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Oxides are made of atoms, after all !


Oxides are made of atoms, after all !

Electronic properties of most solids can be accounted for by simplified theories treating electron-electron interactions "on the average". This is possible because the electrons populating the outermost shells (“conduction electrons”) of the atoms that make up the material “spread” throughout the solid, mostly avoiding coming too close to each other.

 

In some materials (named “strongly correlated”) however, like many transition metal oxides, this description fails because conduction electrons are more concentrated around the atoms, thus the mutual electrostatic repulsion they feel is bound to be more intense.

 

In this situation the specific electronic characteristics of the atoms are more likely to have an influence the properties of the material.
The intense repulsion, for example, is known to spoil metallic properties and can eventually lead to complete localization of the conduction electrons and to an insulating behaviour (Mott transition).

 

Hund’s rules are basic atomic properties that explain why electrons tend to distribute on all orbitals of a given shell, with their spin aligned. This owes to the fact that the mutual repulsion electrons feel on an atom depends on them being in the same or a different orbital and on their relative spin orientation.

 

Luca de’ Medici (LPS) with J. Mravlje and A. Georges (Ecole Polytechnique), have found (solving numerically a low-energy model with the dynamical mean-field theory, see Fig. 1) that Hund’s rules strongly influence the properties of correlated materials : they turn out to strongly promote or suppress the metallic behaviour, depending crucially on the number of conduction electrons.

 

They have also shown (using ab-initio electronic structure calculations with dynamical mean-field theory) that the classification that derives from this model analysis explains the main trends of many early transition-metal oxides (see Fig. 2), like the rarity of half-filled metallic oxides, the ubiquitous bad metallicity of Ru- and Cr- cubic oxides, and the record-high Néel temperature measured in SrTcO3 .

 

The fact that atomic properties like Hund’s rules are so influential on the metallicity of oxides comes as a surprise and this classification is expected to help clarify the behaviour of many other strongly correlated materials.

 

 

Figure 1 : Quasiparticle weight Z (a measure of the strength of correlations in the system, Z=1 for an uncorrelated system, Z=0 for a Mott insulator) of the Hubbard model for 3 degenerate bands of half-width D, as a function of the interaction strength U/D, and for different values of the Hund’s coupling J/U. The gray arrows indicate the effect of increasing Hund’s coupling. The three panels show results for 3 representative fillings of the conduction bands : one electron or one hole per atom (left panel, where metallic behaviour is promoted by Hund’s coupling), half-filling (right panel, where the Mott insulating state is favoured instead), all other fillings (central panel). Hund’s rules have a double, contrasting effect in this last situation (hence dubbed “Janus-faced”) : Z is lowered, but the Mott transition is disfavoured, inducing a strongly correlated bad metal for a large range of interaction strengths.

 

 
Figure 2 : Quasiparticle weight Z (color scale, dark color representing weak correlation, light color strong correlation and the black bars signalling the occurrence of a Mott insulating state), as a function of the interaction strength U/D for all fillings, of a 3-fold degenerate d-electron manifold, typically the conduction bands in early transition metal oxides. The Hund coupling here is J/U=0.15, a typical value in these materials. Compounds are placed at their filling and estimated interaction strength and shown (by ab-initio calculations) to nicely fit in this simple model scheme. Half-filled (n=3) compound are mainly insulators, singly filled (n=1,n=5) are good metals, Cr- and Ru- compounds (n=2,4) are typically strongly correlated bad-metals. SrTcO3 (T Neel ≈1000K) lies very close to the Mott transition, which is where highest Néel temperatures are expected.

 

References  :

 

L. de’ Medici, J. Mravlje and A. Georges, Janus-faced influence of Hund’s rule coupling in strongly correlated materials, Physical Review Letters 107, 256401(2011)

 

Contact  :

Luca de’ Medici : (demedici@lps.u-psud.fr)