Complete crystal field calculation of Zeeman-hyperfine splittings in europium

Abstract

Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare earth ions. These techniques have not yet been applied to the Zeeman-hyperfine structure of Eu${}^{3+}$ because modeling the structure of the $J=0$ singlet levels in Eu${}^{3+}$ requires inclusion of the commonly omitted lattice electric quadrupole and nuclear Zeeman interactions. 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 Eu${}^{3+}$ sites: the C${}_{4v}$ and C${}_{3v}$ sites in CaF${}_2$ and the C${}_2$ site in EuCl${}_3$.6H${}_2$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 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 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.

References in corpus (5)

• Multi-Modal Properties and Dynamics of the Gradient Echo Quantum Memory
• Quantum processing with ensembles of rare earth ions in a stoichiometric crystal
• Hyperfine interactions of ${\text{Er}}^{3+}$ ions in ${\text{Y}}_2{\text{SiO}}_5$: electron paramagnetic resonance in a tunable microwave cavity
• Electron-Nuclear Interactions as a Test of Crystal-Field Parameters for Low Symmetry Systems: Zeeman-Hyperfine Spectroscopy of Ho${}^{3+}$ Doped Y${}_2$SiO${}_5$
• Prediction of the Optical Polarization and High Field Hyperfine Structure Via a Parametrized Crystal-Field Model for the Low Symmetry Centers in Er${}^{3+}$ Doped Y${}_2$SiO${}_5$

Cited by in corpus (1)

• Nuclear T-violation search using octupole-deformed nuclei in a crystal