Electronic Structure of Strongly Correlated Systems

The article reviews the rich phenomena of metal-insulator transitions, anomalous metalicity, taking as examples iron and titanium oxides. The diverse phenomena include strong spin and orbital fluctuations, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. Another important phenomena presented in the article is a valence fluctuation which occur often in rare-earth compounds. We consider some Ce, Sm, Eu, Tm, and Yb compounds such as Ce, Sm and Tm monochalcogenides, Sm and Yb borides, mixed-valent and charge-ordered Sm, Eu and Yb pnictides and chalcogenides R4X3 and R3X4 (R = Sm, Eu, Yb; X = As, Sb, Bi), intermediate-valence YbInCu4 and heavy-fermion compounds YbMCu4 (M = Cu, Ag, Au, Pd). Issues addressed include the nature of the electronic ground states, the metal-insulator transition, the electronic and magnetic structures. The discussion includes key experiments, such as optical and magneto-optical spectroscopic measurements, x-ray photoemission and x-ray absorption, bremsstrahlung isochromat spectroscopy measurements as well as x-ray magnetic circular dichroism.


Atomic
• Local atomic coulomb and exchange integrals are central • Hunds rules for the Ground state -Maximize total spin-Maximize total angular momentum-total angular momentum J =L-S<1/2 filled shell , J=L+S for >1/2 filled shell • Mostly magnetic ground states Plot of the orbital volume /Wigner sites volume of the elemental solid for rare Earth 4f's, actinide 5f's, transition metal 3d's,4d'sand 5d's In compounds the ratio will be strongly reduced because the Element is "diluted" by other components Van der Marel et al PRB 37, (1988)

Elfimov unpublished
What would a mean field theory give you?
Note that there is no spectral weight transfer and a gap closing with doping From half filled. Both opposite to the real situation. The gap Closing is due to the mean field nature.

Dynamic spectral weight transfer
• For finite hoping i.e. U>W but t finite even more weight is transferred from the upper to the lower Hubbard band. This is rather counter intuitive since for increasing t we would have expected to go towards the independent particle limit. However this seems to happen in a rather strange way . The derivative of the low energy spectral weight As a function of doping and the hoping integral t Showing the divergent behavior with t close to zero doping What do we mean by the states below and above the chemical potential The eigenstates of the system with one electron removed or one electron added respectively i.e Photoelectron and inverse photoelectron spectroscopy Photo and inverse Photo electron spectra of the rare earth Metals (Lang and Baer (1984) We note that for Cu metal with a full 3d band in the ground state one particle theory works well to describe the one electron removal spectrum as in photoelectron spectroscopy this is because a single d hole has no other d holes to correlated with. So even if the on site d-d coulomb repulsion is very large there is no phase space for correlation.
The strength of the d-d coulomb interaction is evident if we look at the Auger spectrum which probes the states of the system if two electrons are removed from the same atom If the d band had not been full as in Ni metal we would have noticed the effect of d-d coulomb interaction already in the photoemission spectrum as we will see. More formal from Slater " Quantum theory of Atomic structure chapter 13 and appendix 20 One electron wave function We need to calculate rt g ij Where I,j,r,t label the quantum Numbers of the occupied states and we sum over all the occupied states in the total wave function The d-d coulomb interaction terms contain density -density like integrals, spin dependent exchange integrals and off diagonal coulomb integrals i.e. Where n,n' m,m' are all different. The monopole like coulomb integrals determine the average coulomb interaction between d electrons and basically are what we often call the Hubbard U. This monopole integral is strongly reduced In polarizable surroundings as we discussed above. Other integrals contribute to the multiplet structure dependent on exactly which orbitals and spin states are occupied. There are three relevant coulomb integrals called the Slater integrals; The B and C Racah parameters are close to the free ion values and can be carried over From tabulated gas phase spectroscopy data. " Moores tables" They are hardly reduced in A polarizable medium since they do not involve changing the number of electrons on an ion.