From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model

This is a self-contained review about ferromagnetism in the Hubbard model, which should be accessible to readers with various backgrounds who are new to the field. We describe Nagaoka's ferromagnetism and flat-band ferromagnetism in detail, giving all necessary backgrounds as well as complete (but elementary) mathematical proofs. By studying an intermediate model called long-range hopping model, we also demonstrate that there is indeed a deep relation between these two seemingly different approaches to ferromagnetism. We further discuss some attempts to go beyond these approaches. We briefly discuss recent rigorous example of ferromagnetism in the Hubbard model which has neither infinitely large parameters nor completely flat bands. We give preliminary discussions about possible experimental realizations of the (nearly-)flat-band ferromagnetism. Finally we focus on some theoretical attempts to understand metallic ferromagnetism. We discuss three artificial one-dimensional models in which the existence of metallic ferromagnetism can be easily proved.Comment: LaTeX2e, 72 pages, 17 epsf figures. Many minor corrections made in March 1998. This is the final version, which will appear in Prog. Theor. Phys. 99 (invited paper

Enhancement of ferromagnetism by p-wave Cooper pairing in superconducting ferromagnets

In superconducting ferromagnets for which the Curie temperature $T_{m}$ exceeds the superconducting transition temperature $T_{c}$, it was suggested that ferromagnetic spin fluctuations could lead to superconductivity with p-wave spin triplet Cooper pairing. Using the Stoner model of itinerant ferromagnetism, we study the feedback effect of the p-wave superconductivity on the ferromagnetism. Below $T_{c}$, the ferromagnetism is enhanced by the p-wave superconductivity. At zero temperature, the critical Stoner value for itinerant ferromagnetism is reduced by the strength of the p-wave pairing potential, and the magnetization increases correspondingly. More important, our results suggest that once Stoner ferromagnetism is established, $T_m$ is unlikely to ever be below $T_c$. For strong and weak ferromagnetism, three and two peaks in the temperature dependence of the specific heat are respectively predicted, the upper peak in the latter case corresponding to a first-order transition.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Gate-induced band ferromagnetism in an organic polymer

We propose that a chain of five-membered rings (polyaminotriazole) should be ferromagnetic with an appropriate doping that is envisaged to be feasible with an FET structure. The ferromagnetism is confirmed by a spin density functional calculation, which also shows that ferromagnetism survives the Peierls instability. We explain the magnetism in terms of Mielke and Tasaki's flat-band ferromagnetism with the Hubbard model. This opens a new possibility of band ferromagnetism in purely organic polymers.Comment: 4 pages, 7 figure

Enhanced Ferromagnetic Stability in Cu Doped Passivated GaN Nanowires

Density functional calculations are performed to investigate the room temperature ferromagnetism in GaN:Cu nanowires (NWs). Our results indicate that two Cu dopants are most stable when they are near each other. Compared to bulk GaN:Cu, we find that magnetization and ferromagnetism in Cu doped NWs is strongly enhanced because the band width of the Cu td band is reduced due to the 1D nature of the NW. The surface passivation is shown to be crucial to sustain the ferromagnetism in GaN:Cu NWs. These findings are in good agreement with experimental observations and indicate that ferromagnetism in this type of systems can be tuned by controlling the size or shape of the host materials.Comment: Nano Lett., ASAP Article, 10.1021/nl080261

Double Exchange Ferromagnetism in the Peierls Insulator State

We study the effects of opening of the band gap on the double exchange ferromagnetism. Applying the density-matrix renormalization group method and an analytical expansion from the dimer limit to the one-dimensional double exchange model, we demonstrate for a relevant region of the exchange coupling that, in the weak dimerization regime, the Peierls gap opens in the fully spin-polarized conduction band without affecting its ferromagnetism, whereas in the strong dimerization regime, the ferromagnetism is destroyed and the Mott gap opens instead, leading the system to the antiferromagnetic quasi-long-range order. An insulator version of the double exchange ferromagnetism is thus established.Comment: 5 pages, 3 figures, Phys. Rev. Lett., in pres