  A magnon spin-orbit coupling, induced by the dipole-dipole interaction, is
derived in monoclinic-stacked bilayer honeycomb spin lattice with perpendicular
magnetic anisotropy and antiferromagnetic interlayer coupling. Linear crossings
are predicted in the magnon spectrum around the band minimum in G valley, as
well as in the high frequency range around the zone boundary. The linear
crossings in K and K' valleys, which connect the acoustic and optical bands,
can be gapped when the intralayer dipole-dipole or Kitaev interactions exceed
the interlayer dipole-dipole interaction, resulting in a phase transition from
semimetal to insulator. Our results are useful for analyzing the magnon spin
dynamics and transport properties in van der Waals antiferromagnet.
