Theoretical Investigations Of The Spin Hamiltonian Parameters For The Rare Earth Kramers Ions In Crystals

The crystals doped with rare earth ions are of great usefulness because of its excellent optical and magnetic properties. Electron paramagnetic resonance (EPR) and optical spectra are the effective tools in studying the optical and magnetic properties of crystals and complexes doped with rare-earth ions. EPR experimental results are often described by the spin-Hamiltonian parameters . Unfortunately, the theoretical studies on the spin-Hamiltonian parameters in previous works were usually confined to the simple cases. For the more complicated cases of the rare earth Kramers ions (i.e., the number of/electrons is odd), however, in the previous studies, some contributions (such as the crystal field J-admixtures among the ground states and the excited states and the admixture among the ground doublet and other doublets with the same irreducible representation) to these spin Hamniltonian parameters were often ignored or were not well treated because of the complicity of the problem, and so many experimental results of the spin Hamniltonian parameters of the rare earth Kramers ions in crystals cannot be satisfactorily explained. Since the spin-Hamiltonian parameters for rare earth ions with the Kramers ground doublet are often related to various promising systems, such as laser, luminescence and non-linear optical materials and life matter, the studies on the spin-Hamiltonian parameters for the rare earth Kramers ions are of theoretical and practical significance. In order to overcome the defects of the previous works, in this paper, we investigate theoretically the sp2in Hamiltonian parameters of the lowest Kramers doublet F6 (or T7) for 4f(Ce3+), 4f5(Sm3T% 4f9 (Dy3+) and 4f3(Yb3+) ions in crystals having various symmetries from axis symmetry to rhombic symmetry. The main achievements and innovations are as follows:1. The perturbation formulas of spin-Hamiltonian parameters (g factors g , g and hyperfine structure constants A, A ) for the lowest Kramers doublet F6 or F7 of 2F7/2 of 4f13 (or 4f1 ) ion in tetragonal and trigonal symmetries are established. In these formulas, the contributions due to the covalency effects, the admixture betweenJ=7/2 and J=5/2 states as well as the second-order perturbation (which is not considered in the previous works) are all included.2. By applying the above formulas to some Ce3* (i.e., tetragonal Ce3+ center in CaF2and SrF2crystals) and Yb3^(i.e., tetragonal Yb3+ center in CaF2 crystal; trigonal Yb3+ centers in RXO4 crystals and two trigonal Yb3+ centers in LiNbO3 and LiNbO3:MgO crystals) doped systems, the experimental spin-Hamiltonian data g, g , A,, and AL for these crystals are reasonably explained, we obtain some local structural parameters for two Yb3+ centers in LiNbO3 and LiNbO3:MgO crystals, and these Yb3+ defect centers are reasonably assigned.3. We establish the perturbation formulas of spin-Hamiltonian parameters gx/, gj_, A,, and A?for 4f5 ion in axial symmetry. In these formulas, the contributions to EPR parameters due to (i) the crystal-field J-mixing among the ground 6H5/2, the first excited 6H7/2 and the second excited 6H9/2 states, (ii) the admixtures among the states with the same J values via spin-orbit coupling interaction and (iii) those between the lowest Kramers doublet Fy and the same irreducible representations as Fx in the other 11 Kramers doublets Fx within the states 6Hj ( J=5/2,7/2 and 9/2 ) via crystal-field and angular momentum ( or hyperfme structure ) interactions are included. In addition, the orbital reduction factor k due to the covalency reduction effect is also considered.4. From these formulas, the EPR parameters g , g , A and A for Sm3+ ions in the tetragonal sites of KY3F,0and LiYF4 crystals are calculated by using the free-ion and crystal-field parameters obtained from the optical spectra. The calculated results are in good agreement with the experiment dada. The great difference between the calculated and experimental values in previous work now vanishes.5. We also establish the second-order perturbation formulas of sp...