Title:

The diamagnetic angular momentum of an electron

Diamagnetism is the magnetism exhibited by all materials, even those not normally considered magnetic, in the presence of an applied magnetic field. On a microscopic level, it is associated with the angular momentum acquired by individual electrons in the magnetic field. Recently discovered electron vortices, meanwhile, possess orbital angular momentum even in fieldfree space. In this thesis, I consider the angular momentum of an arbitrary electron wavefunction in a uniform magnetic field. I show that the kinetic orbital angular momentum of the electron can be represented as a sum of three components: the canonical angular momentum associated with a vortex, the angular momentum associated with a cyclotron orbit of the wavefunction as a whole, and a “diamagnetic” angular momentum associated with an internal rotation of the wavefunction that is induced by the magnetic field. I show that the diamagnetic angular momentum depends on the moment of inertia of the electron’s probability distribution, which for free electrons has interesting consequences. Whereas diamagnetism in materials is normally very small compared to the effects of intrinsic magnetic moments, a free electron – for example, in an electron microscope – can have a probability distribution with a much larger average radius. This means that the diamagnetic component can be the dominant contribution to the electron’s angular momentum. On the other hand, the diamagnetic angular momentum may instead be of a similar magnitude to the canonical and/or cyclotron components, in which cases the current density strongly depends on the relative magnitudes and directions of these components. Further, diffraction and interference of the electron’s wave function lead to interesting dynamical effects. I demonstrate that the kinetic angular momentum of the electron can vary with time, which seems at first sight to violate angular momentum conservation. The diamagnetic angular momentum also gives rise to a “Faraday effect” for electrons, analogous to the rotation of the polarization of light in a magnetic field. All of this behaviour is a surprising departure from the simple cyclotron orbit predicted by classical theory.
