The homogeneous state of a ferromagnet-superconductor bilayer (FSB) with the magnetization perpendicular to the layer can be unstable with respect to the formation of vortices in the superconducting layer. The developing topological instability in the FSB leads to formation of domains in which the direction of the magnetization in the magnetic film and the direction of vorticity in the superconducting film alternate together. This is a new, combined topological structure, which does not appear in isolated layers.
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