We study the frequency non-reciprocity of the spin waves in symmetric
CoFeB/Ru/CoFeB synthetic antiferromagnets stacks set in the scissors state by
in-plane applied fields. Using a combination of Brillouin Light Scattering and
propagating spin wave spectroscopy experiments, we show that the acoustical
spin waves in synthetic antiferromagnets possess a unique feature if their
wavevector is parallel to the applied field: the frequency non-reciprocity can
be so large that the acoustical spin waves transfer energy in a unidirectional
manner for a wide and bipolar interval of wavevectors. Analytical modeling and
full micromagnetic calculations are conducted to account for the dispersion
relations of the optical and acoustical spin waves for arbitrary field
orientations. Our formalism provides a simple and direct method to understand
and design devices harnessing propagating spin waves in synthetic
antiferromagnets