  We present a theoretical study of the interplay between cyclotron motion and
spin splitting of charge carriers in solids. While many of our results apply
more generally, we focus especially on discussing the Rashba model describing
electrons in the conduction band of asymmetric semiconductor heterostructures.
Appropriate semiclassical limits are distinguished that describe various
situations of experimental interest. Our analytical fomulae, which take full
account of Zeeman splitting, are used to analyse recent magnetic-focusing data.
Surprisingly, it turns out that the Rashba effect can dominate the splitting of
cyclotron orbits even when the Rashba and Zeeman spin-splitting energies are of
the same order. We also find that the origin of spin-dependent cyclotron motion
can be traced back to Zitterbewegung-like oscillatory dynamics of charge
carriers from spin-split bands. The relation between the two phenomena is
discussed, and we estimate the effect of Zitterbewegung-related corrections to
the charge carriers' canonical position.
