Spin Wave - Spin Wave Scattering in a Heisenberg Ferromagnet

摘要

Consideration is given to the scattering on one spin wave from another in a perfect simple cubic Heisenberg ferromagnet with nearest neighbor exchange only. An orthonormal set of two-spin-wave states is displayed, and the exchange hamiltonian is divided into a diagonal part and an off-diagonal part. The Lippmann-Schwinger scattering equation is solved for two spin derivations, and an exact exchange scattering cross section is obtained. The 'Golden Rule' is used to derive, in Born approximation, the dipole scattering cross section. It is concluded that if the Born approximation is valid for dipole scattering and if the ratio of cross sections is similar for face centered cubic lattices, then in EuS dipole scattering swamps out exchange scattering at low temperatures.