Quantum theory of magnon excitation by high energy electron beams

The role of magnon inelastic scattering in high energy electron diffraction of spin unpolarised electron beams, including vortex beams, is investigated theoretically for a Heisenberg ferromagnet. The interaction is between the atomic magnetic dipoles in the specimen and orbital angular momentum (OAM) of the electron beam. Magnon inelastic scattering by vortex beams is allowed despite many atoms along the magnon spin wave experiencing mixed OAM states. The scattering cross-section is however independent of the vortex beam winding number. In the case of planes waves in ferromagnetic iron, the magnon diffuse scattered intensity is significantly smaller than phonons in the energy loss range currently accessible by state-of-the-art monochromated electron energy loss spectroscopy (EELS). Nevertheless, it is shown that the long-range magnetic field of the atomic dipoles has a similar role to dipole scattering in phonon excitation. This means that magnons could, in principle, be detected using aloof beam EELS, where long acquisition times can be realised without any specimen beam damage, an important pre-requisite for detecting the weak magnon signal.