Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

摘要

We study the zero-temperature spin fluctuations of a two-dimensionalitinerant-electron system with an incommensurate magnetic ground statedescribed by a single-band Hubbard Hamiltonian. We introduce the(broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level througha \emph{spiral spin configuration} with characteristic wave vector$\gmathbf{Q}$ different in general from the antiferromagnetic wave vector$\gmathbf{Q_{AF}}$, and consider spin fluctuations over and above it within theelectronic random-phase (RPA) approximation. We obtain a \emph{closed} systemof equations for the generalized wave vector and frequency dependentsusceptibilities, which are equivalent to the ones reported recently by Brenig.We obtain, in addition, analytic results for the spin-wave dispersion relationin the strong-coupling limit of the Hubbard Hamiltonian and find that at finitedoping the spin-wave dispersion relation has a \emph{hybrid form} between thatassociated with the (localized) Heisenberg model and that associated with the(long-range) RKKY exchange interaction. We also find an instability of thespin-wave spectrum in a finite region about the center of the Brillouin zone,which signals a physical instability toward a different spin- or, possibly,charge-ordered phase, as, for example, the stripe structures observed in thehigh-Tc materials. We expect, however, on physical grounds that for wavevectors external to this region the spin-wave spectrum that we have determinedshould survive consideration of more sophisticated mean-field solutions.