Calculating Hamiltonian parameters for Yb³⁺ in a low-symmetry lattice site, and fitting the structure and levels of Yb³⁺:RETaO₄ (RE=Gd, Y, and Sc)

An iterative method is used to find the values of the Hamiltonian parameters for Yb³⁺ in a given low-symmetry crystalline site. Samples of Yb³⁺:RETaO₄ (RE=Gd, Y, and Sc) were prepared and their structures were determined. Based on the obtained structure data, their orbital-spin parameters and crystal field parameters were fitted by the superposition model (SM). Using the crystal field parameters obtained by the SM fitting as the initial parameters, the Hamiltonian parameters were fitted iteratively. The calculated and experimental energy levels for Yb³⁺:RETaO₄ are consistent, and the maximal mean-root-square deviation is only 2.84 cm^-1, indicating that the method is effective to determine the Hamiltonian parameters of Yb³⁺ in low-symmetry crystalline sites.