Band structure for neutral magnetic dipoles in a periodic magnetic field: A simple spin polarizer

The solution to the Pauli spinor equation for a neutral magnetic dipole in a periodic magnetic field gives rise to an energy band structure as a consequence of Bloch’s theorem. Since the two spin components see differing potentials, it is possible to arrange the magnetic field so that only the kinetic energy corresponding to one spin component is in a band while that of the other is in a band gap. Only one component from an incident beam would propagate through the oscillating field while the other would be completely reflected. Hence, a very efficient polarizing filter is obtained.