Csmgx <sub> 3 </ Sub> (x = Cl, Br, I) Mixed With V-~ (2 +) Spin Hamiltonian Parameters Of The Theory

Electron paramagnetic resonance (EPR) is an effective tool to investigate the optical and magnetic properties of crystals and complexes doped with transition-metal and rare-earth ions. EPR experimental results are usually described by the spin Hamiltonian parameters (zero-field splittings, g factors and hyperfine structure constants).EPR experimental results have been reported for various 3d³ ions (e.g., V²⁺, Cr³⁺) in crystals, and theoretical investigations on the electronic and multiplet structures have also been carried out. In the previous studies, the perturbation formulas of the spin Hamiltonian parameters for 3d³ ions in different symmetries were established, on the basis of the cluster approach where the spin-orbit coupling interaction and the p- orbitals of the ligands were taken into account. The theoretical results based on the above formulas show some improvement, compared with those based on the conventional crystal-field theory where only the spin-orbit coupling of central ions were considered. However, for the ligands (e.g., Br and .I) having very large spin-orbit coupling coefficients, their theoretical results often show poor agreement with the experimental data; because the influence of the spin-orbit coupling of the ligands were overestimated in absence of the ligand s-orbital contributions. In order to overcome the above weakness, one-electron wavefunctions are constructed in this work, by including both the p- and s-orbitals of the ligands based on the cluster approach. According to the perturbation method in strong field scheme, the perturbation formulas of the spin Hamiltonian parameters are established for 3d3 ions in cubic, trigonal and tetragonal symmetries. Meanwhile, the relationships between the molecular orbital coefficients and the spectral parameters or local structures of impurity ions are theoretically determined, and then the spin Hamiltonian parameters are connected with the local structures of the studied systems.(1) The formulas of cubic case are applied to CsMgX₃ (X = Cl, Br, I) doped with V²⁺. It is found that the calculation results (especially for CsMgI₃) by including the...