  Magnet-superconductor hybrid (MSH) systems are a key platform for
custom-designed topological superconductors. Ideally, the ends of a
one-dimensional MSH structure will host Majorana zero-modes (MZMs), the
fundamental unit of topological quantum computing. However, some of the
experiments with ferromagnetic chains show a more complicated picture. Due to
tiny gap sizes and hence long coherence lengths MZMs might hybridize and lose
their topological protection. Recent experiments on a niobium surface have
shown that both ferromagnetic and antiferromagnetic chains may be engineered,
with the magnetic order depending on the crystallographic direction of the
chain. While ferromagnetic chains are well understood, antiferromagnetic chains
are less so. Here we study two models inspired by the niobium surface: a
minimal model to elucidate the general topological properties of
antiferromagnetic chains, and an extended model to more closely simulate a real
system by mimicking the proximity effect. We find that in general for
antiferromagnetic chains the topological gap is larger than for ferromagnetic
ones and thus coherence lengths are shorter for antiferromagnetic chains,
yielding more pronounced localization of MZMs in these chains. While
topological phases for both ferromagnetic and antiferromagnetic chains both
depend on the magnetic moment of the adatoms and the chemical potential, we
find that antiferromagnetic chains also have a strong dependence on the
magnitude of Rashba spin-orbit coupling at the surface.
