Theory Of The Spin Hamiltonian Parameters Of The Crystal Material Of Ru (3 +) Ion Center

Crystals doped with transition-metal (TM) ions have attracted extensible interest of researchers in recent years due to their theoretical and practical significance. Electron paramagnetic resonance (EPR) is a useful technique to study local structure and electronic properties for TM ions in crystals, and many experimental data for spin Hamiltonian parameters (g factor and the hyperfine structure constant) were also measured. Compared with the investigations for 3dn ions, those for the second group TM (4dn) ions with low spin S=1/2 are relatively fewer. For example, the pervious works on 4d5 ions (e.g., Ru³⁺), some important contributions (e.g., ligand orbitals and ligand spin-orbit coupling) to the spin Hamiltonian parameters were usually ignored for simplicity. As a result, some EPR experimental results have not been satisfactorily explained, and the information about local structure properties for these 4d5(Ru³⁺) impurity centers were not determined yet.In order to overcome the weakness of the previous works and the investigation of the spin Hamiltonian parameters for these 4d5 centers to a better extent, in this work, the perturbation formulas of these parameters for 4d5 ions in trigonal and tetragonal symmetries are established. In these formulas, the ligand orbital and spin-orbit coupling contriutions are taken into account based on the cluster approach, and the quantificational relationships between the orbital admixture coefficients and crystal field parameters and between the local defect structure are obtained theoretically. Then these formulas are applied to some trigonal and tetrgonal 4d5 centers (i.e., Ru³⁺ ions in corundum, garnet, PbTiO3, AgCl and AgBr). Based on the studies, the calculated spin Hamiltonian parameters show good agreement with experimental data. By analyzing the EPR results, the information about local structures (e.g., the axial dispalcement of the impurity or nearest ligand ions) in these impurity centers is also obtained.