  Magnon spin transport in a metal-antiferromagnetic insulator-ferromagnetic
insulator heterostructure is considered. The spin current is generated via the
spin Seebeck effect and in the limit of clean sample where the effects of
interface imperfections and lattice defects are excluded. For NiO as an
antiferromagnetic insulator we have a magnetic order of antiferromagnetically
combined planes which are internally in ferromagnetic order. We find that the
sign of the spin current depends on the magnetization direction of the plane
next to the metal resulting in an even-odd effect for the spin current.
Moreover, as long as damping is excluded, this even-odd effect is the only
remaining dependence on the NiO thickness for high temperatures.
