Chirality-dependent scattering of an electron vortex beam by a single atom in a magnetic field

Abstract

Electron magnetic circular dichroism (EMCD) can detect the magnetic properties of materials at the nanoscale, but its wide applications are limited by stringent specimen orientation and noisy signal outputs. To overcome these challenges, electron vortex beams (EVBs) were most recently proposed to develop chirality-dependent EMCD (CEMCD), yet convincing and reproducible CEMCD has not yet been demonstrated. In electron energy-loss spectroscopy (EELS) experiments of EMCD, electron-atom scattering has played a core role. Here, from a model research on the scattering of EVBs by a single atom in a magnetic field, we show a way of generating chirality-dependent scattering which is of potential application to CEMCD. The mechanism is to break the symmetry of the joint occupation probability amplitudes for two scattering channels with opposite magnetic quantum number differences ($\mathrm{\ensuremath{\Delta}}{m}_{j}$), respectively, for two EVBs with opposite topological charges ($l$). Particularly, the Zeeman effect and spin-orbit coupling jointly can lead to this chirality-dependent scattering, signaled as the chirality-dependent differential cross section (DCS) for the EVB. The DCS can be optimized by choosing the magnetic field strength and topological charge for getting the strongest EMCD. Due to angular momentum conservation, $l=\mathrm{\ensuremath{\Delta}}{m}_{j}$ is the optimum topological charge, which could be useful for the selective probe of an internal state. We show that using EVB with a narrow width can relax the requirement of precise controlling of the opening angle and improve the spatial resolution. Finally, we show that chirality-dependent scattering strength decreases with increasing of the impact parameter.