LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS: Fourth Training Course in the Physics of Correlated Electron Systems and High -Tc Superconductors
527(2000); http://dx.doi.org/10.1063/1.1309171View Description Hide Description
The aim of these lectures is to describe theoretical ideas concerning spin-polaron scenario for the charged excitations in a two-dimensional 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 spin-polaron picture. As the presented spin-polaron concept gives a rather simple description of the important lowest excitation band (even in mean-field 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.
527(2000); http://dx.doi.org/10.1063/1.1309172View Description Hide Description
Ferromagnetism 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 single-band Hubbard model is considered a good starting point. It poses a highly non-trivial many-body problem. Basic concepts and methods of many-body 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 Hubbard-Hamiltonian 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 many-body problem. Examples are the zero-bandwidth limit, the strong coupling behavior of the spectral density, weak coupling perturbational treatments, and high-energy expansions. We try a systematic improvement in the evaluation of the Hubbard-Hamiltonian by a series of analytic approximations fulfilling certain sum rules of the spectral density and the above-mentioned exact limiting cases (Sect. III). Starting from two-pole 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 Quantum-Monte Carlo calculations for infinite-dimensional 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 so-called s-f 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 Kondo-lattice and the double-exchange model. As a typical consequence of the s-f exchange a new quasiparticle appears which is called the magnetic polaron. It can be calculated exactly for a non-trivial special case. A selfenergy approach combined with a modified RKKY-theory is proposed to determine selfconsistently the electronic and the magnetic properties of the exchange-coupled s and f electrons.
527(2000); http://dx.doi.org/10.1063/1.1309173View Description Hide Description
We 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 spin-orbital 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 low-spin and high-spin 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 G-AF or to A-AF 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 A-AF phase, with the orbital order stabilized additionally by the Jahn-Teller 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 t-J model, and a large redistribution of spectral weight with respect to mean-field treatments. Finally, we point out some open problems in the present understanding of doped manganites.