Angular dynamics of small nanoparticles induced by non-vortex electron beams

In this work, we present a theoretical study of the angular dynamics of small nanoparticles induced by fast non-vortex electron beams. General expressions for the torque and the angular momentum transferred from an electron to an arbitrary-but small-nanoparticle are obtained using a full-retarded classical electrodynamics approach, within the small particle limit. We applied this methodology to study a particular case of interest: the angular dynamics of spherical nanoparticles with homogeneous and isotropic electromagnetic responses. We analytically calculate the total angular momentum transferred from a swift electron to such nanoparticles, finding that it is electric in nature and it is always in a direction determined by the electron trajectory relative to the center of the nanoparticle. We realize that it is possible to represent the angular momentum transferred as the product of two functions: the extinction cross-section of the nanoparticle and a function that only contains information about the swift electron. We present numerical results for the total angular momentum transferred from a swift electron to an aluminum and a gold nanoparticle. We also present an analysis of the temporal behavior of the torque and the electric dipole moment induced within the nanoparticle by the swift electron. We compare the angular momentum transfer calculated in this work with a previously reported case of vortex beams, finding that, for both aluminum and gold nanoparticles, our results are two orders of magnitude smaller. Finally, we consider a particular case of a frictionless gold spherical nanoparticle of radius a=5nm, obtaining that it can spin with an angular frequency up to 29.3Hz.