  We theoretically investigate the transport of magnon orbitals in a honeycomb
antiferromagnet. We find that the magnon orbital Berry curvature is finite even
without spin-orbit coupling and thus the resultant magnon orbital Hall effect
is an intrinsic property of the honeycomb antiferromagnet rooted only in the
exchange interaction and the lattice structure. Due to the intrinsic nature of
the magnon orbital Hall effect, the magnon orbital Nernst conductivity is
estimated to be orders of magnitude larger than the predicted values of the
magnon spin Nernst conductivity that requires finite spin-orbit coupling. For
the experimental detection of the predicted magnon orbital Hall effect, we
invoke the magnetoelectric effect that couples the magnon orbital and the
electric polarization, which allows us to detect the magnon orbital
accumulation through the local voltage measurement. Our results pave a way for
a deeper understanding of the topological transport of the magnon orbitals and
also its utilization for low-power magnon-based orbitronics, namely magnon
orbitronics.
