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The Role of Hund’s Coupling in Correlated Metals

Jernej Mravlje
p. 89

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1The electrons in atomic shells repel each other through the Coulomb force. When two electrons are placed in the same atomic orbital, the energetic cost of this repulsion is only partially compensated by the attraction of the electron towards the nucleus. The electronic configurations corresponding to the states where electrons are on average further apart are energetically favourable. The configurations found in the ground-state are those in which the electronic spins are maximally aligned. Such behaviour is dubbed Hund's rule coupling after Friedrich Hund who proposed it in 1925.

2What role does Hund’s coupling play in solids? In insulators, which resemble a set of isolated atoms, it is obviously important, as it specifies the size of the atomic magnetic moments. In metals, where Coulomb repulsion is insignificant, it has no effect. What role does it play in the intermediate case of correlated metals, e.g. transition-metal oxides such as ruthenates and recently discovered iron-based superconductors?

3Using the dynamic mean-field theory, Antoine Georges (Collège de France), Luca de’Medici (LPS Orsay) and I have shown that Hund’s coupling has two important effects. (i) The energetic cost of adding an electron is reduced whenever the outer-shell is not half-filled. This induces metallic behaviour. (ii) The other effect relates to degeneracy, which reduces as Hund’s coupling increases, except in the case of a single electron per shell. Weaker atomic degeneracy prevents certain electron transfers between atoms, causing their state to become less metallic. Like the Roman god Janus, Hund’s coupling has two faces, which are sometimes opposites. When the outer shell is filled with more than one electron, but is not yet half full, these two effects largely cancel: the effective repulsion reduces at the same time as the degeneracy. The resulting unusual metal is far from being an insulator, but has reduced kinetic energy. Iron-based superconductors and strontium ruthenates belong to this very interesting category.

4Realising the importance of Hund’s coupling has highlighted the consequences of atomic physics in metals which accounts for the systematic behaviour with the occupancy of the outer shell as the control parameter. In this classification the iron-based superconductors are akin to ruthenates which raises an interesting question: why do the latter not present high temperature superconductivity?

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Jernej Mravlje, « The Role of Hund’s Coupling in Correlated Metals », La lettre du Collège de France [En ligne], 7 | 2015, mis en ligne le 03 novembre 2015, consulté le 21 février 2017. URL :

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Jernej Mravlje

Lecturer, Physics of Condensed Matter (Prof. Antoine Georges)

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