Quantum and thermal fluctuations in a two-dimensional correlated band ferromagnet -- Goldstone-mode preserving investigation with self-energy and vertex corrections

Ferromagnetism in the t-t' Hubbard model is investigated on a square lattice. Correlation effects in the form of self-energy and vertex corrections are systematically incorporated within a spin-rotationally-symmetric scheme which explicitly preserves the Goldstone mode and is therefore in accord with the Mermin-Wagner theorem. Interplay of band dispersion and correlation effects on ferromagnetic-state stability are highlighted with respect to both long- and short-wavelength fluctuations, which are shown to have substantially different behaviour. Our approach provides a novel understanding of the enhancement of ferromagnetism near van Hove filling for t'~0.5 in terms of strongly suppressed saddle-point contribution to the destabilizing exchange part of spin stiffness. Finite-temperature electron spin dynamics is investigated directly in terms of spectral-weight transfer across the Fermi energy due to electron-magnon coupling. Relevant in the context of recent magnetization measurements on ultrathin films, the role of strong thermal spin fluctuations in low dimensions is highlighted, in the anisotropy-stabilized ordered state, by determining the thermal decay of magnetization and T_c within a renormalized spin-fluctuation theory.