Theoretical investigations of the EPR parameters and local structure for Cu2+ in BeO

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors, the hyperfine structure parameters and the quadrupole coupling constant Q) and local structure for Cu²⁺ in BeO are theoretically investigated from the perturbation formulas of these parameters for a 3d⁹ ion under trigonally distorted tetrahedra. The ligand orbital and spin-orbit coupling contributions are included in the basis of the cluster approach, in view of the strong covalency of the [CuO₄]^6? cluster. From the calculations, the impurity Cu²⁺ is suggested not to occupy exactly the ideal Be²⁺ site but to suffer a slight inward displacement (≈0.024 Å) toward the ligand triangle along the C₃ axis. The theoretical EPR parameters show good agreement with the experimental data.     

Theoretical investigations on the spin Hamiltonian parameters and local structures for the trigonal Ni2+ centers in CsMgX3 (X=Cl,Br, I)

The spin Hamiltonian parameters (zero-field splitting and the anisotropic g factors) and the local structures for the trigonal Ni²⁺ centers in CsMgX₃ (X=Cl, Br, I) are theoretically investigated from the perturbation formulas of these parameters for a 3d⁸ ion in trigonally distorted octahedra, by including the ligand s-orbital contributions. Based on the studies, the local impurity-ligand bond angles β related to the C ₃ axis in the Ni²⁺ centers are found to be about 2° larger than the corresponding angles, β_H, in the hosts, due to the size mismatching substitution of Mg²⁺ by Ni²⁺. The theoretical results based on the inclusion of the ligand s-orbital contributions show an improvement when compared with those in the absence of the above contributions, especially for the ligand I^?.     

Investigations on the local structure and g factors for the interstitial Ti3+ in TiO2

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 δϕ′ (≈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.      

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.     

Spin Hamiltonian parameters and local structures for tetragonal and orthorhombic Ir2+ centers in AgCl

The perturbation formulae of the spin Hamiltonian parameters (the anisotropic g factors, hyperfine structure constants and superhyperfine parameters) are established for a 5d⁷ ion in an orthorhombically elongated octahedron based on the cluster approach. These formulae are applied to the theoretical studies of the EPR spectra and the local structures for the tetragonal and orthorhombic Ir²⁺ centers in AgCl. For the tetragonal Ir²⁺ center, the uncompensated substitutional [IrCl₆]⁴ cluster is found to experience a relative elongation of about 0.08 Å along the C ₄ axis due to the Jahn–Teller effect. For the orthorhombic center, the ligand octahedron also suffers Jahn–Teller elongation (by about 0.08 Å) along the [001] (or Z) axis. Meanwhile, the ligand Cl intervening in the impurity Ir²⁺ and the next nearest neighbor silver vacancy V_Ag along the [100] (or X) axis may undergo an inward displacement of 0.004 Å towards the center of the octahedron due to electrostatic repulsion of the V_Ag. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with experimental data for both centers.     

Investigation of the EPR parameters of the rhombic Cu2+ center in (NH4)2Mg(SO4)2·6H2O single crystal

The electron paramagnetic resonance (EPR) parameters (g factors g_x, g_y, g_z and hyperfine structure constants A_x, A_y, A_z) for Cu²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O (DHMS) crystal are theoretically investigated using the high-order perturbation formulas of these parameters. In the calculations, the ligand orbital and spin–orbit coupling for the impurity Cu²⁺ are taken into account; the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the EPR parameters with the local structure of the impurity center. The ligand orbital and the spin–orbit coupling contributions are included on the basis of the cluster approach. Based on the calculation, the theoretical EPR parameters show good agreement with the observed values. The results are discussed.     

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.     

Studies of the g factors and the local structure of the orthorhombic Ni center in KTaO3 crystal

The local structure and the g factor (g_x, g_y, and g_z) of the Ni⁺ center in KTaO₃ are theoretically studied using the perturbation formulas of the g factors for a 3d⁹ ion in orthorhombically elongated octahedra. The orthorhombic field parameters are determined from the superposition model and the local geometry of the system. In view of the covalency, the contributions from the ligand orbital and spin–orbit coupling interactions are taken into account from the cluster approach. In the calculations, the orthorhombic center is attributed to Ni⁺ occupying the host Ta⁵⁺ site, associated with the nearest-neighboring oxygen vacancy V_O along the c-axis. Furthermore, the planar Ni⁺–O²⁻ bonds are found to experience the relative variation ΔR (≈0.076 Å) along the a- and b-axis, respectively, due to the Jahn–Teller effect and the size mismatching substitution of Ta⁵⁺ by Ni⁺. Meanwhile, the effectively positive V_O can make the central Ni⁺ displace away from V_O along the c-axis by about 0.20 Å. The calculated g factors based on the above local distortions show good agreement with the experimental data.