| Electron paramagnetic resonance (EPR) spectrum 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, et. al.). Unfortunately, the theoretical studies on the spin Hamiltonian parameters in previous works were usually confined to the simple case of orbital nondegenerate ground states. For the more complicated case of orbital degenerate ground states, however, the theoretical studies on the spin Hamiltonian parameters are quite few. In addition, in the previous studies, some contributions to these spin Hamiltonian parameters were often ignored or not well treated due to the complicity of the problem and so many experimental results of the spin Hamiltonian parameters of orbital degenerate ground states cannot be satisfactorily explained. Since the spin Hamiltonian parameters for the orbital degenerate ground states are often related to various promising systems doped with transition-metal and rare earth ions, such as laser, luminescence and non-linear optical materials and life matter, the studies on the spin Hamiltonian parameters for orbital degenerate ground states are of theoretical and practical significance. In this paper, we investigate theoretically the spin Hamiltonian parameters of the lowest Kramers doublet F6 for a 3d7 (Co2") ion under octahedral crystal fields and those of F6 (or F7) for a 4fil(Ei>) ion in crystals. Particularly, some contributions to the spin Hamiltonian parameters which were usually ignored or not well treated in the previous works are deeply studied here. The main results and innovations are the follows:(1) The second-order perturbation formulas of the g factors and hyperfine structure constants for the lowest Kramers doublet F6 of a 3d7 ion under various octahedral symmetries (cubic, tetragonal, trigonal and rhombic) are established. In these formulas, the contributions to the spin Hamiltonian parameters from the configuration interaction, covalency effect and low symmetry distortion which were usually ignored or not well treated by the previous workers are included and the parameters related to the above contributions can be calculated from the experimental optical spectral data, the energy matrices of a 3d7 ion under the corresponding symmetry and the local structural parameters of the studied systems.(2) By applying the above formulas to some Co2+ doped systems, we succeed not only in solving some difficult problems (which were not satisfactorily explained, e. g.,why the g factor for CaO:Co2+ is larger than 4.3, whereas that for MgO:Co2+ is smaller than 4.3), but also in correcting some mistakes in the previous works [e. g., the relationship between the sign of low symmetry distortion (elongation or compression) for defect center and that of the anisotropy of g factor Ag(= g//- g?]. By studying the experimental EPR data, we obtain the local structural parameters of these Co2+ defect centers. These structural parameters are qualitatively in consistence not only with the expectation based on the electrostatic interactions, but also with the calculation based on the spin-lattice coupling coefficients.(3) The second-order perturbation formulas of g//, g^, A// and Ax for the lowest Kramers doublet F6 or F7 of a 4f" ion under trigonal and tetragonal symmetries are derived in this paper. In these formulas, (i) the second-order perturbation contributions to the spin Hamiltonian parameters arising from the lowest Kramers doublet (F6 or F7) and other Kramers doublets within 4I15/2 state through crystal field and orbital angular momentum (or the equivalent operator of hyperfme structure) interactions are taken into account and so the weakness of previous works in the limitation of the first-order perturbation calculations is removed; (ii) the contributions to the spin Hamiltonian parameters fr...
|
PDF Full Text Request