Conventional superconductivity is incompatible with ferromagnetism, because the magnetic exchange field tends to spinpolarize electrons and breaks apart the opposite-spin singlet Cooper pairs 1. Yet, the possibility of a long-range penetration of superconducting correlations into strong ferromagnets has been evinced by experiments that found Josephson coupling between superconducting electrodes separated afar by a ferromagnetic spacer 2-7. This is considered a proof of the emergence at the superconductor/ferromagnetic (S/F) interfaces of equalspin triplet pairing, which is immune to the exchange field and can therefore propagate over long distances into the F (ref. 8). This effect bears much fundamental interest and potential for spintronic applications 9. However, a spectroscopic signature of the underlying microscopic mechanisms has remained elusive. Here we do show this type of evidence, notably in a S/F system for which the possible appearance of equal-spin triplet pairing is controversial 10-12 : heterostructures that combine a half-metallic F (La 0.7 Ca 0.3 MnO 3) with a d-wave S (YBa 2 Cu 3 O 7). We found quasiparticle and electron interference effects in the conductance across the S/F interfaces that directly demonstrate the long-range propagation across La 0.7 Ca 0.3 MnO 3 of superconducting correlations, and imply the occurrence of unconventional equal-spin Andreev reflection. This allows for an understanding of the unusual proximity behaviour observed in this type of heterostructures 12,13. The proximity effect, usually described as the penetration or 'leakage' of the superconducting condensate from a S into an overlaying normal metal (N), is on a microscopic level the result of two processes. The first one is the Andreev reflection 14 , through which a normal electron incident into the S/N interface is paired with an electron inside the Fermi sea by the S energy gap, leaving a hole excitation that propagates backwards from the interface. In the conventional picture, the incident electron and the reflected hole must have opposite spins. The second process is the coherent propagation into the N material of the resulting hole/electron phase-conjugated pair 15. The latter carries the superconducting correlations into the N, leading to a finite condensation amplitude over a certain length scale ξ N , as schematically shown in Fig. 1a. In the N, such coherent propagation is limited only by the usual dephasing mechanisms and diverges at zero temperature (T): for diffusive systems ξ N = √h D/2π KT and for ballistic ones ξ N =hv F /2π KT , where D is the electronic diffusion constant, K is the Boltzmann constant and v F is the Fermi velocity 15. In clean metals, at low temperatures, ξ N can be micrometres long. If the LETTERS NATURE PHYSICS

Using heterostructures that combine a large-polarization ferroelectric (BiFeO3) and a high-temperature superconductor (YBa2Cu3O(7-δ)), we demonstrate the modulation of the superconducting condensate at the nanoscale via ferroelectric field effects. Through this mechanism, a nanoscale pattern of normal regions that mimics the ferroelectric domain structure can be created in the superconductor. This yields an energy landscape for magnetic flux quanta and, in turn, couples the local ferroelectric polarization to the local magnetic induction. We show that this form of magnetoelectric coupling, together with the possibility to reversibly design the ferroelectric domain structure, allows the electrostatic manipulation of magnetic flux quanta.