Theory of momentum-resolved magnon electron energy loss spectra: The case of Yttrium Iron Garnet

We explore the inelastic spectra of electrons impinging in a magnetic system. The methodology here presented is intended to highlight the charge-dependent interaction of the electron beam in a STEM-EELS experiment, and the local vector potential generated by the magnetic lattice. This interaction shows an intensity $10^{-2}$ smaller than the purely spin interaction, which is taken to be functionally the same as in the inelastic neutron experiment. On the other hand, it shows a strong scattering vector dependence ($\kappa^{-4}$) and a dependence with the relative orientation between the probe wavevector and the local magnetic moments of the solid. We present YIG as a case study due to its high interest by the community.