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

Observation of the Larmor and Gouy Rotations with Electron Vortex Beams