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SHORTENED ABSTRACT: We study numerically the properties of spin- andcharge-transport in a nanoscale diffusivesuperconductor$\mid$ferromagnet$\mid$superconductor junction when themagnetization texture is non-uniform. Specifically, we incorporate the presenceof a Bloch/Neel domain walls and conical ferromagnetism, including spin-activeinterfaces. The superconducting leads are assumed to be of s-wave type. Weinvestigate how the 0-$\pi$ transition is influenced by the inhomogeneousmagnetization texture and focus on the particular case where the charge-currentvanishes while the spin-current is non-zero. In the case of a Bloch/Neeldomain-wall, the spin-current can be seen only for one component of the spinpolarization, whereas in the case of conical ferromagnetism the spin-currenthas the three components. We explain all of these results in terms of theinterplay between the triplet anomalous Green's function induced in theferromagnetic region and the local direction of the magnetization vector in theferromagnet. Interestingly, we find that the spin-current exhibitsdiscontinuous jumps at the 0--$\pi$ transition points of the criticalcharge-current. We explain this result in terms of the different symmetryobeyed by the current-phase relation when comparing the charge- andspin-current. Specifically, we find that whereas the charge-current obeys thewell-known relation $I_c(\phi) = -I_c(2\pi-\phi)$, the spin-current satisfies$I_s(\phi) = I_s(2\pi-\phi)$, where $\phi$ is the superconducting phasedifference.

Spin-polarized Josephson current in SFS junctions with inhomogeneous magnetization