  Electron beams in Scanning Transmission Electron Microscopes (STEMs) can be
used as a tool to induce movement on nanoparticles. Employing a
classical-electrodynamics approach, it has been reported that the linear
momentum transfer from a STEM-beam electron to a metallic spherical
nanoparticle can be either repulsive or attractive towards the swift electron
trajectory. This is in qualitative agreement with experimental observations.
The interaction time between a swift electron and a nanoparticle is typically
on the order of attoseconds. Hence, the electromagnetic response of the
nanoparticle at short times is of utmost importance. However, it has been
reported that the dielectric function employed in previous studies presented a
non-causal pre-echo at the attosecond timescale, which might have lead to
incorrect unphysical results. Therefore, the validity of these linear momentum
transfer results should be revisited. In this theoretical work, we study the
non-causality effects on the linear momentum transferred from a swift electron
to a metallic nanoparticle, made of either aluminum or gold. Using an efficient
numerical methodology, we found that non-causality, as well as deficient
numerical convergence, may lead to incorrect repulsive linear momentum transfer
results. Contrary to what previous theoretical studies have reported, our
results show that the linear momentum transfer from a swift electron to
spherical aluminum and gold nanoparticles, with radius 1 nm, is always
attractive.
