  We study the magnon bands of twisted bilayer honeycomb quantum magnets using
linear spin wave theory. Although the interlayer coupling can be ferromagnetic
or antiferromagnetic, we keep the intralayer one ferromagnetic to avoid
possible frustration. For the interlayer ferromagnetic case, we find the magnon
bands have similar features with the corresponding electronic energy spectrums.
Although the linear dispersions near the Dirac points are preserved in the
magnon bands of twisted bilayer magnets, their slopes are graduately reduced
with the decrease of the twist angles. On the other hand, the interlayer
antiferromagnetic couplings generate quite different magnon spectra. The two
single-layered magnon spectra are usually undecoupled due to the opposite
orientations of the spins in the two layers. We also develop a low-energy
continuous theory for very small twist angles, which has been verified to fit
well with the exact tight-binding calculations. Our results may be
experimentally observed due to the rapid progress in two-dimensional magnetic
materials.
