  Frustrated quantum magnets not only provide exotic ground states and unusual
magnetic structures, but also support unconventional excitations in many cases.
Using a physically relevant spin model for a breathing pyrochlore lattice, we
discuss the presence of topological linear band crossings of magnons in
antiferromagnets. These are the analogs of Weyl fermions in electronic systems,
which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral
magnon surface states forming arcs at finite energy. We argue that such
antiferromagnets present a unique example in which Weyl points can be
manipulated in situ in the laboratory by applied fields. We discuss their
appearance specifically in the breathing pyrochlore lattice, and give some
general discussion of conditions to find Weyl magnons and how they may be
probed experimentally. Our work may inspire a re-examination of the magnetic
excitations in many magnetically ordered systems.
