  Nonreciprocity, i.e. inequivalence in amplitudes and frequencies of spin
waves propagating in opposite directions, is a key property underlying
functionality in prospective magnonic devices. Here we demonstrate
experimentally and theoretically a simple approach to induce frequency
nonreciprocity in a magnetostatically coupled ferromagnetic bilayer structure
with a nonmagnetic spacer by its geometrical asymmetry. Using Brillouin light
scattering, we show the formation of two collective spin wave modes in
Fe$_{81}$Ga$_{19}$/Cu/Fe$_{81}$Ga$_{19}$ structure with different thicknesses
of ferromagnetic layers. Experimental reconstruction and theoretical modeling
of the dispersions of acoustic and optical collective spin wave modes reveal
that both possess nonreciprocity reaching several percent at the wavenumber of
$22~\cdot~10^4$ rad cm$^{-1}$. The analysis demonstrates that the shift of the
amplitudes of counter-propagating coupled modes towards either of the layers is
responsible for the nonreciprocity because of the pronounced dependence of spin
wave frequency on the layers thickness. The proposed approach enables the
design of multilayered ferromagnetic structures with a given spin wave
dispersion for magnonic logic gates.
