The rare earths are known to have intriguing changes of the valence, depending on the chemical surrounding or geometry. Here, we aim at predicting the transition of valence when passing from the atomic divalent limit to the bulk trivalent limit. This transition is analyzed by addressing clusters of various size for selected rare-earth elements, i.e., Sm, Tb, and Tm, via a theoretical treatment that combines density functional theory with atomic multiplet theory. Our results show that Tm clusters change from pure divalent to pure trivalent at a size of six atoms, while Tb clusters are already divalent for two atoms and stay so until eight atoms and the bulk limit. Instead, Sm clusters are respectively purely divalent up to eight atoms. For larger Sm clusters, a transition to a trivalent configuration is expected and likely accompanied by a regime of mixed valence. The valence of all rare-earth clusters, as a function of size, is predicted from the interpolation of our calculated results. These predictions are argued to be best investigated by spectroscopic measurements. To ease experimental analysis, we provide theoretical spectra, based on dynamical mean-field theory in the Hubbard I approximation.

• Received 19 February 2015
• Revised 3 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.035143