Localization inf-shell metals

Abstract

Anderson's theory of local moments is applied to the $f$-shell metals with the use of parameters for the electronic structure given earlier. A criterion for localization (abrupt in this theory) of $Z_f$ levels per atom is that the resonance width be less than $2U{sin}^2\left(\frac{\pi Z_f}{14}\right)$, with $U$ the intra-atomic repulsion associated with $s-f$ transfer. Americium and the heavier actinides satisfy this criterion, as do all the rare earths except cerium; plutonium is borderline. The traditional term "localized state" is used here though "correlated state" would be more appropriate. For the cases considered the localized states are found to have net spin (or moment) but that is not a necessary condition. They are found to contribute to the $f$-band pressure on the crystal, but reduced by a factor of about $\frac{W_f}{3U}$, equal to 0.09 for americium, where $W_f$ is the itinerant $f$-band width. The localized $f$ levels may themselves be thought to form bands, but with reduced width, and they may even have Fermi surface, though that was not found for the systems considered. A comparison of this state with band ferromagnetism is made. An approximate calculation of the total energy of the localized and delocalized states as a function of volume correctly predicted the large volume and localization for americium.