  We report on the study of electron transport in the oxide heterostructures
with superconductor/magnetic matter (S/M) interfaces where anomaly large
penetration of superconducting correlations in magnetic matter (proximity
effect) is realized. The developed theoretical model based on multilayer
magnetic structure of M-interlayer and experiment show presence of the
long-range proximity effect at S/M-interface with antiferromagnetic (AF)
ordering of the interlayer magnetization. The investigated hybrid
heterostructures include cuprate superconductor, the AF-cuprate interlayer and
conventional superconductor, Nb. The superconducting critical current with
density 1-10A/cm2 and the characteristic voltage, 0.1-0.2 mV, are observed at
liquid helium temperature for 15-50 nm thick M-interlayer made of AF film
CaSrCuO. These heterostructures demonstrate deviation from sin-type
superconducting current-phase relation and had the critical current of the
second harmonic of 10-20% of the first harmonic one. The hybrid
heterostructures with S/AF interface show high sensitivity to the external
magnetic field that is possibly caused by the influence of an external magnetic
field on the canting of magnetic moments of individual layers of AF
-interlayer. Substituting the AF cuprate by a manganite film, no critical
current was observed, although the M- interlayer was made very thin, down to 5
nm.
