Transport in two dimensional periodic magnetic fields

Ballistic transport properties in a two dimensional electron gas are studied numerically, where magnetic fields are perpendicular to the plane of two dimensional electron systemsand periodically modulated both in $x$ and $y$ directions. We show that there are three types of trajectories of classical electron motions in this system; chaotic, pinned and runaway trajectories. It is found that the runaway trajectories can explain the peaks of magnetoresistance as a function of external magnetic fields, which is believed to be related to the commensurability effect between the classical cyclotron diameter and the period of magnetic modulation. The similarity with and difference from the results in the antidot lattice are discussed.