  Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are
produced in electron microscopes where they are controlled and focused using
magnetic lenses. We observe various rotational phenomena arising from the
interaction between the OAM and magnetic lenses. First, the Zeeman coupling,
proportional to the OAM and magnetic field strength, produces an
OAM-independent Larmor rotation of a mode superposition inside the lens.
Second, hen passing through the focal plane, the electron beam acquires an
additional Gouy phase dependent on the absolute value of the OAM. This brings
about the Gouy rotation of the superposition image proportional to the sign of
the OAM. A combination of the Larmor and Gouy effects can result in the
addition (or subtraction) of rotations, depending on the OAM sign. This
behaviour is unique to electron vortex beams and has no optical counterpart, as
Larmor rotation occurs only for charged particles. Our experimental results are
in agreement with recent theoretical predictions.
