Detection of magnetic impurities using electron vortex beams

Abstract

Electron vortex beams generated by a transmission electron microscope (TEM) are employed to study magnetic properties of an impurity often embedded in materials. Compared to the optical wave, a higher spatial resolving power of electron waves enables the detection of impurities on the nanoscale. Here, we investigate theoretically the interaction of the twisted electrons and the magnetic impurity in which the magnetic dipole moment is taken as a demonstration element. In addition to the usual optical phase, the inhomogeneous vector potential generated by the magnetic dipole moment makes an additional contribution to the intrinsic orbital angular momentum of the twisted electrons, resulting in a dipole-dependent Gouy phase shift. By interfering the outgoing twisted electron beam with a reference cylindrical wave, one can determine the magnitude and orientation of the magnetic dipole directly via the rotational and deformed interference pattern. Furthermore, the pattern is shown to be sensitive to the width of the beam in the focal plane, which provides an effective way to reveal the influence of impurities on the twisted electrons more intuitively and distinctly. The obtained results demonstrate the usefulness of the twisted electron beams for probing the nanoscale magnetism of impurity by TEM, while the proposed model provides the conceptual basis for future developments of the TEM method.