Krzysztof Kucab

Magnetic ordering of itinerant systems in modified CPA approximation

Abstract We will analyze the itinerant model for ferromagnetism with both single-site and two-site electron correlations. We will include band degeneration into the model. This will allow us to consider the on-site exchange interactions in the Hamiltonian. The modified Hartree–Fock approximation for the two-site interactions will be used. This approximation will give the relative one spin band broadening with respect to the other, in addition to the shift in position of majority and minority spin bands. Next, we will use the coherent potential approximation technique (CPA) with two self-energies. One will describe the on-site correlation and the second one the inter-site correlation. We will separate from these self-energies, the linear terms arising from Hartree–Fock approximation which will be applied to both; the on-site and inter-site interactions. These terms will contribute to the effective molecular field and the remaining ones (non-linear) will contribute to the correlation factors. The Green function technique and CPA decoupling will allow for the change in the shape of spin bands, which has been described by the correlation factors and which will decrease the kinetic energy of the system. The gain in kinetic energy due to the on-site and inter-site correlation factors will drive the ferromagnetism and significantly reduce the effective Hartree field necessary to create this ordering.

Competition between superconductivity and antiferromagnetism in the extended Hubbard model

We investigate a mean-field theory of the extended Hubbard model for the coexistence of antiferromagnetism (AF) and superconductivity (SC) in high-temperature homogeneous superconductive materials. We calculate the ordering parameter and the critical temperature as a function of filling. It is concluded that the superconducting state is destroyed when the antiferromagnetic state develops. For weak Coulomb correlation we show that the superconducting d-wave ordering parameter, which by itself has a maximum in the limit of a half-filled Hubbard band, goes to zero in the presence of antiferromagnetic ordering. Our phase diagram of antiferromagnetic and d-wave superconductivity critical temperatures as a function of filling resembles the experimental evidence.

Appearance of antiferromagnetism and superconductivity in superconducting cuprates

Abstract We represent the superconducting ceramic compounds by the single band extended Hubbard model. We use this model for solving the simultaneous presence of antiferromagnetism and the d -wave superconductivity in the Hartree–Fock (H–F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U . The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d -wave superconductivity away from the half filled point reducing its occupation range approximately to the experimental range in the YBaCuO compound. The CP approximation used for the Coulomb repulsion is justified by the large ratio of Coulomb repulsion to the effective width of perturbed density of states being reduced by the hopping interaction. The experimentally observed fast disappearance of antiferromagnetism is supported in calculations by the relatively large value of the total width of unperturbed density of states and the high values of the hopping interaction. It is shown that our model is capable of describing the electron doped compounds as well.

Antiferromagnetic ordering of itinerant systems in modified mean-field theory

Abstract This is an analysis of the itinerant model for antiferromagnetism, in which is included both on-site and inter-site electron correlations. We also consider the band degeneration, which brings into the Hamiltonian the on-site exchange interactions. The Green function technique is used and the coherent potential approximation (CPA) decoupling for the on-site Coulomb repulsion. This decoupling combined with the modified Hartree–Fock approximation for the inter-site interactions generates the change in shape of the spin bands with growing interaction constants, which is described by the correlation factors and which decreases the kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism. The on-site and inter-site interactions act together towards the antiferromagnetism. Their cooperation decreases the interaction constants required for the antiferromagnetic ordering. This new approach allows for the antiferromagnetic instability in the purely itinerant model at the half-filling in the split band limit. This situation describes the high temperature superconducting cuprates.

Coexistence of ferromagnetism and superconductivity: The role of kinetic interactions, kinetic correlations, and external pressure

Abstract We use the Hubbard type model to describe the coexistence between superconductivity (SC) and ferromagnetism (F). Our Hamiltonian contains single-site and two-site interactions. All inter-site interactions will have included the inter-site kinetic correlation: 〈 c i σ + c j σ 〉 within the Hartree–Fock approximation. To obtain the SC transition temperature T SC and Curie temperature T C we use the Green’s functions method. The numerical results show that the singlet SC is eliminated by F, but the triplet SC is either enhanced or depleted by F, depending on the carrier concentration and direction of a superconducting spin pair with respect to magnetization. The kinetic correlation is capable of creating superconductivity. We find that the ferromagnetism created by change of the bandwidth can coexist with singlet superconductivity. In the case of triplet superconductivity the ferromagnetism creates different critical SC temperatures for the A 1 and A 2 phase (the pair’s spin parallel and antiparallel to magnetization, respectively).

Energy Harvesting in the Nonlinear Piezoelastic Systems Driven by Harmonic Excitations with Asymmetrical Shape of the Potential Energy

We examine the influence of potential energy asymmetry on the power generated by energy harvesting system. We present results for the system consisting of two masses (magnets) attached to piezoelastic oscillators which vibrate in the magnetic field produced by the magnets attached directly to the harvesting device. The nonlinearity of the system is achieved by the variable strength of the magnetic fields produced by the static magnets. We additionally examine the influence of disproportion between piezoelastic beams stiffness, which is described by the mistuning parameter.

Band Magnetism with Inter-Site Correlations and Interactions

We introduce the Hamiltonian to describe narrow band electrons. The physics of driving forces towards ferromagnetism is re-examined. Using different approximations it has been shown that the magnetic moments created by inter-site interaction and inter-site kinetic correlation decrease quickly with temperature. As a result of these interactions and the realistic density of states (DOS) the Curie temperatures calculated after fitting magnetic moments to their low temperature values are realistic. In the past the Curie temperatures calculated using only the on-site interaction were much higher than the experimental temperatures.

Magnetic ordering of itinerant systems in modified mean field theory: antiferromagnetism

Abstract We analyze the itinerant model for antiferromagnetism, which was developed previously by Plischke, Mattis, Brouers and Mizia. In this model we include both; single-site and two-site electron correlations. Additionally, including band degeneration into the model allows for considering intra-atomic exchange interactions in the Hamiltonian. The modified Hartree–Fock approximation for the two-site interactions is used. This approximation gives the spin band narrowing, which is the same for both spin directions and affects the possibility of antiferromagnetic ordering. We use the Green function technique and CPA decoupling. This allows for the change in shape of the spin bands, described by the correlation factors, which decreases the kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism.