Factors Gx Research Articles

Investigations on the EPR parameters and local structures for the substitutional Ti3+ and W5+ centers in stishovite

Abstract Local structures and electron paramagnetic resonance (EPR) parameters (g factors g x , g y , and g z ) for the substitutional Ti3+ and W5+ centers in stishovite are theoretically investigated by using the high-order perturbation formulas of these parameters for a d1 ion in rhombically compressed octahedra. In the calculation formulas, the related molecular orbital coefficients are obtained from the cluster approach, and the relevant crystal-field (CF) parameters are determined from the superposition model, which enables to connect these CF parameters and, hence, the studied g factors with the local structures of the Ti3+ and W5+ centers in stishovite. Based on the calculations, the impurity–ligand bond lengths parallel and perpendicular to the C 2-axis are found to be R′|| (≈1.751 and 1.717 Å) and R′⊥ (≈1.788 and 1.806 Å) with the planar bond angles θ′ (≈89.0° and 88.2°) for the studied [TiO6]9− and [WO6]7− clusters, respectively. The calculated results are in good agreement with the experimental data, and the validity of the results is discussed.

Theoretical explanation of spin-Hamiltonian parameters and local structure for the orthorhombic MnO2 −4 clusters in K2CrO4 : Mn6 + crystal

ABSTRACTIn this paper, the spin-Hamiltonian parameters (g factors gx, gy, gz and hyperfine structure constants A Ax, Ay, Az) and the absorption spectrum of K2CrO4 : Mn6 + crystal are theoretically explained by using the high-order perturbation theory, the double-spin-orbit-coupling model theory and the double-mechanism theory (the crystal field mechanism and the charge-transfer (CT) mechanism). The calculation results show that the contribution of the CT mechanism cannot be neglected for Mn6 + ions in orthorhombic clusters with the ground state .

Studies of the local distortions for nd1 (Mo5+ and W5+) impurities in KTP crystals

4d1 (Mo5+) and 5d1 (W5+) impurities doped into nonlinear optical crystals KTiOPO4 (KTP) can occupy the inequivalent Ti1 and Ti2 sites and exhibit orthorhombically compressed octahedral nd1 (n=4, 5) centres arising from the Jahn–Teller effect. Closely relevant to the electronic levels as well as optical and magnetic properties of these materials, the above local distortions can be suitably reflected by the anisotropic electron paramagnetic resonance (EPR) signals with the paramagnetic nd1 probes. This work stresses on the theoretical studies of the EPR parameters (g factors gx, gy, gz and hyperfine structure constants Ax, Ay, Az) and local distortions for the above nd1 impurity centres in a consistent way. The local distortions are characterised by the relative axial compression ratios ρ (≈0.040, 0.032 and 0.031) and the relative planar bond length variation ratios τ (≈0.030, 0.015 and 0.012) for Mo5+ centre I and W5+ centres II and III, respectively, which are larger than those of host Ti1 and Ti2 sites.

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 gx, gy, gz and hyperfine structure constants Ax, Ay, Az) 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 g factors and optical spectral band positions for Cr5+ in Sr2(VO4)Cl crystal

The EPR g factors gx, gy, gz and the optical spectral band positions for Cr5+ at the rhombically distorted tetrahedral V5+ site in Sr2(VO4)Cl crystal are calculated from the high-order perturbation formulas based on the two-mechanism model. In the calculations the optical band positions are obtained from the crystal-field energy levels used and the contributions to g factors from both the crystal field mechanism and charge transfer mechanism (which is omitted in the widely used crystal field theory) are included. The calculated results are in reasonable agreement with the experimental values. The calculations suggest that for the high valent state d1 ion (e.g., Cr5+ considered) in crystals, the exact theoretical calculations of g factors should take both crystal field and charge transfer mechanisms into account.

Theoretical investigation of optical and paramagnetic resonance spectra of [NiF6]4− clusters with orthorhombic symmetry

The ground state absorption spectra of [NiF6]4− clusters with orthorhombic symmetry (Ni2+ in NiF2 crystal and Ni2+-doped ZnF2 crystal, D2h point group) are theoretically calculated and assigned by diagonalization of 45×45 complete energy matrix for 3d8 configuration and the spin-Hamiltonian (SH) parameters (zero-field splitting D and E, and g factors gx, gy, gz) are studied by use of high-order perturbation method, in the frame of semi-empirical molecular orbital (MO) scheme based on strong crystal field framework. In those energy matrix, all the configuration interactions though the cubic crystal field (CF), the orthorhombic crystal field, the Coulomb interaction are taken into account. The calculated results are in good agreement with the experimental data. The local structure (bond length and bond angle) of [NiF6]4− clusters are determined, and the results shows that the structure data given by Stout are more plausible than those given by Baur.

