Ferromagnetism in the t-t' Hubbard model: interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy ($1\mathrm{/}\mathcal{N}$) 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 DOS is sufficiently asymmetric and strongly peaked near band edge, as for fcc lattice with finite $t^{\mathrm{\prime }}$. For short-wavelength modes, behavior of a characteristic energy scale $\omega^* \sim T_c$(magnon-DOS-peakenergy)isinexcellentagreementwiththe$T_c$vs\mathrm{.}$n$ behavior within DMFT, both with respect to 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.