ICTP2012: Innovations in Strongly Correlated Electronic Systems

Kristjan Haule (Center for Materials Theory, Rutgers University, USA)

Physics of Hunds metals and its relevance for Ruthenates and Iron pnictides and Chalcogenides.

Blogged by Natasha Perkins

Kristjan Haule started with acknowledging collaborators.

In the standard theory of solids electrons are well described wave ( quasiparticles) – Bloch theory. This is the good starting point for numerical calculations. For example, one can make  very good estimations of the gaps in semiconductors.

The problem of standard theory in correlated metals  comes from the fact that we do not  know which part of  electrons is localized and  which part  of electrons is itinerant.  Electrons have dual nature.

It is very challenging to deal with systems which are partly localized and partly itinerant. Our main focus is in understanding the electronic structure of complex correlated materials. We try to understand experiments – optics, ARPES, STM. We also developing DMFT as a computational tool.

Our workhorse is the DMFT. I do not know how many of you are familiar with that, so I briefly overview the technique.  The basic is – one spin is interacting with Weiss mean field. Details can be learned from RMP 2006. The DMFT is exact in the limit of large dimensionality. IN DMFT the special fluctuations are ignored. They can be partially taken into account in the cluster DMFT, but even one site DMFT often gives good description of systems with correlated electrons.

The simple test of the DMFT is to study the molecular hydrogen. When we pool apart the molecule, we should recover to H2 ions. This is in fact a nontrivial problem, and many numerical approaches have big difficulty in doing this. For example, HF fails, LDA fails, but DMFT captures exact atomic limit accurate at large R.

 Some people argue that DMFT does not work well. I will convince you that this is wrong. It is important to take local things correctly which we can do in DMFT.  

Piers asks about the symmetry. Cristjan answers that good choice of local symmetry help producing good results. You solve the HF first, look for the local symmetry, and then add correlations. 

 Next, Cristjan presents basic equations of the DMFT: Baym-Kadanoff functional, HF+DMFT approximation, LDA+DMFT approximation. He also discusses the double counting problem.

Next question is from Andy about the sum rules. Can you satisfy them by DMFT.

 Nest, let us discuss Hund’s coupling in impurities.

Old experiments on Kondo problem- magnetic impurities. High spin due to Hunds couplings. It is difficult to screen it, 1973 paper by Okada and Yosida  (Progress of theoretical physics) .  Having Hund’s coupling or  not having it make a huge difference. This paper was forgotten for many years  but its importance became obvious after discovering of pnictides.  Because otherwise how can we understand strong correlations in d5 systems.

Hund is important in understanding of correlation in itinerant metals. Fe has  one electron more than half-filled case, and Ru has one electrons less. Hubbard U is not the only relevant parameter. The Hund bring correlation in these systems.

Andrey: can you say a couple of words how you calculate local susceptibility in the presence of the Hund’s coupling? Cr.: I have to be careful with my answer. The local approximation in DMFT is done in real space. But of course, it will not be local in the band picture.

In order to get some insights in the role of Hund’s coupling, let us start with half-filed case. N=5. When you add one electron, you got a double occupancy. You have much less number of paths for screening. This leads to orbital and spin blocking of electron transport.

Next, let us discuss the phase diagram of 3 band Hubbard model. It turns out that the role of Hund’s coupling varies significantly with the number of electrons ( paper by L. de Medici).

At half-filling  orbital degrees of freedom are frozen. As orbital fluctuations are blocked, and you have only spin fluctuations.Now you switch spin-orbit coupling. This will allow orbital fluctuations.

We can compute orbital and spin susceptibilities. Orbital fluctuations are substantial away from half-filling, while spin fluctuations are maximum at half-filling.

 Let us go to specific materials.

Sr2RuO4. If there is no JH, you have small mass enhancement and it is the same for all orbitals. Once you switch JH, you have orbital differentiation. You would think that may be you can explain it just by U, but if you do it you will get a wrong trend. If you look to the coherence T, you will see that xy orbital has much lower coherence T compared with yz, zx orbitals.

There is a discussion between H.Kee and Cristijan  about the role of eg orbitals, pnictides vs ruthenates.

 If you look to 2 particle quantities, coherence temperature is even smaller.

 Few words about transport – huge anisotropy in optics  due to combination of orbital differentiation and matrix elements.

Very quickly about optics of Hunds’ metal.

 In Hubbard system you have Drude peak and Hubbard bands. In pnictides, there is a redistribution of weight with energy scale of JH.   The incoherent regime is very pronounced. There are sub-unitary powerlaws over an intermediate T and intermediate frequencies.

Very slow spin fluctuations but fast orbital fluctuations coupled to each other with leads to apparent powerlaws. DMFT can get powerlaws at very in self energy.

Question: what makes mass anisotropic? The answer is the crystal field. The orbital with occupation close to unity is the heaviest.

Andy: the band renormalization in pnictides and ruthenates are very different. Can you distinguish this by DMFT? Local in the band picture and local in the direct space is not the same thing. Self-energy in the band representation is very different from the self-energy in local representation.

YBK: What is the good way to estimate JH?

Answer: RPA is the standard way. It turns out that JH is not screened much compared with U. The ionic value is very close to the band value. Known for many years, starting with Sawadsky paper.