Investigations on the spin Hamiltonian parameters for Yb3+ ion in Bi2Sr2YCu2O8

Many theoretical and experimental works have been done to understand the several characteristics of the Bi2Sr2YCu2O8. Since the electron paramagnetic resonance (EPR) is a powerful tool to analyze the electronic and magnetic properties of paramagnetic impurities in compounds, studies on the above EPR parameters would be helpful to the investigations of the characteristics for the superconductors. In this paper, EPR parameters anisotropic g factors gx, gy, gz, and the hyperfine structure constants Ax, Ay and Az of the two orthorhombic Yb3+ centers in Bi2Sr2YCu2O8 are theoretically studied from the perturbation formulas of these parameters for a 4f13 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 obtained from the superposition model and the local structure of the impurity Yb3+ ion occupying the host Bi3+ site. The calculated EPR parameters are reasonable agree with the observed values.

Unified calculations of the optical and electron paramagnetic resonance spectral data for Ce3+ ion in Y3Ga5O12 crystal

Seven crystal field energy levels (obtained from the optical spectra) and three g factors gx, gy and gz (obtained from electron paramagnetic resonance (EPR) spectra) for Ce3+ ion in Y3Ga5O12 crystal are calculated together by diagonalizing a complete energy matrix. The Hamiltonian of this energy matrix includes all the interactions for 4f1 ion Ce3+ in rhombic crystal field and under an external magnetic field, and so the optical and EPR data can be studied in a unified way. The calculated crystal field energy levels are in better agreement with the experimental values than the calculated values in the previous paper, and the g factors (which have not been calculated previously) are explained reasonably. The results are discussed.

Theoretical Investigations on the Off-Center Displacement of Co2+ in SrO by Analyzing Its Anisotropic g Factors

The off-center displacement of Co2+ ion in SrO crystal is investigated by analyzing its anisotropic g factors gx, gy and gz through diagonalization of the 6 × 6 energy matrix within 4T1 ground state for a 3d7 ion under rhombic symmetry. In the matrix, the contributions from the admixtures of various J( = 1/2, 3/2, 5/2) states and the fourth-order term Dη of rhombic crystal-fields and the ligand orbitals and spin-orbit coupling interactions, which are usually ignored in the previous studies, are considered. Both g factors (gx = 4.172, gy = 5.004 and gz = 2.133) and the off-displacement value (ΔR ≈ 0.023 nm) show good agreement with the experimental data.

THEORETICAL STUDIES OF THE LOCAL STRUCTURES AND SPIN HAMILTONIAN PARAMETERS FOR THE RHOMBICNi2+CENTERS INAgX(X=Cl,Br)

The local structures and the spin Hamiltonian parameters (zero-field splittings D and E and the anisotropic g factors gx, gyand gz) for the rhombic Ni2+centers in AgX ( X = Cl , Br ) are theoretically studied from the perturbation formulas of these parameters for a 3d8ion 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 VAgalong 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 VAgalong the [110] axis, while the ligands closest to the VAgundergo 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.

STUDIES OF THE LOCAL STRUCTURE AND THE g FACTORS FOR THE ORTHORHOMBICTi3+CENTER IN YAP

The local structure and the g factors for the orthorhombic Ti3+center in YAP are theoretically studied from the perturbation formulas of the g factors gx, gyand gzfor a 3d1ion in orthorhombic symmetry based on the cluster approach. The observed large anisotropy of the g factors may be attributed to the significant low-symmetrical (tetragonal and orthorhombic) distortion near the Al3+site occupied by the impurity Ti3+. The calculated g factors in this work show reasonable agreement with the experimental data.

Optical spectra and spin Hamiltonian parameters for rhombic Zr3+ in Y3Al5O12

The four optical spectrum bands (or d-d transitions) and six spin Hamiltonian parameters (g factors gx, gy, gz and hyperfine structure constants Ax, Ay, Az) of the rhombic Zr3+ (4d1) center in Y3Al5O12 crystal are calculated from the complete diagonalization (of energy matrix) method and the perturbation theory method. The calculated results from both methods are not only close to each other but also in good agreement with the experimental values. It appears that the two microscopic theory methods (which are very close to those used in a 3d1 system) are effective in the explanations of the optical and electron paramagnetic resonance spectra for a 4d1 system. From the calculations, the optical spectrum bands are reassigned and the defect structure of the rhombic Zr3+ center in Y3Al5O12 crystal is estimated.

