Induced Ferromagnetism due to Superconductivity in Superconductor-Ferromagnet structures

We consider a superconductor-ferromagnet (S/F) structure and assume that above the superconducting transition temperature $T_c$ the magnetic moment exists only in F. {In a simple model of the ferromagnet (the exchange field is of the ferromagnetic type for all energies)}we show by an explicit calculation that below $T_c$ the magnetic moment may penetrate the superconductor. {In this model} its direction in S is opposite {to the magnetization of free electrons} in the ferromagnet. The magnetization spreads over a large distance which is of the order of the superconducting coherence length ${\xi }_S$ and can much exceed the ferromagnet film thickness. At the same time the magnetic moment in the ferromagnet is reduced. This inverse proximity effect may explain the reduction in magnetization observed in recent experiments and may lead to a strong interaction between the ferromagnetic layers in F/S/F structures.