Hill limit (solid-state) (original) (raw)

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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 {\displaystyle 4f} {\displaystyle 4f} or 5 f {\displaystyle 5f} {\displaystyle 5f} 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 {\displaystyle r_{H}} {\displaystyle r_{H}} is defined as twice the radius of the f {\displaystyle f} {\displaystyle 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 {\displaystyle f} {\displaystyle 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.

  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. ^ Liu, Min; Xu, Yuanji; Hu, Danqing; Fu, Zhaoming; Tong, Ninghua; Chen, Xiangrong; Cheng, Jinguang; Xie, Wenhui; Yang, Yi-feng (2017). "Symmetry-enforced heavy-fermion physics in the quadruple-perovskite CaCu3Ir4O12". arXiv:1705.00846v1.