The optical Faraday effect describes the rotation of linear polarization upon propagation through a medium in the presence of a longitudinal magnetic field. The effect arises from a different phase delay between the right and left handed polarization components of the light. In this paper we predict a Faraday effect for a completely different system: electron vortices. Free electron vortex states were recently observed in transmission electron microscopy experiments, and they introduce new degrees of freedom into the probing of matter with electron beams. We associate a rotation of a vortex superposition with the fact that different phases are acquired by oppositely handed vortices propagating in a magnetic field. We show that, in contrast to the optical Faraday effect, the rotation of the electron beam occurs in vacuum and arises from the intrinsic chirality of the constituent vortex states.

We show that an electron moving in a uniform magnetic field possesses a time-varying "diamagnetic" angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields.

We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular momentum of the cyclotron orbit of the wavefunction, and a diamagnetic angular momentum. The cyclotron and diamagnetic angular momenta are found to be separable according to the parallel axis theorem. This means that rotations can occur with respect to two or more axes simultaneously, which can be observed with superpositions of vortex states.