Superconductivity suppression by ferromagnetism in bi- and tri-layers of La$_{0.7}$Ca$_{0.3}$MnO$_3$\ ferromagnets and high-T$_c$\ YBa$_2$Cu$_3$O$_{7-\delta}$

Large magnetoresistance occurs in F/S/F trilayers of highly spin-polarised La$_{0.7}$Ca$_{0.3}$MnO$_3$\ ferromagnet and high-T$_c$\ superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ for antiferromagnetic (AF) alignment of the manganite layers. We discuss the relative importance of spin diffusion across the superconductor, proximity effect at the F/S interface and stray fields due to domain walls of the ferromagnet based on magnetoresistance and magnetisation measurements of bilayers and trilayers of various thickness of superconductor and ferromagnet.