  Magnetic excitation in a spin dimer system on a bilayer honeycomb lattice is
investigated in the presence of a zigzag edge, where disordered and ordered
phases can be controlled by a quantum phase transition. In analogy with the
case of graphene with a zigzag edge, a flat edge magnon mode appears in the
disordered phase. In an ordered phase, a finite magnetic moment generates a
mean-field potential to the magnon. Since the potential is nonuniform on the
edge and bulk sites, it affects the excitation, and the dispersion of the edge
mode deviates from the flat shape. We investigate how the edge magnon mode
evolves when the phase changes through the quantum phase transition and discuss
the similarities to ordered spin systems on a monolayer honeycomb lattice.
