The features of the hysteresis in a ferromagnetic film on the surface of a hard-magnetic antiferromagnet with domain structure

The exchange bias phenomenon and the hysteresis loop features of a thin ferromagnetic film on a rough surface of a hard-magnetic antiferromagnet have been studied theoretically. The model of such interface with a periodical structure of atomic steps has been proposed. These atomic steps are associated with the bulk inhomogeneous distribution of the magnetization in the ferromagnetic film similar to the system of domain walls. This structure leads to a complicated field dependence of magnetization. The hysteresis curve may be asymmetric and may split into two hysteresis loops, which are separated by a horizontal plateau, i.e., by the area with constant field-independent magnetization. Similar behavior of the field dependence has been observed recently in various ferro/antiferromagnetic systems. The field dependence of the magnetization has been obtained analytically in the long-wave approximation for various characteristics of the ferromagnetic film (thickness, value of exchange interaction and magnetic anisotropy) and interface, i.e., the period of the inhomogeneous structure and exchange interaction through the interface. The analytical results are confirmed by numerical simulations for the corresponding discrete system with a more complicated structure of the interface.