  The analytical theory for a ferromagnetic antiferromagnetic bilayer with a
compensated interface has been developed using an explicit expression for the
interfacial interaction energy density. A stability of a solution describing
domain walls within ferromagnetic and antiferromagnetic films has been
investigated. It is shown that even for high values of surface interaction
strength a transverse instability originates within the antiferromagnetic film,
because the deviation of the unit antiferromagnetic vector out of the interface
plane becomes energetically favorable in large enough external magnetic field.
However, it is possible to stabilize the spin distribution near the interface
assuming additional in-plane anisotropy within the antiferromagnetic layer. In
principle, this opens a way to control exchange bias just avoiding a
complicated problem of domain rearrangement within the antiferromagnetic film.
