We present a comprehensive study into the inelastic spectra obtained by electrons interacting with magnetic materials. The main focus is on the charge-dependent interaction of the electron beam, in an electron microscope, via the local vector potential generated by the magnetic lattice in terms of the spin-scattering function. This methodology allows direct comparison between charge-dependent and purely spin-dependent interactions. Our results for the double differential cross-section show strong scattering vector dependence ($q^{-2}$) and linear dependence with the electron probe’s momentum. Additionally, we explore the intensity dependence on the relative orientation between the electron probe wavevector and the local magnetic moments of the solid, using YIG as a case study due to its importance as a platform material for magnonics.
In this work, we also introduce a methodology for calculating the spin-scattering function, particularly in confined geometries such as thin films, for both collinear and non-collinear spin-structures materials. Through case studies involving bcc Fe(100), YIG(100), NiO(100) and NiO(111), we illustrate the effects of film thickness and crystal orientation on magnon modes in three different magnetic systems, ferromagnetic, ferrimagnetic and antiferromagnetic, respectively. The quasi-momentum quantisation results in granularity in the inelastic spectra in the reciprocal space path, reflecting thin film orientation. This approach captures softer modes arising from the partial interaction of magnetic moments near the surface in thin film geometry, concurrently with the bulk modes.
Furthermore, we explore the influence of magneto-crystalline anisotropy, demonstrating its effect by increasing the overall hardness of magnon modes. Specifically, introducing surface anisotropy leads to a shift of surface-related magnon density of states (DOS) peaks to higher energies, that could result in surface-confined modes.
Finally, we performed calculations for the phase and group velocity of the magnons in these structures, further elucidating their behaviour in confined geometries.
