  Here we study the electronic properties of cuprate/manganite interfaces. By
means of atomic resolution electron microscopy and spectroscopy, we produce a
subnanometer scale map of the transition metal oxidation state profile across
the interface between the high $T_c$ superconductor YBa$_2$Cu$_3$O$_{7-\delta}$
and the colossal magnetoresistance compound (La,Ca)MnO$_3$. A net transfer of
electrons from manganite to cuprate with a peculiar non-monotonic charge
profile is observed. Model calculations rationalize the profile in terms of the
competition between standard charge transfer tendencies (due to band mismatch),
strong chemical bonding effects across the interface, and Cu substitution into
the Mn lattice, with different characteristic length scales.
