Investigations of the optical spectra and spin-Hamiltonian parameters for the rhombic Yb 3+ centers in garnets

Abstract

Two complete diagonalization (of energy matrix) methods (CDM-I and CDM-II) are used to calculate the six optical spectral band positions and nine spin-Hamiltonian (SH) parameters ( g factors g i and hyperfine structure constants 171 A i , 173 A i , where i= x, y, z) for Yb 3+ ions in the rhombic dodecahedral sites of garnets Y 3Al 5O 12, Lu 3Al 5O 12 and Y 3Ga 5O 12. In CDM-I, the Hamiltonian concerning energy matrix does not contain the Zeeman and hyperfine interaction terms, whereas in CDM-II, it does. So, in CDM-I, the SH parameters are obtained by first-order perturbation method or the equivalence between SH and Zeeman term (or hyperfine interaction term) and in CDM-II, the SH parameters and optical spectral band positions are calculated together. The results obtained from both methods are not only close to each other, but also in reasonable agreement with the observed values. So the second-order perturbation formulas of SH parameters developed recently are incorrect and unnecessary.