  We analyze the energy band structure of a two-dimensional electron gas in a
periodic magnetic field of a longitudinal antiferromagnet by considering a
simple exactly solvable model. Two types of states appear: with a finite and
infinitesimal longitudinal mobility. Both types of states are present at a
generic Fermi surface. The system exhibits a transition to an insulating regime
with respect to the longitudinal current, if the electron density is
sufficiently low.
