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[en] The spin-Hamiltonian parameters (g factors g||, gperpendicular and hyperfine structure constants 161A||, 161Aperpendicular, 163A||, 163Aperpendicular) for Dy3+ at the tetragonal Hf4+ site of HfSiO4 crystal are calculated from the diagonalization (of energy matrix) method. In the method, we add the Zeeman (or magnetic) and hyperfine interaction terms to the conventional Hamiltonian used in the calculations of crystal-field energy levels. The 66x66 energy matrix concerning the new Hamiltonian is established by considering the ground multiplet 6H15/2 and the first to fifth excited multiplets 6HJ (where J=13/2, 11/2, 9/2, 7/2 and 5/2), and the crystal-field parameters in the energy matrix are calculated from the superposition model. From the calculations, the spin-Hamiltonian parameters of HfSiO4:Dy3+ are explained reasonably and the signs of hyperfine structure constants for 161Dy3+ and 161Dy3+ isotopes in HfSiO4 are suggested. The results are discussed.