Equal-spin Andreev reflection from quasiparticle interference effects in high-T$_{C}$/half metallic ferromagnet junctions*

We report evidence for long-range superconducting correlations in the half-metallic ferromagnet (F) La$_{0.7}$Ca$_{0.3}$MnO$_{3}$, obtained from conductance measurements along the c-axis in SFS and SF junctions (with S the high-T$_{C}$ superconductor YBa$_{2}$Cu$_{3}$O$_{7})$. Well below the superconducting T$_{C}$, we observed oscillations in the differential conductance as a function of the voltage bias, in which we identified two sets of resonances: i) quasiparticle interferences in the S (top) layer (Tomasch resonances) and ii) in the half-metallic F layer (McMillan-Rowell resonances). Both of them imply Andreev-like reflections at the SF interface and the coherent propagation of the resulting phase-conjugated quasiparticles through the entire S and F layers thickness (up to 30 nm for the F layer). Because conventional Andreev reflection and the coherent long-range propagation of the outcoming opposite-spin electron/hole pairs are heavily suppressed in strongly polarized ferromagnets, the observation of the above effect implies the occurrence of equal-spin Andreev reflection at the studied SF interfaces.