Theory of localized magnons in Ni++ - Doped manganese salts

There has been a series of optical experiments recently in which one or two magnons are created in the vicinity of a Ni++ impurity in RbMnF3, KMnF3, and MnF2. The single-magnon excitations can be understood using existing Green's-function theory. We find that this theory; which uses the Holstein-Primakoff transformation, is adequate for the host (spin 52) but leads to certain difficulties at the impurity (spin 1), even in the present case where the impurity-host coupling is large. The line shape for the pair modes can be calculated when one of the two magnons is highly localized, thus allowing the three-body problem to be solved as an effective two-body problem. We show that if the lattice contains one magnon localized on the impurity itself, the impurity acts as though its spin were reduced from S′ to S′ - 1 (i.e., as a vacancy, in the case of Ni). Many of the experiments can be explained without a detailed knowledge of the Ni-Mn exchange, which is fortunate in the case of the rutile structure where it is probably complicated. We briefly discuss the g factors of the various modes and show that they can lead to useful information about the spatial extent of the excitations.