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We consider two types of magnetic Josephson junctions~(JJ). They are formedby two singlet superconductors~S and magnetic layers between them so that theJJ is a heterostructure of the S$_{\text{m}}$/n/S$_{\text{m}}$ type,where~S$_{\text{m}}$ includes two magnetic layers with non-collinearmagnetization vectors. One layer is represented by a weak ferromagnet andanother one---the spin filter---is either conducting strong ferromagnet(nematic or N\nobreakdash-type JJ) or magnetic tunnel barrier withspin-dependent transparency (magnetic or M\nobreakdash-type JJ). Due to spinfiltering only fully polarized triplet component penetrates the normal n~wireand provides the Josephson coupling between the superconductors~S. Althoughboth filters let to pass triplet Cooper pairs with total spin~$\mathbf{S}$parallel to the filter axes, the behavior of nematic and magnetic JJs iscompletely different. Whereas in the nematic case the charge and spincurrents,~$I_{\text{Q}}$ and~$I_{\text{sp}}$, do not depend on mutualorientation of the filter axes, both currents vanish in magnetic~JJ in case ofantiparallel filter axes, and change sign under reversing the filter direction.The obtained expressions for~$I_{\text{Q}}$ and~$I_{\text{sp}}$ show clearly aduality between the superconducting phase~$\varphi$ and the angle~$\alpha$between the exchange fields in the weak magnetic layers.

Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics