Itinerant Electron Model Research Articles

Antiferromagnetism in the exact ground state of the half-filled Hubbard model on the complete bipartite graph

As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph $\L={\cal A}\cup{\cal B}$ with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal B}$). In this paper we analytically find the {\it exact} ground state for $N_{A}=N_{B}=N$ at half filling for any $N$; the repulsion has a maximum at a critical $N$-dependent value of the on-site Hubbard $U$. The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for $N \ra \inf$. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero $U$ even in the thermodynamic limit. We are aware of no previous explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.

Segregation in the Falicov--Kimball Model

The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov-Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov-Kimball model, this corresponds to having a single `compact' domain that has no heavy particles.

Long-Range Orders in Models of Itinerant Electrons Interacting with Heavy Quantum Fields

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on Zd, d \ 2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the ‘‘Ising spins’’ are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to p. We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed.

EPR of a fullerene-molecule-derived paramagnetic center as a mesoscopic conducting object

Discussion of theg-factor value of fullerene is based on the model of itinerant electrons restricted to the surface of the fullerene molecule C60. The Ag shift, i.e., the difference between the experimentalg-factor and theg-factor of free electron Δg = g − 2.0023 for C60−1 is negative as for a very small metallic conducting particle.g-factor value is proportional to the interaction between itinerant electrons in the conduction band, thus the Δg is negative for C60−1 and C60−3 having less than half filled conduction band, while Δg is positive for C60+ where the conduction band is almost filled.

Theoretical approach to the Curie temperature shift in FM1/NM/FM2/SUB (ferromagnetic metal 1/nonmagnetic metal/ferromagnetic metal 2/substrate) systems

An itinerant-electron model is proposed for investigating the Curie temperature shift in indirectly coupled itinerant ferromagnetic metal/nonmagnetic metal/ferromagnetic metal (FM2)/substrate structures. The Coulomb correlation between the electrons in the ferromagnetic metal is treated by using the spectral density approach. The magnetic susceptibility is used to determine the Curie temperature shift due to the interlayer exchange coupling. The relation between the Curie temperature shift and the interlayer exchange coupling is studied. It shows that the Curie temperature shift is related to the strength of the interlayer exchange coupling due to FM2 sublayers other than that of the whole system at high temperature. Good agreements with experiments are obtained.

Volume expansion and Curie temperature enhancement in rare earth–iron based nitrides with TbCu7 structure

Abstract In the present paper, a study of the effect of the volume change on the Curie temperature of R–Fe–N and R–Fe–Ti–N compounds with TbCu 7 structure has been performed. Our results indicate that the relationship between dln T C /dln V and the Curie temperature T C in rare earth –iron based nitrides with TbCu 7 structure can be well described in terms of the itinerant-electron model formalism.

Volume expansion and Curie temperature enhancement in R2Fe17Nx compounds

Abstract In the present paper a study of the effect of the volume change on the Curie temperature of R 2 Fe 17 N x compounds has been performed. Our results indicate that the relationship between dln T C /dln V and the Curie temperature T C in R 2 Fe 17 N x compounds can be well described in terms of the itinerant-electron model formalism.

Magnetovolume properties of Y2Fe17−xMx alloys (M=Si or Al)

Abstract The temperature dependences of the ac susceptibility under high pressure and the lattice parameters and the linear thermal expansion coefficients have been studied for Y2Fe17, Y2Fe15.3Si1.7 and Y2Fe15.3Al1.7. A large negative pressure shift of the Curie temperature TC and a large positive spontaneous magnetostriction below TC have been observed. A correlation between TC and dTC/dP values for these alloys was not found. The existence of a noncollinear magnetic state in Y2Fe17 under high pressure has been confirmed. The obtained results are qualitatively analyzed with both the localized moments model and the itinerant electron model.

