  We present a relativistic description of electron vortex beams in a
homogeneous magnetic field. Including spin from the beginning reveals that
spin-polarized electron vortex beams have a complicated azimuthal current
structure, containing small rings of counterrotating current between rings of
stronger corotating current. Contrary to many other problems in relativistic
quantum mechanics, there exists a set of vortex beams with exactly zero
spin-orbit mixing in the highly relativistic and nonparaxial regime. The well
defined phase structure of these beams is analogous to simpler scalar vortex
beams, owing to the protection by the Zeeman effect. For states that do show
spin-orbit mixing, the spin polarization across the beam is nonuniform
rendering the spin and orbital degrees of freedom inherently inseparable.
