Magnon-Magnon Interactions in Doped Antiferromagnets

There have been a series of optical experiments recently in which two magnons are created on or near an impurity in an antiferromagnet. It is shown that if at least one of these magnons is localized around the impurity, the three-body problem reduces to a series of effective two-body problems. Green's function methods have been used to calculate the line shapes for ${\mathrm{Ni}}^{++}$-doped RbMn${\mathrm{F}}_3$ and KMn${\mathrm{F}}_3$, giving good agreement with experiment.