Hill limit (solid-state) explained

In solid-state physics, the Hill limit is a critical distance defined in a lattice of actinide or rare-earth atoms.^[1] These atoms own partially filled

4 f or 5 f levels in their valence shell and are therefore responsible for the main interaction between each atom and its environment. In this context, the hill limit r _{H} is defined as twice the radius of the f -orbital.^[2] Therefore, if two atoms of the lattice are separate by a distance greater than the Hill limit, the overlap of their f -orbital becomes negligible. A direct consequence is the absence of hopping for the f electrons, ie their localization on the ion sites of the lattice.

Localized f electrons lead to paramagnetic materials since the remaining unpaired spins are stuck in their orbitals. However, when the rare-earth lattice (or a single atom) is embedded in a metallic one (intermetallic compound), interactions with the conduction band allow the f electrons to move through the lattice even for interatomic distances above the Hill limit.

See also

• Anderson impurity model

Notes and References

1. Hill, H. H. The Early Actinides: the Periodic System’s f Electron Transition Metal Series, in Plutonium 1970 and Other Actinides (AIME, New York, 1970)
2. 1705.00846v1 . Liu . Min . Xu . Yuanji . Hu . Danqing . Fu . Zhaoming . Tong . Ninghua . Chen . Xiangrong . Cheng . Jinguang . Xie . Wenhui . Yang . Yi-feng . Symmetry-enforced heavy-fermion physics in the quadruple-perovskite CaCu3Ir4O12 . 2017 .