Octahedral Ni <sup> 2 + </ Sup> Ion Of The Local Structure And Spin Hamiltonian Parameters,

Crystals doped with transition-metal ions have attracted extensive attention of researchers due to the fundamental and practical significance. Electron paramagnetic resonance (EPR) is a useful technique to study defect structures and electroninc properties for transition-metal ions in crystals, and many experimental data have been reported by previous EPR studies. EPR experimental results are usually described by the spin Hamiltonian parameters, e.g., zero-field splittings D and E, g factors. Theoretical analyses of these parameters can provide reliable information about local structures around the transition-metal ions which is helpful to understand the optical and magnetic properties of these materials.As an important system among the transition-metal group, Ni²⁺(3d⁸) has been extensively investigated due to the promising applications in tunable solid state laser and the unique spectroscopic properties in crystals. To study structure properties of this ion, the EPR experiments have been performed on various Ni²⁺ doped crystals in these decades, and the spin Hamiltonian parameters were measured. Comparatively, theoretical interpretations to these spin Hamiltonian parameters were unadequate, which also contain some imperfectness in the theoretical models and calculation methods. In order to overcome the above weakness and to investigate the spin Hamiltonian parameters for 3d8 ions to a better extent, in this work, the perturbation formulas of these parameters for a 3d8 ion in various symmetries (trigonal, tetragonal and rhombic) are established from the scheme of the crystal-field theory. In these formulas, the ligand (-p and -s) orbital and spin-orbit coupling contriutions are taken into account based on the cluster approach, and the relationships between some important parameters (e.g., the orbital admixture coefficients and crystal field parameters) and defect structures are established theoretically. Then these formulas are applied to the trigonal CsMgX₃:Ni²⁺ (X=Cl,Br,I) and tetragonal and rhombic AgX:Ni²⁺ (X=Cl,Br) systems. These EPR experimental results are satisfactorily explained, and the information about local structures of the impurity ion is also acquired.For CsMgX)3:Ni²⁺, local stress arising from substitution of host Mg²⁺ by larger Ni²⁺ can induce compression of the ligand octahedra along C3 axis. The above axial compression leads to an increase of about 2°for the impurity-ligand bond angle related to C3 axis as compared with the host values, which transforms the ligand octahedra from significant elongation in the hosts to slight elongation in the impurity centers. From calculations, the contributions from the ligand s-orbitals (which were usually neglected in the previous studies) should be taken into account, especially for the ligand I?. As for the tetragonal AgX:Ni²⁺ systems, the halide ligand intervening in the next nearest neighbouring silver vacancy VAg along [100] (or C4 axis) and the impurity Ni²⁺ is found to suffer an inward displacement (≈0.11 or 0.15(A|°) for AgCl or AgBr, respectively) towards Ni²⁺ due to the electrostatic repulsion. In the rhombic AgX:Ni²⁺ centers, Ni²⁺ is found to suffer an off-center displacement 0.092 (A|°) (or 0.335(A|°)) for AgCl (or AgBr) towards the nearest neighbouring VAg along [110] axis, while the ligands closest to the VAg undergo a small shift 0.065(A|°)(or 0.006(A|°)) away from (or towards) the VAg.