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arXiv:cond-mat/9802101 · Physical review. B, Condensed matter

Ferromagnetism in a Hubbard model for an atomic quantum wire: A realization of flat-band magnetism from even-membered rings

Ryotaro Arita, Kazuhiko Kuroki, Hideo Aoki, Akio Yajima, Masaru Tsukada, Satoshi Watanabe, Masahiko Ichimura, T. Onogi, Tomihiro Hashizume

Published Mar 15, 1998• 34 citations
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Abstract

We have examined as a Hubbard model on a chain of squares, which was as proposed by Yajima et al. as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a nonfrustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensifies, as the Hubbard $U$ is increased. The exact-diagonalization method is used to show that the critical value of $U$ is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band.

DOI
10.1103/physrevb.57.r6854

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We have examined as a Hubbard model on a chain of squares, which was as proposed by Yajima et al. as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a nonfrustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensifies, as the Hubbard UUU is increased. The exact-diagonalization method is used to show that the critical value of UUU is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band.
We examined the magnetic property of newly extended \ensuremath{\Delta}-chain Hubbard models which may be relevant to quantum atomic wires formed on solid surfaces. We rigorously show that the extended models exhibit so-called flat-band ferromagnetism, based on the Mielke-Tasaki theorem. Moreover, we numerically find that the ferromagnetic state is stable against some deviations from completely flat band, by using the exact diagonalization method. The present result will be also useful as a guiding principle to design magnetic materials that possibly display the flat-band ferromagnetism.
We have studied the magnetic properties of a certain class of Hubbard models proposed as models for quantum atomic wires with flat single-particle bands. These Hubbard models belong to a class of models to which Mielke-Tasaki theorem for flat-band ferromagnetism can be applied. We also found that the Mielke-Tasaki theorem is applicable in networks of quantum atomic wires. The present findings will be useful for producing flat-band ferromagnetism in quantum atomic wires and two dimensional networks.
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion U>UcU>{U}_{c}U>Uc​, where Uc{U}_{c}Uc​ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small Uc{U}_{c}Uc​, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion Uc{U}_{c}Uc​ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.
The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.
We examined a one-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping with up to 32 sites by means of the density-matrix renormalization-group method. The model has two energy bands and includes the flat-band model studied by Tasaki as a special case. The model with finite band dispersion is found to show metallic (saturated) ferromagnetism for a sufficiently strong interaction. No partially polarized ground state is found. The interaction necessary to realize a ferromagnetic ground state becomes weak when the electron density is decreased from the quarter-filling.
We investigate the magnetization of the ground state of the one-dimensional flat-band Hubbard model as a function of the electron filling, using exact diagonalization techniques. Our calculation shows that the systems with odd n holes added to half-filling bands for a sufficiently large U (the on-site Coulomb repulsion energy) have a saturated ferromagnetic ground state, which is nondegenerate except for the trivial spin degeneracy. Dependences of the critical value of U on the size and on λ (a parameter of the system) are also investigated. For all values of λ, it is found that the ground state is a saturated ferromagnetic state if U is sufficiently large. Moreover, we find that the critical U for the saturated ferromagnetic ground state is almost independent on the system size, at least, for the system near quarter-filling. These facts indicate that even if the system size go to infinity, the ferromagnetic ground state can be exist for a finite U .