& Elsevier]

The local structure and the spin Hamiltonian parameters (the zero-field splitting D, the g factors g//, g⊥ and the hyperfine structure constants A// and A⊥) for the trigonal Mn2+ center in Bi4Ge3O12 are theoretically studied from the perturbation formulas of these parameters for a 3d5 ion in trigonal symmetry. The impurity Mn2+ replacing host Bi3+ is not found to occupy the exact Bi3+ site but to suffer a large off-center displacement by about 0.36 Å towards the center of the oxygen octahedron along the C3-axis due to the size and charge mismatching substitution. The calculated spin Hamiltonian parameters based on the above displacement show good agreement with the observed values. The results and the mechanism of the impurity displacement are discussed. [ABSTRACT FROM AUTHOR]

The local structure and the spin Hamiltonian parameters (the zero-field splitting D, the g factors g//, g⊥ and the hyperfine structure constants A// and A⊥) for the trigonal Mn2+ center in Bi4Ge3O12 are theoretically studied from the perturbation formulas of these parameters for a 3d5 ion in trigonal symmetry. The impurity Mn2+ replacing host Bi3+ is not found to occupy the exact Bi3+ site but to suffer a large off-center displacement by about 0.36 Å towards the center of the oxygen octahedron along the C3-axis due to the size and charge mismatching substitution. The calculated spin Hamiltonian parameters based on the above displacement show good agreement with the observed values. The results and the mechanism of the impurity displacement are discussed. [ABSTRACT FROM AUTHOR]

The spin Hamiltonian (SH) parameters g factors g|, g⊥ and the hyperfine structure constants A| and A⊥ for the tetragonal Cu2+ centers (i.e., [CuX4(H2O)2] clusters) in NH4X(X = Cl, Br, I) are theoretically investigated by means of the diagonalization procedure of complete (10×10) energy matrix (DPCEM) for a 3d9 ion in tetragonal symmetry. The crystal-field parameters in the energy matrix are determined from the superposition model. The calculated SH parameters are in reasonable agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The local structures for V2+ in CsMgX3 (X=Cl, Br, I) are theoretically investigated from the perturbation formulas of the EPR parameters (zero-field splitting, g factors and the hyperfine structure constants) for a 3d3 ion in trigonal symmetry based on the cluster approach. In these formulas, the contributions from the s-orbitals of the ligands, which were usually neglected in the previous treatments, are considered here. Based on the studies, we find that the local angles β (between the impurity-ligand bonding lengths and the C3 axis) in the V2+ centers are larger than the angles β H in the hosts, leading to the positive angular distortions . The theoretical EPR parameters (particularly the results for CsMgI3) show improvement compared with those in absence of the ligand s-orbital contributions or the above angular distortions. [Copyright &y& Elsevier]

Abstract: The EPR parameters zero-field splitting D, g factors g // and g ⊥ for the four centers (C1–C4) in PbTiO3:Cr3+ bulks and nanopowders are theoretically investigated from the perturbation formulas of the EPR parameters for a 3d3 ion in tetragonally distorted octahedra. Based on the studies, the impurity displacements ΔZ′ away from the center of the octahedron are obtained by analyzing the experimental EPR data. The results of the calculated D values in this work are compared with those based on the superposition model analyses in the previous works. The sign and magnitude of D and the impurity displacements in these centers are discussed. [Copyright &y& Elsevier]

Abstract: The defect structure for Mn2+ in KTaO3 is theoretically studied by using perturbation formulas of the spin Hamiltonian (SH) parameters for 3d5 ions in tetragonal symmetry based on the strong-field scheme. By analyzing the electron paramagnetic resonance (EPR) data of the studied system, we suggest that the impurity Mn2+ ion occupy the dodecahedral K+ site, rather than the octahedral Ta5+ site. Based on the studies, it is found that the Mn2+ impurity undergoes an off-center displacement away from the ideal K+ site by about 0.60Å along the C 4 axis. The above displacement is qualitatively consistent with the recent result based on the generalized gradient approximation (GGA) and that obtained from EPR and dielectric spectroscopy studies. [Copyright &y& Elsevier]

The EPR g factors for the tetragonal and orthorhombic Er3+ sites in ErBa2Cu3O7-δ high-Tc superconductors are theoretically studied by using the perturbation formulas of the g factors for a 4f11 ion in tetragonal and orthorhombic symmetries. In these formulas, the contributions to the g factors from the second-order perturbation terms and the admixture of various states are taken into account. The relevant crystal-field parameters are determined from the local geometrical relationship of the magnetic Er3+ sites and the superposition model (SPM). The theoretical g factors for Er3+ of both symmetries are in agreement with the observed values, by adjusting the related SPM parameters. The lowest Kramers doublets are found to be, respectively, (Γ7+Γ8) and (Γ5+Γ6) for the tetragonal and orthorhombic ErBa2Cu3O7-δ superconductors. The above studies may be helpful to understand the change of the Er3+ anisotropy from Ising- to XY-like as the symmetry varies from orthorhombic to tetragonal. [Copyright &y& Elsevier]

