For certain nonmagnetic solids with low symmetry the occurrence of spin-polarized longitudinal currents is
predicted. These arise due to an interplay of spin-orbit interaction and the particular crystal symmetry. This
result is derived using a group-theoretical scheme that allows investigating the symmetry properties of any
linear response tensor relevant to the field of spintronics. For the spin conductivity tensor it is shown that only the
magnetic Laue group has to be considered in this context.Within the introduced general scheme also the spin Hall
and additional related transverse effects emerge without making reference to the two-current model. Numerical
studies confirm these findings and demonstrate for (Au1−xPtx )4Sc that the longitudinal spin conductivity may be
on the same order of magnitude as the conventional transverse one. The presented formalism only relies on the
magnetic space group and therefore is universally applicable to any type of magnetic order.