Spin Hamiltonian parameters and defect structure for the X-ray-induced NbLi4+ center in LiNbO3 crystal

The spin Hamiltonian (SH) parameters (g factors gx, gy, gz and hyperfine structure constants Ax, Ay, Az) of the low-symmetry NbLi4+ antisite defect center in the X-ray-irradiated congruent undoped LiNbO3 crystal are calculated from the high-order perturbation formulas of SH parameters for d1 ions. The calculated results are in reasonable agreement with the experimental values. Some information related to the defect structure of the NbLi4+ center (characterized mainly by the NbLi4+ displacement Δz from the ideal Li+ site along C3 axis and the displacement Δx of O2− ions in the oxygen triangle between NbLi4+ and NbNb5+) is obtained from the calculations. These displacements are consistent with the expectation based on the electrostatic interaction and electron cloud overlap. The results are discussed.

The g Factors and Defect Structure of Orthorhombic Dy3+ Ions in CdF2 Crystals

The electronic paramagnetic resonance g factors gx, gy and gz of an orthorhombic Dy3+ center in CdF2 are studied by the perturbation formulae of the g factors for a 4f9 ion in orthorhombic symmetry. In these formulae, the contributions to g factors due to J-mixing among the ground 6H15/2, the first excited 6H13/2 and the second excited 6H11/2 states via crystal-field interaction, lead to admixtures among the states with the same J-value via spin-orbit coupling. In addition, the admixtures between the lowest Kramers doublet Γγ and other 20 Kramers doublets Γ x within the states 6HJ (J = 15/2, 13/2 and 11/2) via crystal-field and orbital angular momentum interactions are considered. In the above orthorhombic center, the impurity Dy3+ is associated with co-doped crystals with alkali metal ions in the [110] axis. By analyzing the g factors, we find that the impurity Dy3+ ion does not reside in the ideal Cd2+ site but moves towards the co-doped alkali metal ion along the [110] direction by a displacement Δ Z ≈ 0.272 Å.

CALCULATION OF EPR PARAMETERSgFACTORS FORCe3+ION INYBa2Cu3O6+xSUPERCONDUCTOR

The perturbation formulae of EPR parameters g factors gx, gyand gzfor the lowest Kramers doublet of 4f1ion in orthorhombic symmetry are established. In these formulae, the contributions of the covalency effects, the admixture between J=7/2 and J=5/2 states as well as the second-order perturbation (which is not considered in the previous works) via crystal-field and orbital angular momentum interactions are all included. According to these formulae, and by using the superposition model, the g-factors gx, gyand gzfor Ce3+center in YBa2Cu3O6+ xsuperconductor are calculated. The results are discussed.

Mössbauer and electron paramagnetic resonance study of the double-exchange and Heisenberg-exchange interactions in a novel binuclear Fe(II/III) delocalized-valence compound

In this paper we present the characterization by UV-VIS, Mössbauer, and EPR spectroscopy of [L2Fe2(μ-OH)3](ClO4)2⋅2CH3OH⋅2H2O, with L=N,N′,N″-trimethyl-1,4,7-triazacyclononane, a novel dimeric iron compound, which is shown to possess a central exchange-coupled delocalized-valence Fe(II/III) pair. Complete delocalization of the excess electron in the dimeric iron center is concluded from the indistinguishability of the two iron sites in Mössbauer spectroscopy. Mössbauer, EPR, and magnetic susceptibility data imply a system spin St =9/2 for the ground state. This finding is explained as being a consequence of the double-exchange interaction which is generated by the delocalized electron. Experimental values obtained from UV-VIS, Mössbauer, and EPR spectroscopy are for the double-exchange parameter B=1300 cm−1, the g factors gx,y =2.04 and gz =2.3, the parameters for zero-field splitting D=4 cm−1 and E≊0 cm−1, and for the hyperfine parameters ΔEQ =−2.14 mm s−1, Ax,y =−21.2 T, Az =−27 T, and δ=0.74 mm s−1. From our temperature-dependent studies we assign to the first excited state a spin-octet with an excitation energy Δ>175 cm−1. From this value a lower bound of −235 cm−1 has been deduced for the exchange-coupling constant J. In the framework of a simplified description of the iron atoms by unperturbed 3d orbitals, the values of the A tensor components as well as the quadrupole splitting ΔEQ can be interpreted in a consistent manner by assuming the excess electron being delocalized over two dσ orbitals centered at the two iron sites of the dimer and directed along the iron–iron axis as the z direction.