Experimental and theoretical study of the crystal-field levels and hyperfine and electron-phonon interactions inLiYF4:Er3+

Abstract

We have measured high resolution absorption spectra for the ${}^{4}{\stackrel{\ensuremath{\rightarrow}}{{I}_{15/2}}}^{4}{I}_{13/2}{,}^{4}{I}_{11/2}$ infrared transitions of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{LiYF}}_{4}.$ Positions of crystal-field levels and their widths were precisely determined and analyzed. Hyperfine structure of ${}^{167}\mathrm{Er}$ totaling $\ensuremath{\sim}0.2 {\mathrm{cm}}^{\ensuremath{-}1}$ was observed. Experimental data are described by a theory that operates with a realistic model of the lattice dynamics and with the crystal-field parameters and electron-phonon coupling constants calculated in the framework of the exchange charge model. The hyperfine splittings of the odd mass number isotope ${}^{167}\mathrm{Er}$ are calculated taking into account both magnetic dipole and electric quadrupole hyperfine interactions. The simulated hyperfine structure is in good agreement with the experimentally observed one. The one-phonon relaxation rates within the ${}^{4}{I}_{11/2}$ and ${}^{4}{I}_{13/2}$ crystal-field manifolds are calculated using the correlation functions of the ${\mathrm{Er}}^{3+}$ ion and ligand displacements. The results of these calculations agree within an order of magnitude with the measured homogeneous linewidths of the corresponding zero-phonon transitions from the ground state at low temperatures.