Systematics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mi>f</mml:mi></mml:math>electron energies relative to host bands by resonant photoemission of rare-earth ions in aluminum garnets

Abstract

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 ${R}_{x}{\mathrm{Y}}_{3\ensuremath{-}x}{\mathrm{Al}}_{5}{\mathrm{O}}_{12} (R=\mathrm{Gd},$ Tb, Dy, Ho, Er, Tm, Yb, and Lu and $0&lt;~x&lt;~3),$ 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 ${4f}^{n}$ ground-state energies of these ions range from 700 meV above the valence band maximum for ${\mathrm{Tb}}^{3+}$ to 4.7 eV below the valence band maximum for ${\mathrm{Lu}}^{3+},$ and all ground-state energies, except for ${\mathrm{Tb}}^{3+},$ are degenerate with valence band states. An empirical model is successful in describing the relative energies of the ${4f}^{n}$ 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 ${\mathrm{Ce}}^{3+}$ 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.