Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare-earth ions. However, a computational crystal-field calculation of ${\mathrm{Eu}}^{3+}$incorporating the lattice electric quadrupole and nuclear Zeeman interactions has not been performed. Here, we include these terms in a computational model to fit the crystal-field levels and the Zeeman-hyperfine structure of the ${}^{7}F_0$ and ${}^{5}D_0$ states in three ${\mathrm{Eu}}^{3+}$sites: the ${\mathrm{C}}_{4v}$ and ${\mathrm{C}}_{3v}$ sites in ${\mathrm{CaF}}_2$and the ${\mathrm{C}}_2$ site in ${\mathrm{EuCl}}_3·6{\mathrm{H}}_2\mathrm{O}$. Close fits are obtained for all three sites which are used to resolve ambiguities in previously published parameters, including quantifying the anomalously large crystal-field-induced state mixing in the ${\mathrm{C}}_{3v}$ site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for ${\mathrm{Eu}}^{3+}$important for quantum information applications of these ions, such as relative transition strengths. The model could be used to improve crystal-field calculations for other non-Kramers singlet states. We also present a spin Hamiltonian formalism without the normal assumption of no $J$ mixing, suitable for other rare-earth ion energy levels where this effect is important.

• Received 27 October 2021
• Revised 20 February 2022
• Accepted 11 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.125141