Abstract. High frequency dynamics of Nb/Au/YBaCuO heterojunctions on tilted NdGaO 3 substrates have been studied. The both integer and non-integer Shapiro steps have been observed at mm-wave frequencies. Unconventional dependence of the critical current and the amplitudes of Shapiro steps vs. applied microwave power have been registered. Observed behavior deviates from existing theories of Josephson effect for junctions made from conventional or d-wave superconductors. Although the maximal size of the heterojunctions was smaller than the Josephson penetration depth, calculated from an averaged value of the critical current density, the experimental magnetic field dependences I C (H) deviate from the Fraunhofer pattern, pointing on non-uniform distribution of superconducting current density. Experimental results could be speculatively explained by origination of self-induced fractional magnetic vortices, which may take place in a junction where the amplitude and the phase of superconducting current alternate significantly over the junction area. Introducing a new lengthscale, which is much smaller than the Josephson penetration depth, the fractional vortices are considered, modifying the high frequency dynamics, namely the ac Josephson effect. Experimental results have been analyzed taking into account the second harmonic of superconducting current-phase relation and the influence of heterojunction capacitance. Introduction It is known that in metal-oxide superconductors with high critical temperature, for example in YBCO, the d-wave symmetry of superconducting order parameter (D-superconductor) is predominant one in the basal (a-b) plan
