Localized Magnons (Theory)

Abstract

The Heisenberg Hamiltonian for impure ferro — or antiferromagnets is of the class originally discussed by Lifshitz⁽¹⁾ in his work on the properties of the energy spectra of disordered systems. Within the simple (non-interacting) spin wave approximation, applicable in the low temperature limit, the problem is closely analogous to that of phonons in impure lattices, to which the general theory was first applied. One expects (and finds) for appropriate impurity parameters true localized modes at energies outside the pure crystal spin wave band and virtual modes (or “resonances”), with finite lifetimes, at energies within the band. However, even in this simple picture, there is no analog to the most easily treated disordered lattice — with a single isotopic impurity. The spin magnitude enters dynamically in the exchange interaction and the “force constant” associated with a magnetic impurity must therefore be changed along with its “mass.” In general, the substitutional impurity may differ from the atom it replaces in the exchange constants coupling it to its neighbors as well as in spin magnitude.