We consider the ground state magnetic phase diagram of the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping in terms of electronic density and interaction.We treat commensurate ferro-and antiferromagnetic, as well as incommensurate (spiral) magnetic phases. The first-order magnetic transitions with changing chemical potential, resulting in a phase separation (PS) in terms of density, are found between ferromagnetic, antiferromagnetic and spiral magnetic phases. We argue that the account of PS has a dramatic influence on the phase diagram in the vicinity of half-filling. The results imply possible interpretation of the unusual behavior of magnetic properties of one-layer cuprates in terms of PS between collinear and spiral magnetic phases. The relation of the results obtained to the magnetic properties of ruthenates is also discussed.PACS numbers:

The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.

The investigation of the ground magnetic state of the single band Hubbard model for already more than a half century has been an important and topical fun damental problem. In recent decades, the case of two dimensional lattices closely related to the problem of high temperature superconductivity has been intensely studied. Conventionally, the ground state for the bipartite lattices is a Néel antiferromagnetic (AFM) insulator [1,2].The types of instability of the antiferromagnetic state in the presence of doping or the finite next near est neighbor hopping integral have still been incom pletely revealed. According to the classical work by Nagaoka [1], when one charge carrier is added, the ground state on the bipartite lattice is the saturated fer romagnetic (FM) one. This statement can also be con sidered as a reasonable hypothesis in the case of finite doping [1,3,4].Scenarios of the possible doping induced magnetic ordering include the phase separation of different types: to the ferromagnetic and antiferromagnetic phases [5] or the phase of the superconducting elec tron liquid and the Néel antiferromagnetic phase [6]. An alternative scenario is the formation of the spiral magnetic state. It was considered within different approaches: the analysis of the momentum depen dence of the generalized static magnetic susceptibility for the bare spectrum [7], the Hartree-Fock approxi mation (small and moderate U/W values, where U is the parameter of the Coulomb repulsion and W is the bandwidth) [8,9], and the t-J model (large U/W val ues) [10].Incommensurate structures are observed in doped high temperature superconducting cuprates as the dynamic magnetic order [11], in the layered cerium based systems [12], and in iron based high tempera ture superconductors [13]. In addition, the consider ably enhanced incommensurate magnetic fluctuations are observed in strontium ruthenates at low tempera tures [14] (see discussion in [9,15,16]).The study of the magnetic phase diagram of the two dimensional Hubbard model taking into account the electron transfer only between the nearest neigh bors (t' = 0, where t(t') is the integral of the transfer between the nearest (next nearest) neighbors) within the Hartree-Fock approximation predicts that the spiral magnetic states are implemented in a wide range of parameters, especially at moderate values U Շ W [17]. It was shown in [9] that the inclusion of the next nearest neighbor electron transfer (t' ≠ 0) into the Hamiltonian considerably changes the magnetic phase diagram of the ground state. The results obtained are in qualitative agreement with the experi mental data for the magnetic structure of the layered high temperature superconducting cuprates in the case of low doping (there are considerable quantitative discrepancies) [18].The effect of the electron correlations on the stabil ity of the spiral magnetic states using the slave boson method was considered in [19]. The phase diagram of the Hubbard model was built in the nearest neighbor The formation of the spiral magnetic order ...

The ground-state magnetic phase diagram (including collinear and spiral states) of the single-band Hubbard model for the face-centered cubic lattice and related metal-insulator transition (MIT) are investigated within the slave-boson approach by Kotliar and Ruckenstein. The correlation-induced electron spectrum narrowing and a comparison with a generalized Hartree-Fock approximation allow one to estimate the strength of correlation effects. This, as well as the MIT scenario, depends dramatically on the ratio of the next-nearest and nearest electron hopping integrals [Formula: see text]. In contrast with metallic state, possessing substantial band narrowing, insulator one is only weakly correlated. The magnetic (Slater) scenario of MIT is found to be superior over the Mott one. Unlike simple and body-centered cubic lattices, MIT is the first order transition (discontinuous) for most [Formula: see text]. The insulator state is type-II or type-III antiferromagnet, and the metallic state is spin-spiral, collinear antiferromagnet or paramagnet depending on [Formula: see text]. The picture of magnetic ordering is compared with that in the standard localized-electron (Heisenberg) model.

The metal-insulator transition (MIT) for the square, simple cubic, and body-centered cubic lattices is investigated within the t-t ′ Hubbard model at half-filling by using both the generalized for the case of spiral order Hartree-Fock approximation (HFA) and Kotliar-Ruckenstein slave-boson approach. It turns out that magnetic scenario of MIT becomes superior over non-magnetic one. The electron correlations lead to some suppression of the spiral phases in comparison with HFA. We found the presence of metallic antiferromagnetic (spiral) phase in the case of three-dimensional lattices.