Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy $(1∕\mathcal{N})$ expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the density of states (DOS) is sufficiently asymmetric and strongly peaked near the band edge, as for the fcc lattice with finite $t^{\prime }$. For short-wavelength modes, the behavior of a characteristic energy scale ${\omega }^{*}\sim T_c$ (magnon DOS peak energy) is in excellent agreement with the $T_c$ vs $n$ behavior within dynamical mean field theory, with respect to both the stable range of densities $(0.20<n<0.85)$ as well as the optimal density $n=0.65$. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.

• Received 28 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.064412