Volume expansion and Curie temperature enhancement in R 3(Fe, M) 29 (M=Mo and V) and their nitrides

In the present paper, based on the investigation of the structure and magnetic properties of R 3(Fe, M) 29 (M=Mo and V) and their nitrides, a study on the effect of the volume change due to the nitrogenation on the Curie temperature of these compounds has been performed. The (d ln T C)/(d ln V) values were derived by comparing the change of the Curie temperature and volume before and after nitrogenation. Our results indicate that the relationship between (d ln T C)/(d ln V) and Curie temperature T C agrees with an itinerant electron model formalism.

Ferromagnetism and a temperature-driven reorientation transition in thin itinerant-electron films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.

Anomalous magnetic properties of cerium ions in the compounds (R = Tb, Dy)

The lattice parameters and spontaneous magnetizations of the pseudobinary compounds (R = Tb, Dy) are reported. The analysis of these results revealed the mutability of the Ce 4f ferromagnetism. The change of the degree of delocalization of the Ce 4f electron is used to analyse the changes of the lattice parameter and the spontaneous magnetic moment. A metamagnetic phase transition can be observed for each of the systems investigated, , when the Ce concentration x is about 0.5. The critical phase field increases with the Ce concentration, and the itinerant-electron model has been applied to analyse the tendency towards change of the critical phase field with x.

The Electronic Structure and the Fermi Surface of .ALPHA.-Cerium.

On the basis of the itinerant 4f electron model, the electronic structure is calculated for α-Ce by a relativistic linear augmented-plane-wave method. The Fermi surface is found to consist of small electron and hole pockets as well as the multiply-connected hole sheet. The multiply-connected hole sheet holds no open orbit, and this result is not inconsistent with the recent experimental result for the high-field magnetoresistance.

Optical studies of nanoscale materials incorporated in the space of zeolite crystals

Optical spectroscopy is used for the characterization of the quantum electronic state of nanoscale materials incorporated in zeolite crystals. Alkali metal clusters generated in zeolite exhibit interesting phenomena in optical properties as well as magnetic ones. Potassium clusters incorporated in zeolite LTA have shown ferromagnetism at low temperatures. The origin of the ferromagnetism was explained by the itinerant electron model. The infrared spectrum and magnetization curves, however, suggest that the itinerant electron model is not applicable to the ferromagnetism. Magnetic properties are interpreted based on the model of ferrimagnetism. Polarized micro-optical spectroscopy suggests the possibility of the one-dimensional array of potassium clusters in zeolite MOR single crystal

Thermodynamic Quantities and Defect Structure of La0.6Sr0.4Co1−yFeyO3−δ(y=0–0.6) from High-Temperature Coulometric Titration Experiments

The partial energies and entropies of O2in perovskite-type oxides La0.6Sr0.4Co1−yFeyO3−δ(y=0, 0.1, 0.25, 0.4, 0.6) were determined as a function of nonstoichiometryδby coulometric titration of oxygen in the temperature range 650–950°C. An absolute reference value ofδwas obtained by thermogravimetry in air. The nonstoichiometry at a given oxygen pressure and temperature decreases with iron contenty. At low nonstoichiometries the oxygen chemical potential decreases withδ. The observed behavior can be interpreted by assuming random distribution of oxygen vacancies, an electronic structure with both localized donor states on Fe, and a partially filled itinerant electron band, of which the density of states at the Fermi level scales with the Co content. The energy of the Fe states is close to the energy at the Fermi level in the conduction band. The observed trends of the thermodynamic quantities can be interpreted in terms of the itinerant electron model only when the iron content is small. At high values ofδthe chemical potential of O2becomes constant, indicating partial decomposition of the perovskite phase. The maximum value ofδat which the compositions are single-phase increases with temperature.

Ground states and low-temperature phases of itinerant electrons interacting with classical fields: A review of rigorous results

We review, from a unified point of view, a general class of models of itinerant electrons interacting with classical fields. Applications to the static Holstein, Kondo, and Hubbard models are discussed. The ground state structure of the classical field is investigated when the electron band is half-filled. Some of the results are also valid when there is a Hubbard interaction between spin up and spin down electrons. It is found that the ground states are either homogeneous or period two Néel configurations, depending on the geometry of the lattice and on the magnetic fluxes present in the system. In the specific models, Néel configurations correspond to Peierls, magnetic or superconducting instabilities of the homogeneous state. The effect of small thermal and quantum fluctuations of the classical fields are reviewed in the context of the Holstein model. Many of the results described here originate from the work of Elliott Lieb and collaborators.

