Magnon dispersion in bilayers of two-dimensional ferromagnets

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