Theory and simulations of angular momentum transfer from swift electrons to spherical nanoparticles in scanning transmission electron microscopy

Electron beams in scanning transmission electron microscopy (STEM) exert forces and torques on study samples, with magnitudes that allow the controlled manipulation of nanoparticles (a technique called electron tweezers). Related theoretical research has mostly focused on the study of forces and linear momentum transfers from swift electrons (like those used in STEM) to nanoparticles. However, theoretical research on the rotational aspects of the interaction would benefit not only the development of electron tweezers but also other fields within electron microscopy such as electron vortices studies. Starting from a classical-electrodynamics description, we present a theoretical model, alongside an efficient numerical methodology, to calculate the angular momentum transfer from a STEM swift electron to a spherical nanoparticle. We show simulations of angular momentum transfers to aluminum, gold, and bismuth nanoparticles of different sizes. We found that the transferred angular momentum is always perpendicular to the system's plane of symmetry, displaying a constant direction for all the cases considered. In the simulations, the angular momentum transfer increased with the radius of the nanoparticle but decreased as the speed of the electron or the impact parameter increased. Also, the electric contribution to the angular momentum transfer dominated the magnetic one, being comparable only for high electron speeds (greater than 90% of the speed of light). Moreover, for nanoparticles with 1 nm radius of the studied materials, it was found that the small-particle approximation (in which the nanoparticles are modeled as electric point dipoles) is valid and accurate to compute the angular momentum transfer as long as the impact parameter is greater than four times the nanoparticle's radius and that the electron's speed exceeds 50% of the speed of light. We believe that these findings contribute to the understanding of rotational aspects present in STEM experiments, and might be useful for further developments in electron tweezers and other electron microscopy related techniques.