Optical Spectrum of Triply Ionized Erbium in Calcium Tungstate

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Abstract
The energy levels of the 4I ground term of Er3+ in single crystals of CaWO4 were established by absorption and fluorescence spectra measurements. The measurements were made using crystals at temperatures of 2, 20, and 85°K. The energy level scheme allows an interpretation of the 1.612‐μ four‐level CaWO4:Er3+ laser transition and shows the terminal energy level of this transition to be 318 cm−1 above the ground state rather than 375 cm−1 as reported by Kiss and Duncan. An effective Hamiltonian of the form suggested by Karayianis was diagonalized in a basis of Russell–Saunders wavefunctions to obtain the calculated energy levels and wavefunctions for the entire ground term of Er3+. The calculation takes into account the complete J mixing of the states within the ground term and is equivalent to determining the effects of the spin–orbit interaction to better than second order. An rms deviation of 18 cm−1 was found as the best agreement between the calculated and experimental energy levels using the Hamiltonian: H = λ1(L·S) + λ2(L·S)2 + λ3(L·S)3 + ΣlmBlm†Clm . The empirically determined parameters are (in cm−1) λ1 = − 613, λ2 = − 19.3, λ3 = − 0.499, B20 = 404, B40 = − 685, B60 = 12.4, B44 = 728, ReB64 = 452 , and ImB64 = 164 . Using wavefunctions determined with these parameters, the g factors were calculated for the states of the ground term. The calculated and measured g factors for the two lower energy states are in good agreement where the calculated values are g‖ (ground state) = 1.265, g⊥ (ground state) = 8.487, g‖* (first excited state) = 3.22, and g⊥* (first excited state) = 7.06, and the measured values in the same order are g‖ = 1.247, g⊥ = 8.400, g‖* = 3.42 , and g⊥* = 6.98 . A Γ5,6 ground state wavefunction is compatible with the results obtained here, whereas a Γ7,8 ground state wavefunction is not. Previous studies had not established the ground state wavefunction uniquely.