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We report a theoretical study of the equilibrium spin current (ESC) flowing in a ferromagnet/ferromagnet (FM/FM) graphene junction with noncollinear magnetizations, in which the FM correlation in graphene is induced by depositing an FM insulator on it. Using the scattering matrix method, we derived an analytical expression of the ESC which is formally the same as that of a normal FM/FM junction. The ESC comes from the exchange coupling between the two FM magnetizations. Owing to the linear dispersion of graphene, the ESC disappears in the one-dimensional case, while it exists in the two-dimensional case. It exhibits damped oscillations with change in the Fermi energy, the layer length between the two FM regions, and the FM exchange splitting. It is also found that ESC in FM/FM graphene junctions has electron-hole inversion symmetry whereas it has electron-hole inversion antisymmetry in normal FM/FM junctions.

We investigate theoretically the equilibrium transverse charge and spin currents flowing in a hybrid Josephson junction composed of two triplet p-wave superconductors and a Rashba spin-orbit coupling (RSOC) layer in between. Through a symmetry analysis, we show that the transverse currents originate from the breaking of mirror symmetries due to the misalignment of d-vectors in the two triplet superconductor leads. Besides, the mirror symmetries strongly constrain the dependence of the transverse currents on both the absolute and relative angles of the d-vectors. The symmetry analysis is confirmed by the numerical calculations based on the lattice Matsubara Green's function method. The dependence of the transverse currents on the RSOC strength as well as the middle layer length is also addressed. These findings shed new light on the equilibrium spintronics device design and are useful for identifying the order parameter symmetries of p-wave superconductors.