Probing magnons with high-energy electrons: theoretical insights into spin and charge scattering in STEM-EELS

In this work, we provide fundamental insights into the scattering mechanisms of non-spin-polarised electron beams with magnetic systems, as implemented in modern meV-level scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS) instruments. We demonstrate that the charge contribution to electron-probe-magnon scattering is significant, exhibiting a near-quadratic dependence on the electron probe’s momentum. This contribution can surpass spin-based interactions by orders of magnitude at higher beam acceleration voltages. Furthermore, unlike spin-based interactions, the charge-based interaction strongly depends on the relative angle between the probe’s wavevector and the local magnetic moments. We derive analytical expressions for both spin-based and charge-based interactions in EELS, comparing them with established inelastic neutron scattering results and elucidating conditions under which each scattering mechanism dominates. This formalism is applied to yttrium iron garnet, a prototypical magnonic material. Our findings are crucial for guiding future experiments and data analysis in nanomagnonics, paving the way for high spatial resolution magnon spectroscopy via STEM-EELS.