Systematics of4felectron energies relative to host bands by resonant photoemission of rare-earth ions in aluminum garnets

The energies of trivalent rare-earth ions relative to the host valence band were measured for a series of rare-earth-doped yttrium aluminum garnets RₓY_3-xAl₅O₁₂ (R=Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu and $0<~x<~3),$ using ultraviolet photoemission spectroscopy. The $4f$ photoemission spectra were acquired using synchrotron radiation, exploiting the $4d$ to $4f$ ``giant resonance'' in the $4f$ electron photoemission cross section to separate the $4f$ contribution. Theoretical valence band and $4f$ photoemission spectra were fit to experimental results to accurately determine electron energies. The measured 4fⁿ ground-state energies of these ions range from 700 meV above the valence band maximum for Tb³⁺ to 4.7 eV below the valence band maximum for Lu³⁺, and all ground-state energies, except for Tb³⁺, are degenerate with valence band states. An empirical model is successful in describing the relative energies of the 4fⁿ ground states for rare-earth ions in these materials. This model is used to estimate the positions of the lighter rare-earth ions, giving good agreement with published excited-state absorption and photoconductivity measurements on Ce³⁺ in yttrium aluminum garnet. It is shown that the energies of the $4f$ electrons relative to the valence band can be estimated from the photoemission spectrum of the undoped host, providing a simple method for extending these results to related host crystals. The success of this model suggests that further studies of additional host compounds will rapidly lead to a broader picture of the effect of the host lattice on the $4f$ electron binding energies.