  Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in
antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially
periodic noncollinear magnetic texture gives rise to topological bulk magnon
bands characterized by nonzero Chern numbers. We find topologically-protected
chiral magnonic edge states over a wide range of magnetic fields and
Dzyaloshinskii-Moriya interaction values. Moreover, and of particular
importance for experimental realizations, edge states appear at the lowest
possible energies, namely, within the first bulk magnon gap. Thus,
antiferromagnetic skyrmion crystals show great promise as novel platforms for
topological magnonics.
