Rare-earth - boron bonding and 4f state trends in $\mathcal{R}B_4$ tetraborides
Z. P. Yin and W. E. Pickett

The B-B bonding, boron-rare earth coupling, and the changes in $4f$ states across the lanthanide series in $R$B$_4$ ($R$ = rare earth) compounds are studied using the correlated band theory LDA+U method. A set of boron bonding bands can be identified that are well separated from the antibonding bands. Separately, the ``dimer B'' $2p_z$ orbital is non-bonding ({\it viz.} graphite and MgB$_2$), but mixes strongly with the metal $4d$ or $5d$ states that form the conduction states. The bonding bands are not entirely filled even for the trivalent compounds (thus the cation $d$ bands have some filling), which accounts for the lack of stability of this structure when the cations are divalent (with more bonding states unfilled). The trends in the mean $4f$ level for both majority and minority, and occupied and unoccupied, states are presented and interpreted.

© 2008 The American Physical Society.