Stability of Ferromagnetism in Many-Electron Systems

D. F. Wang

Rainer Strack, D. Vollhardt

Rainer Strack, D. Vollhardt

Junha Kang, Taekoo Oh, Junhyun Lee +1 more

Despite its abundance in nature, predicting the occurrence of ferromagnetism in the ground state is possible only under very limited conditions such as in a flat band system with repulsive interaction or in a band with a single hole under infinitely large Coulomb repulsion, etc. Here, we propose a general condition to achieve saturated ferromagnetism based on the quantum geometry of electronic wave functions in itinerant electron systems. By analyzing the spin excitations of multi-band repulsive Hubbard models with an integer band filling, relevant to either ferromagnetic insulators or semimetals, we show that quantum geometry stabilizes the Goldstone mode in the strongly correlated limit. Our theory indicates the stability of ferromagnetism in a large class of insulators and semimetals other than the previously studied flat band systems and their variants. Moreover, we rigorously prove that saturated ferromagnetism is forbidden in any system with trivial quantum geometry, which includes every half-filled system. We believe that our findings reveal a profound connection between quantum geometry and ferromagnetism, which can be extended to various symmetry-broken ground states in itinerant electronic systems.

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.

K.L. Yao, Yi Qin, Qingmei Liu +1 more

By using density matrix renormalization group (DMRG) method a model for organic molecule-based ferromagnetic chain is proposed. It is found that the ground states of undoped and doped systems both exhibit ferrimagnetic ordering. The e - e repulsion plays an important role in the stability of the ferromagnetic state either in doped system or undoped system. For the undoped system, each unit cell contains half of the total spins, which is consistent with Lieb's theorem. It is convinced that when the system is doped with one electron, a charge density wave is excited, which decreases the amplitude of spin density wave, therefore acting against the stability of ferromagnetic state.