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Journal of the Magnetics Society of Japan

Ferromagnetism in Hubbard models for Quantum Atomic Wires

M. Ichimura, Koichi Kusakabe, Shinji Watanabe, T. Onogi

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.3379/jmsjmag.23.676

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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 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 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.