Abstract
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.

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