Understanding the valency of rare earths from first-principles theory

The rare-earth metals have high magnetic moments and a diverse range of mag netic structures(1). Their magnetic properties are determined by the occupa ncy of the strongly localized 4f electronic shells, while the outer 5-d ele ctrons determine the bonding and other electronic properties(2). Most of th e rare-earth atoms are divalent, but generally become trivalent in the meta llic state, In some materials, the energy difference between these valence states is small and, by changing some external parameter (such as pressure) , a transition from one to the other occurs. But the mechanism underlying t his transition and the reason for the differing valence states are not well understood. Here we report first-principles electronic-structure calculati ons that enable us to determine both the valency and the lattice size as a function of atomic number, and hence understand the valence transitions. We iind that there are two types of f electrons: localized core-like f electr ons that determine the valency, and delocalized band-like f electrons that are formed through hybridization with the s-d bands and which participate i n bonding. The latter are found only in the trivalent systems; if their num ber exceeds a certain threshold, it becomes energetically favourable for th ese electrons to localize, causing a transition to a divalent ground state.