What comes into my mind is the three-magnon process, in which an optical magnon with k=0 and ω=ω0 splits into two acoustic magnons, one k=k1,ω=ω02, the other k=−k1,ω=ω02. Note that in this process energy and momentum are conserved. This 3-magnon process can lead to a finite life time.
Not sure.
This post imported from StackExchange Physics at 2014-08-22 05:08 (UCT), posted by SE-user D-K