Complete crystal-field calculation of Zeeman hyperfine splittings in europium

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 Eu3+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 F07 and D05 states in three Eu3+sites: the C4v and C3v sites in CaF2and the C2 site in EuCl3·6H2O. 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 C3v site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for Eu3+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.