Semiclassical Landau quantization of spin-orbit coupled systems

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 wave function. We compare the resulting semiclassical spectrum with exact results which are obtained for a variety of spin-orbit interactions in two-dimensional systems.