  The rich and unconventional physics in layered 2D magnets can open new
avenues for topological magnonics and magnon valleytronics. In particular,
two-dimensional (2D) bilayer quantum magnets are gaining increasing attention
due to their intriguing stacking-dependent magnetism, controllable ground
states, and topological excitations induced by magnetic spin-orbit couplings
(SOCs). Despite the substantial research on these materials, their topological
features remain widely unexplored to date. The present study comprehensively
investigates the magnon topology and magnon valley-polarization in honeycomb
bilayers with collinear magnetic order. We elucidate the separate and combined
effects of the SOC, magnetic ground-states, stacking order, and inversion
symmetry breaking on the topological phases, magnon valley transport, and the
Hall and Nernst effects. The comprehensive analysis suggests clues to determine
the SOC's nature and predicts unconventional Hall and Nernst conductivities in
topologically trivial phases. We further report on novel bandgap closures in
layered antiferromagnets and detail their topological implications. We believe
the present study provides important insights into the fundamental physics and
technological potentials of topological 2D magnons.
