Absorption Spectrum and Zeeman Effect of the Transitions “5I8” → “3K8” and “5I8” → “5G4” in Holmium Ethylsulfate

Abstract

The absorption spectrum and Zeeman effect of the ground term and two excited terms of Ho^3 + were measured in the $C_{\text{3h}}$ point symmetry of hexagonal single crystals of holmium ethylsulfate. Magnetic‐field strengths from 0 to 27 900 G were employed for studying the behavior of the energy levels in both the HsC (magnetic field perpendicular to $c$ axis) and HpC (magnetic field parallel to $c$ axis) crystal orientations. When the single crystals were rotated about the $c$ axis in the HsC case, a 60° periodicity was observed in the energies of some of the Zeeman components and in the intensities of some of the lines. The angle $\phi$ defined by Murao, Spedding, and Good (MSG), which describes the angle between the $a$ and $x$ axes in the basal plane of the crystal was found to be 5° ± 2° for both holmium ethylsulfate and 10 mole % holmium in yttrium ethylsulfate. At high magnetic‐field strengths, since the magnetic splitting could no longer be considered small compared to the crystal‐field splitting, the second‐order perturbation treatment of MSG was not sufficient to account for the periodic energy behavior of the levels or the intensity behavior of the lines. The energy behavior was in good agreement with a more recent theoretical treatment for the case where the crystal and magnetic splittings are comparable and with calculations performed in this work in which the observed crystal‐field levels were perturbed by approximate matrix elements of the Zeeman interaction. These matrix elements were calculated using the approximate wavefunctions obtained by diagonalizing the parameterized $C_{\text{3h}}$ crystal‐field matrix which gave the best agreement with the crystal‐field splittings of the ${“}^3{K}_8”$ as observed in this paper. Due to the large nuclear moment and high $J$ values of the holmium ion, we were able to resolve the nuclear hyperfine structure in a number of absorption lines. When the magnetic field was along the $c$ axis of the crystal, it was found that an apparent change in the selection rules, and a distinct change in the hyperfine patterns occurred in the neighborhood of field strengths where levels in the ground term with different crystal quantum numbers were expected to cross. This behavior was explained theoretically by including the effects of matrix elements of hyperfine interaction which are not diagonal in $\mu$ . These elements prevent the crossing, and patterns calculated in this way were, within the limits of our resolution, in good agreement with the experimental results.