  We determine magnon spectra of an atomic bilayer magnet with ferromagnetic
intra- and both ferro- and anti- ferromagnetic interlayer coupling. Analytic
expressions for the full magnon band of the latter case reveal that both
exchange interactions govern the fundamental magnon gap. The inter and
intralayer magnetic ordering are not independent: the intralayer ferromagnetism
stabilizes antiferromagnetic inter-layer order. The topology of these
exchange-anisotropy spin models without spin-orbit interaction turns out to be
trivial.
