Ferromagnetism in the degenerate Hubbard model

We study the ground state of the doubly degenerate Hubbard model in the strong coupling limit. For this limit, we obtain new exact results: when there are N ? 1 electrons, the ground state is ferromagnetic and there is a ferromagnetic orbital ordering; when the number of electrons is between N and 2N, the ground state is also ferromagnetic due to the intra-atomic Hund's coupling. For this second case, we give an estimate of the Curie temperature.     

Ferromagnetism in the Hubbard model on fcc-type lattices

The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges. Received: 6 August 1997 / Accepted: 20 August 1997     

Ferromagnetism and metal-insulator transition in the disordered Hubbard model

A detailed study of the paramagnetic to ferromagnetic phase transition in the one-band Hubbard model in the presence of binary-alloy disorder is presented. The influence of the disorder (with concentrations x and 1-x of the two alloy ions) on the Curie temperature T(c) is found to depend strongly on electron density n. While at high densities, n>x, the disorder always reduces T(c); at low densities, n相似文献   

Ferromagnetism in Hubbard model in many-electron operator representation

The Hubbard model for a metal with strong correlations is considered in the representation of many-electron X-operators. General self-consistent expressions are obtained for the one-particle Green function taking into account fluctuation corrections. The stability regions of the saturated and unsaturated ferromagnetism in the ground state on the n-U plane (n is the electron concentration and U is the Coulomb interaction parameter) are determined for various bare densities of states (semi-elliptic band and the square, cubic, and hypercubic lattices).     

Ferromagnetism in the two-dimensional Hubbard model with long-range hopping

The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t _ij ～ ? q ^Ri?Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q _c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.     

Ferromagnetism in the single-band Hubbard model: An exact high-temperature expansion

The first ten terms of the high-temperature expansion of the susceptibility of the single-band Hubbard model in the strong correlation limit are obtained for arbitrary electron density. The series is analyzed by ratio methods and Padé approximants. A critical temperature is found for 0.2 0.8; for > 1 further terms in the series are required.Supported in part by the National Research Council of Canada.     

Nagaoka Ferromagnetism in Two-Band Hubbard Model

In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.     

Ferromagnetism,spiral magnetic structures and phase separation in the two-dimensional Hubbard model

The quasistatic approximation and equation-of-motion decoupling for the electron Green's functions are applied to trace the effect of electronic dispersion and electron correlations on the ferromagnetism of two-dimensional itinerant-electron systems. It is found that next-nearest-neighbor hopping t′$t\prime$ is of crucial importance for ferromagnetism formation yielding the magnetic phase diagram which is strongly asymmetric with respect to half-filling. At small t′$t\prime$ in the vicinity of half-filling the ferromagnetic phase region is restricted by the spin-density wave instability, and far from half-filling by one-particle (spin-polaron) instability. At t′$t\prime$ close to t/2$t/2$ ferromagnetism is stabilized at moderate Hubbard U   due to substantial curvature of the Fermi surface which passes in the vicinity of the van Hove singularity points. The results obtained are of possible importance for high-_Tc$T_{\mathrm{c}}$ compounds and layered ruthenates.     

Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δ_cr = 0.407 for the SKA spin wave and of δ_cr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.     

Ferromagnetism in the Hubbard Model: A Constructive Approach

It is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. Here we describe our rigorous and constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid. We introduce a class of Hubbard models in any dimensions which are nonsingular in the sense that both the Coulomb interaction and the density of states (at the Fermi level) are finite. We then prove that the ground states of the models exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with our earlier results, the present work provides nonsingular models of itinerant electrons with only spin-independent interactions where low energy behaviors are proved to be that of a healthy ferromagnetic insulator.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δ_cr = 0.29 and we obtain an estimate of U_cr = 63 t for the critical coupling which is considerably better than the best estimate of U_cr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.     

Ferromagnetism in the Hubbard Model with a Gapless Nearly-Flat Band

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.     

Ferromagnetism in one-dimensional Hubbard model induced by the next-nearest-neighbor hopping at electron density 3/2

Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest- neighbor hopping amplitude tl tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the tl-U plane.     

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.