Periodic ground states in simple models of itinerant fermions interacting with classical fields

A model of itinerant lattice electrons interacting with classical nuclei is studied. The electrons can interact between themselves via a Hubbard on-site term. It is shown that, in the ground state of the half-filled band, the nuclei form a periodic crystal. More precisely for a cubic lattice they form a chessboard state under some appropriate condition on the hopping matrix. This generalizes known results previously obtained for the Falicov-Kimball model. The case where fermions are replaced by hard-core bosons in this later model is also discussed. More generally models of fermions interacting with classical scalar or vector fields are briefly considered. The mathematical technique used is “reflection positivity” adapted to the case of Fermi statistics.

Itinerant-electron ferrimagnetism of transition-metal compounds

The onset of ferrimagnetic spin moment is investigated on the itinerant-electron model for compounds composed of magnetic and non-magnetic transition-metal atoms. The d-states of non-magnetic atoms mix with those of the magnetic atoms. In the magnetic state the strength of the d-d mixing is different in the majority and minority spin bands and then the magnetic moment on non-magnetic atom is induced. By using a two-band model, the induced moment on the non-magnetic atoms is shown explicitly to align in either the parallel or antiparallel direction to that of the magnetic atoms, depending on the value of intra-atomic Coulomb integral on the magnetic atom.

Detailed ferromagnetic resonance study of amorphous Fe-rich alloys. I: re-entrant behaviour and low-lying magnetic excitations

Results of exhaustive ferromagnetic resonance (FMR) measurements performed on amorphous (a-) alloys at temperatures ranging from 10 to 500 K are presented and discussed in the light of existing theoretical models. The peak-to peak FMR linewidth consists of two contributions: one originating from two-magnon and multiple-magnon scattering processes and the other arising from the Laundau - Lifshitz - Gilbert damping mechanism. for the alloys with , as in other re-entrant (RE) systems, increases exponentially as the temperature is lowered through the RE transition temperature . The Landé splitting factor is independent of both temperature and Co concentration, whereas the Gilbert damping parameter is temperature-independent but decreases with increasing x. For all the alloys in question, thermal demagnetization is mainly due to spin-wave (SW) excitations and the SW stiffness coefficient D renormalizes with temperature in accordance with the predictions of the itinerant-electron model. SW modes in the alloys with soften at and D possesses a reduced but finite value in the RE state. Competing interactions present in the parent alloy a- confine the direct exchange interactions (DEIs) to the nearest neighbours only and partial replacement of Fe with Co progressively tilts the balance in favour of ferromagnetic interactions between Fe spins with the result that DEIs now involve next-nearest neighbours too and the divergence in at low temperatures is completely suppressed for x > 4.

Fermi Surface of CeRu2within Local-Density Functional Theory

The Fermi surface is investigated for the heavy-electron compound CeRu 2 , which is known as a type-II superconductor exhibiting anomalous magnetic properties, on the basis of the itinerant-electron model for the 4 f electrons. The energy band structure is calculated by a relativistic linear augmented-plane-wave method with the exchange-correlation potential in the local-density approximation. The Fermi surface is found to consist of a set of six small hole pockets, a large multiply-connected hole sheet and a set of three complex electron sheets and a set of three small electron pockets. Recent experimental results for the de Haas-van Alphen effect are explained reasonably well in terms of the large hole sheet and the small electron pockets except for the cyclotron effective mass. It seems that many frequency branches may have been missed in the experiment. A nesting property of the Fermi surface is also investigated.

Spin polarization of valence band satellites of nickel

We have observed spin- and angle-resolved photoemission spectra of Ni(110) in the whole valence band region including so-called 6 eV, 9 eV and 13 eV satellites. It was found that the spin polarization of the satellites are well explained by the atomic model, while the 3d valence band widths in the majority and minority spin states are consistent with those expected by the itinerant electron model.