  We consider a ferromagnetic/antiferromagnetic bilayer on a triangular lattice
in the framework of the planar Heisenberg model. The impact of the geometrical
frustration in this system on the magnetization curves and the exchange bias
phenomenon is studied. The magnetization curves and the phase diagram for such
systems are obtained. We observe horizontal plateaus and a split of the
hysteresis loop on the magnetization curves. It is shown that the shift of the
hysteresis loop (exchange bias) occurs for the systems with a magnetically hard
antiferromagnet.
