  Magnon-phonon hybrid excitations are studied theoretically in a
two-dimensional antiferromagnet with an easy axis normal to the plane. We show
that two magnon bands and one phonon band are intertwined by the magnetoelastic
coupling through a nontrivial SU(3) topology, which can be intuitively
perceived by identifying a skyrmion structure in the momentum space. We develop
a continuum theory as the long-wavelength approximation to the tight-binding
model, showing our results are insensitive to lattice details and generally
applicable to two-dimensional antiferromagnets. The theoretical results can be
probed by measuring the thermal Hall conductance as a function of the
temperature and the magnetic field. We envision that the magnetoelastic
coupling in antiferromagnets can be a promising venue in search of various
topological excitations, which cannot be found in magnetic or elastic models
alone.
