LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS: Fourth Training Course in the Physics of Correlated Electron Systems and High Tc Superconductors

Theory of the spinpolaron for 2D antiferromagnets
View Description Hide DescriptionThe aim of these lectures is to describe theoretical ideas concerning spinpolaron scenario for the charged excitations in a twodimensional antiferromagnet in normal state. The distinctive feature of our approach consists in treating a local polaron (not a bare hole) as a zero approximation for a quasiparticle. Then we dress this excitation by antiferromagnetic spin waves. The realization of this concept in the framework of several models demonstrates that many unusual features may have a natural explanation through the spinpolaron picture. As the presented spinpolaron concept gives a rather simple description of the important lowest excitation band (even in meanfield approach) we strongly believe that in the near future this concept will be useful for theoretical investigations of such a phenomena as superconductivity and normal kinetic properties of HTSC and other strongly correlated systems.

Ferromagnetism and electronic correlations
View Description Hide DescriptionFerromagnetism belongs to the oldest phenomena in solid state physics being, however, even today not yet fully understood. The main shortcoming for an understanding of this basic phenomenon is the lack of a general, unified theory. The different types of magnetic materials need for their description rather different theoretical models, each of them with a fairly restricted range of validity. To avoid misunderstandings it is therefore recommendable to start the discussion with a simple but clear classification of magnetism and to address the respective theoretical models to the appropriate classes of materials (Sect. I). The most prominent models are inspected in detail in the following sections. For an at least qualitative description of ferromagnets with itinerant magnetic moments (bandferromagnets) the singleband Hubbard model is considered a good starting point. It poses a highly nontrivial manybody problem. Basic concepts and methods of manybody theory are therefore shortly introduced (Sect. II) as far as they are vital for the understanding of the following: Green functions, spectral densities, selfenergies, quasiparticles, quasiparticle densities of states, quasiparticle bandstructures, Starting with the HubbardHamiltonian and several exactly solvable limiting cases are discussed (Sect. II). The latter are important for the construction of reliable approaches to the not rigorously tractable manybody problem. Examples are the zerobandwidth limit, the strong coupling behavior of the spectral density, weak coupling perturbational treatments, and highenergy expansions. We try a systematic improvement in the evaluation of the HubbardHamiltonian by a series of analytic approximations fulfilling certain sum rules of the spectral density and the abovementioned exact limiting cases (Sect. III). Starting from twopole approaches (Hubbard I, spectral density approach (SDA), …) via different alloy analogies and some applications of dynamical mean field theory we come to a conclusion for a magnetic phase diagram. The calculated Curie temperatures are compared with numerically essentially exact, recent QuantumMonte Carlo calculations for infinitedimensional lattices. The role of physically decisive correlation functions, which lead to bandshifts and bandwidth corrections, and the quasiparticle damping on the stability of (ferro) magnetism is investigated. While the Hubbard model gives a frame for the itinerant moment systems the socalled sf model is used to describe magnetic materials (insulators, semiconductors, metals) which take their magnetic properties from localized moments. It traces back the characteristic features of these systems to an interband exchange interaction between localized magnetic electrons (f) and itinerant conduction electrons (s). It is in principle identical to the Kondolattice and the doubleexchange model. As a typical consequence of the sf exchange a new quasiparticle appears which is called the magnetic polaron. It can be calculated exactly for a nontrivial special case. A selfenergy approach combined with a modified RKKYtheory is proposed to determine selfconsistently the electronic and the magnetic properties of the exchangecoupled s and f electrons.

Magnetic and orbital ordering in cuprates and manganites
View Description Hide DescriptionWe address the role played by orbital degeneracy in strongly correlated transition metal compounds. The mechanisms of magnetic and orbital interactions due to double exchange (DE) and superexchange (SE) are presented. Specifically, we study the effective spinorbital models derived for the ions as in and for the ions as in for spins and respectively. The magnetic and orbital ordering in the undoped compounds is determined by the SE interactions that are inherently frustrated, carrying both antiferromagnetic (AF) and ferromagnetic (FM) channels due to lowspin and highspin excited states, respectively. As a result, the classical phase diagrams consist of several magnetic phases which all have different orbital ordering: either the same orbitals ( or ) are occupied, or two different linear combinations of orbitals stagger, leading either to GAF or to AAF order. These phases become unstable near orbital degeneracy, leading to a new mechanism of spin liquid. The model for ions in collosal magnetoresistance compounds provides an explanation of the observed AAF phase, with the orbital order stabilized additionally by the JahnTeller effect. Possible extensions of the model to the doped compounds are discussed both for the insulating polaronic regime and for the metallic phase. It is shown that the spin waves are well described by SE in the insulating regime, while they are explained by DE for degenerate orbitals in the metallic FM regime. Orbital excitations contribute to the hole dynamics in FM planes of characterized by new quasiparticles reminiscent of the tJ model, and a large redistribution of spectral weight with respect to meanfield treatments. Finally, we point out some open problems in the present understanding of doped manganites.