  We show that in superlattices with alternating superconducting (S) and
ferromagnetic (F) layers the spontaneous magnetic field induced in the
superconducting layers due to the electromagnetic proximity effect becomes
dramatically enhanced compared to the previously studied S/F bilayers. The
effect reveals itself for the in-plane orientation of the magnetic moments both
for ferromagnetic and anti-ferromagnetic ordering of the moments in the F
layers. In the finite size samples the magnetic field decays from the sample
surface towards the bulk of the structure, and the decay length strongly
depends on the relative orientation of the sample surface, the layers planes
and magnetic moments in the F layers. The obtained results provide additional
insights into experimental data on the neutron scattering in Nb/Gd
superlattices.
