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

Abstract

Ferromagnetism in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ 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 of correlation effects on the ferromagnetic-state stability are highlighted with respect to both long- and short-wavelength fluctuations, which are shown to have substantially different behaviors. Our approach provides an understanding of the enhancement of ferromagnetism near the van Hove filling for ${t}^{\ensuremath{'}}\ensuremath{\sim}0.5$ 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.