Ground-Term Energy Levels of Triply Ionized Holmium in Calcium Tungstate

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Abstract
The energy levels of the 5I ground term of Ho3+ in single crystals of CaWO4 were established by absorption and fluorescence spectra measurements. The measurements were made using crystals at temperatures near 2, 20, and 85°K. Most of the observed transitions can be accounted for by the electric dipole selection rules. Magnetic dipole selection rules cannot be ruled out for some of the lower energy transitions, however. Calculations were made to determine the effects of the crystalline host material on the Ho3+ energy levels. 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 Ho3+. Such a 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. In the calculation, an rms deviation of 10 cm−1 was found as the best agreement between the theoretical 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 yielding this rms deviation are (in cm−1): λ1 = − 487.9, λ2 = − 6.601, λ3 = − 0.1801, B20 = 436, B40 = − 664, B44 = 779, B60 = − 33, ReB64 = 558 , and ImB64 = 196 . The g‖ factor for the ground state of Ho3+ in CaWO4 was calculated to be 13.675. This is in agreement to within 0.12% of the experimental value of 13.691 ± 0.006 reported by Kirton.