The superconducting current has been observed in mesa-heterostructures Nb/Au/Sr2IrO4/YBa2Cu3Ox with Sr2IrO4 interlayer thickness d=5 and 7 nm and in-plane sizes L=10-50 mcm. A strontium iridate, Sr2IrO4, is known as a canted antiferromagnetic insulator at low temperatures and characterized also by the strong spin-orbit interaction due to the impact of the IrO2 plane. The superconducting critical current density jC =0.3 A/cm^2 for the case d=7 nm was observed at T=4.2K. The temperature dependences of the superconducting critical current IC(T) and the voltage position on the I-V curve of the gap singularity of the Nb electrode show an increase with decreasing temperature and corresponds to the expected BCS behavior of the Nb energy gap. The critical current is very sensitive to the influence of an external magnetic field and reduces twice at an external magnetic field (H=0.2 Oe for L=40-50 mcm) comparable with the earth magnetic field; The magnetic field dependence IC(H) at low H was narrower than the Fraunhofer pattern about 1.5 times. Both the integer and fractional Shapiro steps at voltages V=(m/n)(h/2e)fe were observed under microwave radiation at frequencies fe=38 GHz and fe=50 GHz. Fractional Shapiro steps (m/n=1/2, 3/2) may point on the presence of the second harmonic in the superconducting current-phase relation.
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