Longitudinal spin fluctuations in Heisenberg ferromagnets: the hydrodynamic regime

The dynamics associated with the magnetization fluctuations in Heisenberg ferromagnets in an external field is investigated both by a purely microscopic approach and by a projection operator technique which emphasizes the role of quasi-conserved, collective dynamical variables. Particular attention is devoted to «hydrodynamic» wave vectors and frequencies; in such a situation the projection operator technique proves very convenient, and in particular at low temperatures the inclusion of the momentum density in the set of relevant variables gives rise to a new excitation, referred to as «second magnon» by previous authors. Its appearance in the longitudinal spectra is studied for arbitrary dimensionalityd: in particular, the theory is applied both to thed=1 classical case (where second magnons have been observed in simulation experiments) and to thed=3 quantum case, where the conditions for the observability of the effect in real systems are discussed.