Octahedral 3d 3 And 3d 9 Ion Cluster Ligand Superhyperfine Structure Parameters Of The Theoretical Research

Electron paramagnetic resonance (EPR) spectrum is a useful tool to investigate optical and magnetic properties of crystals doped with transition-metal and rare-earth ions. EPR experimental results are usually characterized by the spin Hamiltonian parameters, i.e., zero-field splitting, g factors, hyperfine structure constants of central ions and super hyperfine structure parameters of legends. Since the spin Hamiltonian parameters are sensitive to local structures of the paramagnetic centers, investigations on these parameters can provide helpful information about local structure of the centers.As important model systems, 3d³ and 3d⁹ ions (e.g., V²⁺, Cu²⁺) have been extensively investigated by means of EPR technique, and useful experimental data for the spin Hamiltonian parameters were also measured. However, these studies were mainly related to g factors and hyperfine structure constants, and the investigations on the super hyperfine structure parameters of legends are fewer. In the previous works, the theoretical treatments on the super hyperfine structure parameters were generally carried out by introducing various adjustable parameters and fitting the experimental data, since the relationships between the model parameters in the super hyperfine structure parameters have not been established. In addition, the contributions from the charge-transfer mechanism were usually ignored for these systems, particularly for 3d3 ions in fluorides. In order to overcome the above shortcoming in the previous works, single-electron wave functions are established for 3d3 and 3d9 ions in octahedral, by including the contributions from the legend orbital and charge-transfer mechanism based on the cluster approach. By using the perturbation method, the perturbation formulas of the super hyperfine structure parameters for octahedral 3d3 and 3d9 systems are derived. Meanwhile, some important parameters, such as crystal-field parameters and molecular coefficients, are theoretically connected with the covalence of the systems. Thus, the difficulties of many adjustable parameters and neglecting of charge-transfer contributions are also removed.The above formulas are applied to the tetragonal Cu²⁺ centers in K₂PdX₄ (X=Cl, Br) and the cubic V²⁺ centers in AF (A=Li, Na). By considering the contributions from the legend orbital and the charge-transfer mechanism, the theoretical superhyerpfine structure parameters for these systems are in good agreement with the experimental data, by adopting much less adjustable parameters. It is found that the charge-transfer contributions are significant for these systems and cannot be neglected for simplicity. For example, the charge-transfer contributions are about one half those of the conventional crystal-field contributions.