Octahedron Of Rh <sup> + </ Sup> Ion Of The Local Structure And Spin Hamiltonian Parameters

Crystals doped with transition-metal ions have attracted extensible attention of researchers due to the fundamental and practical significance. Usually, the properties of these doped materials depend mainly on local structures around the trnaition-metal ions, which can be explored with the aid of the electron paramagnetic resonance (EPR). The experimental results of the EPR measurements are usually characterized by the spin Hamiltonian parameters (e.g., zero-field splittings, g factors and hyperfine structures constants). Generally speaking, EPR investigations have been extensively carried out for the first group (3dⁿ) transition-metal ions in crystals. Comparatively, the studies on the second group (4dⁿ) ions are much fewer.Among the second group transition-metal ions, 4d⁷ (e.g., Rh²⁺) is an important system due to the three 4d holes. The EPR experiments on this ion in various crystals were performed in these decades, and the spin Hamiltonian parameters have been measured. Unfortunately, no satisfactory interpretation to the above results has been made. The spin Hamiltonian parameters in the previous works are generally treated from the simple second-order perturbation formulas, with the related energy denominators taken as the adjustable parameters. In addition, the spin Hamiltonian parameters also fail to correlate to the local structures of these impurity centers. In order to overcome the above imperfectness in the previous studies, in this work, the high-order perturbation formulas of the g-factors and the hyperfine structure constants for 4d⁷ ions in tetragonal and orthorhombic symmetries are established on the basis of the crystal-field theory. Importantly, the relationships between the spin Hamiltonian parameters and the local structures are theoretically established.These formulas are then applied to some tetragonal and orthorhombic Rh²⁺ centers in LiD and AgCl. As for LiD:Rh²⁺ with very small ligand spin-orbit coupling coefficient and covalency, the ligand contributions are neglected for simplicity. For AgCl:Rh²⁺ with large ligand spin-orbit coupling coefficient and significant covalency, the ligand contributions are taken into account from the cluster approach. In addition, some model parameters (e.g., tetragonal or orthorhmbic field parameters, molecular orbital coefficients) in the formulas are determined from the local structures and experimental optical spectra of the studied impurity centers. Based on the studies, the calculated spin Hamiltonian parameters for all these Rh²⁺ centers show good agreement with the experimental data, and the information about the impurity local structures are also obtained for various systems. For the tetragonally compressed LiD:Rh²⁺ {A} center, the intervening ligand D^- in Rh²⁺ and the next nearest neighbouring vacancy V_Li is founded to shift towards Rh²⁺ by an amount△Z_A≈0.01(?) along the C₄ axis due to the electrostatic repulsion of the V_Li. Orthorhombic elongated {O} center is assigned to the relative elongationδ≈0.072(?) of the ligand octahedron along [001] axis due to the Jahn-Teller effect, associated with one next nearest neighbouring V_Li along [100] axis. The intervening ligand may also suffer a displacement△X_o≈0.11(?) towards Rh²⁺ along this direction. For the high temperature (HT) tetragonally compressed center in AgCl:Rh²⁺, the intervening ligand D^- in Rh²⁺ and the vacancy V_Ag is founded to shift towards Rh²⁺ along the C₄ axis by about 0.112(?). For the tetragonally elongated Rh²⁺ center without no charge compensation and the low temperature (LT) orthorhombic center in AgCl, the impurity-ligand bonds are found to suffer the elongations ofδ(≈0.116(?)) andδ'(≈0.079(?)), respectively, due to the Jahn-Teller effect. In addition, the intervening Cl^- in [100] axis also displace towards Rh²⁺ by about 0.01(?) due to the electrostatic repulsion of the V_Ag.