Spin-Wave—Spin-Wave Scattering in a Heisenberg Ferromagnet

Abstract

We have obtained an exact solution describing the scattering of two spin waves in a simple cubic Heisenberg ferromagnet by solving the Lippmann-Schwinger equation for states with two spin deviations. The scattering amplitude is infinite at the energies of bound states discovered by Wortis, and the cross section agrees at long wavelengths with the approximate result obtained by Dyson. The methods used here are relatively conventional, and are generally applicable to any situation in which two excitations in a lattice interact via short-range forces.