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The six optical band positions and six spin-Hamiltonian parameters [g factors g(parallel to), g(perpendicular to) and hyperfine structure constants A(parallel to)((171)Yb(3+)), A(perpendicular to)((171)Yb(3+)), A(parallel to)((173)Yb(3+)), A(perpendicular to)((173)Yb(3+))] for Yb(3+) ion at the tetragonal Y(3+) site of KY(3)F(10) crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14 x 14 complete energy matrix for 4f(13) ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A(parallel to), A(perpendicular to) for the isotopes (171)Yb(3+) and (173)Yb(3+) in KY(3)F(10) are suggested. The results are discussed. (C) 2011 Elsevier B.V. All rights reserved.