Analysis of the optical spectrum of Ho3+ in LiYF4

The energy levels for Ho³⁺ in single crystal LiYF₄ from 0–21,300 cm^?1 have been determined from polarized absorption and fluorescence spectra using crystals at temperatures between 4 and 300°K. Energy level assignments were made initially by comparing the crystal spectra with energy levels calculated by using crystal field parameters interpolated from previously reported analyses of Nd³⁺, Er³⁺ and Tm³⁺ in LiYF₄. The energy level scheme identifies energy levels in the 10 lowest J-multiplets and gives calculated energies for the next six higher J-multiplets. The crystal field parameters were varied to obtain a best fit between experimental and theoretical energies, and the final values B₂₀ = 410, B₄₀ = ? 615, B₄₄ = 819, B₆₀ = ? 27.9 and B₆₄ = 677 ± i32.8 cm^?1 give an r.m.s. fit of 2.78 cm^?1. The calculations were made by diagonalizing the crystal field Hamiltonian, H_x = Σ_kmB_kmC_km, in the space of ten lowest J-multiplets spanned by intermediate coupled free-ion wavefunctions calculated using the free-ion parameters of Carnall et al. for Ho in aqueous solution. The calculated g_∥ for the Γ_3.4 ground state of 13.63 compares favorably with a previously reported value of 13.3 ± 0.1.