Electron-nuclear interactions as a test of crystal field parameters for low-symmetry systems: Zeeman hyperfine spectroscopy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi mathvariant="normal">Ho</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math>-doped <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Y</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:math>

High-resolution Zeeman spectroscopy of electronic-nuclear hyperfine levels of ${}^{5}{\mathrm{I}}_{8}\ensuremath{\rightarrow}{}^{5}{\mathrm{I}}_{7}$ transitions in ${\mathrm{Ho}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ is reported. Crystal-field parameters determined for the two ${C}_{1}$ symmetry sites in ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ are successfully used to model the Zeeman-hyperfine data, including the prediction of avoided crossings between hyperfine levels under the influence of an external magnetic field. The two six- and seven-coordinate substitutional sites may be distinguished by comparing the spectra with crystal-field calculations.

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