The spin Hamiltonian parameters gǁ, g⊥, Aǁ and A⊥ for Er3+ ion in LiYF4 are investigated by using the perturbation formulas of these parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the spin Hamiltonian parameters from the second-order perturbation terms and the admixtures of different states are considered. The relevant crystal field parameters are calculated from the superposition model and the local structural parameters of the Y3+ site occupied by impurity Er3+. The theoretical optical spectra within 4I15/2 and 4I13/2 states and the spin Hamiltonian parameters obtained in this work are consistent with the observed values. [Copyright &y& Elsevier]

The local structures and the electron paramagnetic resonance (EPR) parameters g factors gǁ, g⊥ and the hyperfine structure constants Aǁ and A⊥ for Er3+ in PbMoO4 and SrMoO4 are theoretically investigated by using the perturbation formulas of the EPR parameters for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the EPR parameters from the second-order perturbation terms and admixtures of different energy levels are considered. Based on the studies, we find that the impurity-ligand bonding angles related to the four-fold axis in the impurity Er3+ centers are reduced by about 1.26 and 1.04° compared with those in host PbMoO4 and SrMoO4 crystals, respectively. The calculated EPR parameters are consistent with the observed values. The validity of the results is discussed. [Copyright &y& Elsevier]

The local structure of the trigonal Co2+ center in MgTiO3 is theoretically investigated by using the perturbation formulas of the spin Hamiltonian parameters for a 3d7 ion in trigonal symmetry based on the cluster approach. From the studies, it can be found that the impurity Co2+ ion substitutes for Mg2+ rather than Ti4+ ion, and that the Co2+ takes an outward displacement (≈0.02 A˚) away from the center of the oxygen octahedron along the C3 axis in MgTiO3. The theoretical spin Hamiltonian parameters calculated from the above displacement show good agreement with the observed values. The validity of the results is discussed based on the impurity displacement model for corundum-type structures. [Copyright &y& Elsevier]

The perturbation formulas of EPR g factors g&z.dfnc; and g⊥ for the lowest Kramers doublet of 6H15/2 of a 4f9 ion in trigonal symmetry are established in this paper. In these formulas, besides the contribution due to the interaction within the lowest 6H15/2 manifolds considered in the previous papers, the contributions due to the J-mixing among the 6H15/2, 6H13/2 (first excited state) and 6H11/2 (second excited state) via crystal-field interaction, the admixtures among the states with the same J value via spin-orbit coupling interaction and those between the lowest Kramers doublet Γγ and other Kramers doublets ΓX within the states 6HJ (J=15/2, 13/2, 11/2) via crystal-field and orbital angular momentum interactions are included. From these formulas, the g factors g&z.dfnc; and g⊥ for the trigonal Dy3+ center in ThO2 crystal are calculated. The results are discussed. [Copyright &y& Elsevier]

Abstract: The spin Hamiltonian (SH) parameters (g factor, the hyperfine structure constant A as well as the superhyperfine parameters A′ and B′) for LiF:Mn2+ are theoretically investigated from the perturbation formulas of these parameters for a 3d5 ion under ideal octahedra. The related molecular orbital coefficients and the unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively determined from the cluster approach in a uniform way. The calculated SH parameters show good agreement with the experimental data. The results are discussed. [Copyright &y& Elsevier]

Abstract: The spin Hamiltonian parameters g factors g i (i = x, y, z) and the hyperfine structure constants A i of vitamin B12r have been theoretically studied from the perturbation formulas of these parameters for a Co2+(3d7) ion with low spin (S =1/2) in rhombically distorted octahedra. The related crystal-field parameters are determined from the point-charge-dipole model and the local structure around Co2+ in vitamin B12r. The theoretical spin Hamiltonian parameters are in good agreement with the experimental data. [Copyright &y& Elsevier]

Abstract: The perturbation formulae of the Spin Hamiltonian Parameters (EPR parameters anisotropic gyromagnetic factors g x , g y , g z and hyperfine structure constants A x , A y , A z ) for the lowest Kramers doublet of 2F5/2 of 4f1 ion in orthorhombic symmetry are established. In these formulae, the contributions of the covalence effects, the admixture between J =5/2 and J =7/2 states as well as the second-order perturbation are all included. The crystal field parameters for the studied Pr4+ center are calculated from the superposition model and the crystal structure data. Based on the perturbation equations and related parameters, the g factors g x , g y , g z and hyperfine structure constants A x , A y , A z for orthorhombic Pr4+ ion in SrCeO3 are calculated. The results are in reasonable agreement with the observed values. The results are discussed. [Copyright &y& Elsevier]

The anisotropic g factors g// and g⊥ for the tetragonal Er3+ center associated with Er3+ on Y3+ site in YBa2Cu3Oy (6

Abstract: We study perturbations of black holes absorbing dark energy. Due to the accretion of dark energy, the black hole mass changes. We observe distinct perturbation behaviors for absorption of different forms of dark energy onto the black holes. This provides the possibility of extracting information whether dark energy lies above or below the cosmological constant boundary . In particular, we find in the late time tail analysis that, differently from the other dark energy models, the accretion of phantom energy exhibits a growing mode in the perturbation tail. The instability behavior found in this work is consistent with the Big Rip scenario, in which all of the bound objects are torn apart with the presence of the phantom dark energy. [Copyright &y& Elsevier]