Hubbard model and the origin of ferromagnetism

Andreas Mielke, Hal Tasaki

A. Greco, Matías Bejas, Andreas P. Schnyder

We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping ${t}^{\ensuremath{'}}$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two Van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two Van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from interband contributions to the spin susceptibility. These interband contributions only arise if there is one holelike and one electronlike Fermi surface, which is the case for fillings in between the two Van Hove fillings. We discuss implications for experimental systems and propose a test on how to identify these types of ferromagnetic fluctuations in experiments.

M. Gulácsi, György Kovács, Zsolt Gulácsi

We model conducting pentagon chains with a multi-orbital Hubbard model and prove that well below half filling, exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimension and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat-band ferromagnetism requires, where on every site a Hubbard term is present. In our case, only a small percentage of, even randomly distributed, sites are only interacting.

Wolfgang Nolting, Michael Potthoff, T. Herrmann +1 more

Rongming Wang

The authors investigated the frustration effect when next-nearest-electron hopping causes itinerant ferromagnetism in a one-dimensional Hubbard model.By using the exact diagonalization method and the density-matrix renormalization-group technique,it was shown that the next-nearest electron hopping term stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n when the system is small.Furthermore,by calculating the local spin-spin correlation function,we found the ferromagnetic state becomes unstable as the length of the system increases.A further study showed that the ferromagnetic relationships of the system become weaker when the system's size increases.In addition,the system will transit to the anti-ferromagnetic correlation when the system reaches critical length.These observed results demonstrate on the one hand that an itinerant ferromagnetic phase exists in the electron-mixing area of small-sized material in the one-dimensional Hubbard model,and on the other hand,these observations should be helpful in understanding the origin of the itinerant ferromagnetism observed recently in some metallic and metallic oxide clusters.

Ben Hur Bernhard