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Spin current and spin accumulation near a Josephson junction between a singlet and triplet superconductor

We consider a Josephson junction with an arbitrary transmission coefficient $\mathcal{D}$ between a singlet and a triplet superconductor with the latter order parameter characterized by a d-vector of the form ($k_x\hat{y}-k_y\hat{x}$). Various quantities such as the tunnelling current, spin accumulation, and spin current are calculated via the quasiclassical Green's functions. We also present a symmetry argument on the existence of these quantities and their dependencies on the phase difference across the junction. A physical picture is also given in terms of the Andreev states near the junction.