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This is a theoretical investigation of the exchange bias phenomenon, and the properties of a thin magnetic film's magnetization hysteresis loop, on the rough surface of a hard-magnetic antiferromagnet. An interface model with a periodic structure of atomic steps is presented. These atomic steps are associated with a spatially inhomogeneous distribution of the ferromagnetic film magnetization, akin to a system of domain walls. This structure leads to a complicated external field dependence of magnetization: the hysteresis curve can assume an asymmetrical shape and “fall apart” into two hysteresis loops, divided by a “horizontal plateau,” or an area with constant field-independent magnetization. Such field dependence behavior has been recently observed experimentally in different ferro/antiferromagnet systems. The field dependence of magnetization has been obtained analytically using the long-wave …