  We present a detailed theoretical study of oxygen molecules in high
rotational states (molecular superrotors) interacting with an external magnetic
field. The system shows rich dynamics, ranging from a spin-selective splitting
of the angular distribution over molecular alignment to an inversion of the
rotational direction. We find that the observed magneto-rotational effects are
due to a spin-mediated precession of the orbital angular momentum around the
magnetic field. Analytical expressions for the precession frequency in the
limits of weak and strong magnetic fields are derived and used to support the
proposed mechanism. In addition, we provide the procedure for a numerical
treatment of oxygen superrotors in an external magnetic field.
