  Skyrmions are topologically nontrivial, magnetic quasi-particles, that are
characterized by a topological charge. A regular array of skyrmions - a
skyrmion crystal (SkX) - features the topological Hall effect (THE) of
electrons, that, in turn, gives rise to the Hall effect of the skyrmions
themselves. It is commonly believed that antiferromagnetic skyrmion crystals
(AFM-SkXs) lack both effects. In this Rapid Communication, we present a
generally applicable method to create stable AFM-SkXs by growing a two
sublattice SkX onto a collinear antiferromagnet. As an example we show that
both types of skyrmion crystals - conventional and antiferromagnetic - exist in
honeycomb lattices. While AFM-SkXs with equivalent lattice sites do not show a
THE, they exhibit a topological spin Hall effect. On top of this, AFM-SkXs on
inequivalent sublattices exhibit a nonzero THE, which may be utilized in
spintronics devices. Our theoretical findings call for experimental
realization.
