  In a superconducting ferromagnet, the superconducting state appears in the
ferromagnetic phase where usually a domain structure has already developed. We
study the influence of the superconducting screening currents on a stripe
structure with out-of-plane magnetization, in a film of arbitrary thickness. We
find that superconductivity always induces a shrinkage of the domains, and
there is a critical value of penetration depth below which a mono-domain
structure is more stable than the periodic one. Furthermore we investigate the
possible different effects of singlet and triplet superconductivity on the
domain width, as well as the conditions for the existence of vortices in the
domains. The obtained results are then discussed in light of the experimental
data of superconducting ferromagnets URhGe, UGe2, and UCoGe.
