Quantized Orbital Angular Momentum Transfer and Magnetic Dichroism in the Interaction of Electron Vortices with Matter

Following the very recent experimental realization of electron vortices, we consider their interaction with matter, in particular, the transfer of orbital angular momentum in the context of electron energy-loss spectroscopy, and the recently observed dichroism in thin film magnetized iron samples. We show here that orbital angular momentum exchange does indeed occur between electron vortices and the internal electronic-type motion, as well as center-of-mass motion of atoms in the electric dipole approximation. This contrasts with the case of optical vortices where such transfer only occurs in transitions involving multipoles higher than the dipole. The physical basis of the observed dichroism is explained.

Figure 1

The relevant coordinate frames in the description of the interaction between a Bessel electron vortex and a two-particle neutral system. Position within the beam, $\mathbf{r}$, is described in cylindrical coordinates about the frame $xyz$; the center of mass of the atom is located at $\mathbf{R}$, and the atomic electron is described by $\mathbf{q}$ in spherical coordinates relative to the center of mass. Projection in the $xy$ plane indicates azimuthal angles ${\Phi }_r$, ${\Phi }_R$, and ${\varphi }_e$ of the beam, atomic center of mass and atomic electron, respectively.