We examine the orbital and magnetic order of the two orbital Hubbard model within dynamical mean field theory. The model describes the low energy physics of a partially filled $e_g$-band as can be found in some transition metal compounds. The model shows antiferromagnetic as well as ferromagnetic phases. For stabilizing ferromagnetism we find that Hund's coupling is particularly important. Quarter filling represents a very special situation in the phase diagram, where the coupling of spin, charge, and orbital degrees of freedom are involved. Exactly at quarter filling we find a metal insulator transition (MIT) between two almost fully polarized ferromagnetic states. This MIT can be tuned by changing the local interaction strength and seems to be a first order transition at zero temperature. Apart from these ferromagnetic states we were also able to stabilize antiferromagnetic and charge ordered phases at quarter filling, depending on the interaction parameters.

Orbital and magnetic order in the two-orbital Hubbard model

A general approach for the description of correlated hopping in infinite dimensions, which is based on an expansion over electron hopping around the atomic limit, is developed. Such an approach keeps the dynamical mean-field theory local ideology and allows one to calculate the thermodynamical functions. A grand-canonical potential functional and a $\ensuremath{\Phi}$-derivable theory that does not introduce the self-energy is proposed. As limiting cases the Falicov-Kimball model with correlated hopping and the model with broken bonds (``diluted'' conductor) are investigated, and the connection with the Blackman-Esterling-Berk coherent potential approximation approach in the theory of the binary alloy with off-diagonal disorder is considered.

Dynamical mean-field theory of correlated hopping: A rigorous local approach

We present a new method to calculate optical properties of strongly correlated systems. It is based on dynamical mean field theory and it uses as an input realistic electronic structure obtained by local density functional calculations. Numerically tractable equations for optical conductivity, which show a correct non-interacting limit, are derived. Illustration of the method is given by computing optical properties of the doped Mott insulator La_{1-x}Sr_xTiO_3.

Calculations of Optical Properties in Strongly Correlated Materials

In the present paper, we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction, which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum, we find energy gap width and criteria of metal-insulator transition.

Metal-insulator transition in a doubly orbitally degenerate model with correlated hopping

We analyze the Hubbard model with added hopping interaction within the full Hubbard III approximation In the Green's-function decoupling process, the intersite kinetic correlation functions are included This is an extension of our previous paper [G G\'orski and J Mizia, Phys Rev B 79, 064414 (2009)] in which the basic Hubbard model with the intersite kinetic correlations was analyzed in the framework of the coherent potential approximation (CPA) In the CPA method, the up-spin electrons propagated in the lattice of frozen down-spin electrons The full Hubbard III solution used now takes into account the itinerancy of down-spin electrons The combined effect of the hopping interaction and intersite kinetic correlation leaves the position of spin bands unaffected, but it deforms the density of states (DOS) of electrons, changing in this way the average electron energy It is the main driving force behind the ferromagnetism as opposed to the rigid shift of the entire band, which takes place in the conventional Stoner magnetism In the numerical calculations, we have used the bands with symmetrical DOS (semielliptic or bcc-like DOS) and also with asymmetrical DOS resembling the fcc DOS The spontaneous ferromagnetic transition was obtained under the combined action of the hopping interaction and the intersite correlation in the systems that contain even a moderately strong peak in the DOS, such as the bcc- and fcc-like DOS

Hubbard III approach with hopping interaction and intersite kinetic correlations

In the present paper the ground state of a double orbitally degenerate model at weak intra-atomic interaction is studied using the Green functions method. Beside the diagonal matrix elements of electron-electron interactions the model includes correlated hopping integrals and inter-atomic exchange interaction. The influence of orbital degeneracy with Hund's rule coupling, correlated hopping and inter-atomic direct exchange on the ferromagnetic ordering is investigated. The expressions for ground state energy and magnetization, the criterion of transition from paramagnetic to ferromagnetic ground state as functions of the model parameters are obtained. The obtained results are compared with some experimental data for magnetic materials.

Ground-state ferromagnetism in a doubly orbitally degenerate model

The electron correlations in narrow energy bands are examined within the framework of the Hubbard model, generalized by taking into account the correlated hopping of electrons Electronic conductivity and ferromagnetic ordering stabilization in the system with various forms of electronic density of states are studied The in∞uence of magnetic fleld, temperature and the form of density of states on concentration dependence of conductivity and magnetization is investigated The correlated hopping is shown to cause the electron{hole asymmetry of transport and ferromagnetic properties of narrow band materials

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Mott Transition, Ferromagnetism and Conductivity in the Generalized Hubbard Model

In this paper we study the ground state ferromagnetism in a doubly orbitally degenerate Hubbard model generalized by taking into account correlated hopping and inter-atomic exchange interaction. We find that an important role in the stabilization of ferromagnetism is played by the intra- and inter-atomic exchange interactions as well as correlated hopping, which allows us to describe the metallic paramagnetic-ferromagnetic transition with a realistic relationship between the above-mentioned exchange interactions. The expression for magnetization and the criterion of ferromagnetic ground state stability are derived. The obtained results are compared with some experimental data for magnetic materials.

Itinerant ferromagnetism of systems with double orbital degeneracy

The electron correlations in narrow energy bands are examined within the framework of the modied form of polar model. This model permits to analyze the effect of strong Coulomb correlation, inter-atomic exchange and correlated hopping of electrons and explain some peculiarities of the properties of narrow-band materials, namely the metal-insulator transition with an increase of temperature, nonlinear concentration dependence of Curie temperature and peculiarities of transport properties of electronic subsystem. Using a variant of generalized Hartree-Fock approximation, the single-electron Green’s function and quasi-particle energy spectrum of the model are calculated. Metal-insulator transition with the change of temperature is investigated in a system with correlated hopping. Processes of ferromagnetic ordering stabilization in the system with various forms of electronic DOS are studied. The static conductivity and effective spin-dependent masses of current carriers are calculated as a function of electron concentration at various DOS forms. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.

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L. Didukh

Papers

Metal-insulator transition in a doubly orbitally degenerate model with correlated hopping

Ground-state ferromagnetism in a doubly orbitally degenerate model

Mott Transition, Ferromagnetism and Conductivity in the Generalized Hubbard Model

Itinerant ferromagnetism of systems with double orbital degeneracy

Electron correlations in narrow energy bands: modified polar model approach