  Topological electronics has extended its richness to non-electronic systems
where phonons and magnons can play the role of electrons. In particular,
topological phases of magnons can be enabled by the Dzyaloshinskii-Moriya
interaction (DMI) which acts as an effective spin-orbit coupling. We show that
besides DMI, an alternating arrangement of Heisenberg exchange interactions
critically determines the magnon band topology, realizing a magnonic analog of
the Su-Schrieffer-Heeger model. On a honeycomb ferromagnet with perpendicular
anisotropy, we calculate the topological phase diagram, the chiral edge states,
and the associated magnon Hall effect by allowing the relative strength of
exchange interactions on different links to be tunable. Including weak
phonon-magnon hybridization does not change the result. Candidate materials are
discussed.
