Two-magnon bound states in Heisenberg ferromagnets

A generalized theory of bound two-magnon states in three-dimensional isotropic Heisenberg ferromagnets is given and the passage to the limit in which the total number of spins tends to infinity is handled rigorously. Powerful methods, mostly of the trace-inequality type, are developed for determining upper and lower bounds to the number of such bound states in the latter limit. These methods constitute the central contribution of this paper. In the latter we apply them to investigate the existence of bound two-magnon states in body-centered Heisenberg ferromagnets whose nonvanishing exchange interactions are those of the nearest-neighbor type. In work reported elsewhere, we have employed these methods to study spin-wave impurity states in Heisenberg ferromagnets. They should be useful for determining bounds on the number of localized states in solids in many cases when interactions extending over several orders of neighbors are operative.