  A semiclassical quantization condition is derived for Landau levels in
general spin-orbit coupled systems. This generalizes the Onsager quantization
condition via a matrix-valued phase which describes spin dynamics along the
classical cyclotron trajectory. We discuss measurement of the matrix phase via
magnetic oscillations and electron spin resonance, which may be used to probe
the spin structure of the precessing wavefunction. We compare the resulting
semiclassical spectrum with exact results which are obtained for a variety of
spin-orbit interactions in 2D systems.
