Abstract
The spin superconductor state is the spin-polarized triplet exciton condensate,which can be viewed as a counterpart of the charge superconductor state.As an analogy of the charge Josephson effect,the spin Josephson effect can be generated in the spin superconductor/normal metal/spin superconductor junctions.Here we study the spin supercurrent in the Joseph-son junctions consisting of two spin superconductors with noncollinear spin polarizations.For the Josephson junctions with out-of-plane spin polarizations,the possible π-state spin supercurrent appears due to the Fermi momentum-splitting Andreev-like reflections at the normal metal/spin superconductor interfaces.For the Josephson junctions with in-plane spin polarizations,the anomalous spin supercurrent appears and is driven by the misorientation angle of the in-plane polariza-tions.The symmetry analysis shows that the appearance of the anomalous spin Josephson current is possible when the combined symmetry of the spin rotation and the time reversal is broken.