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Abstract We have carried out an experimental investigation of the spin-wave dynamics in the Au/CoFeB/Au multilayer consisting of a ferromagnetic film with thicknesses of 0.8, 0.9 and 1.0 nm. We employed the Brillouin light scattering spectroscopy to measure the frequency of the spin waves in dependence on the wave vector. Additionally, we characterized the samples by ferromagnetic resonance measurements. We found that the considered samples exhibit perpendicular magnetic anisotropy with low damping, indicating small pumping effects. Furthermore, we found a nonreciprocal dispersion relation pointing at a non-negligible Dzyaloshinskii–Moriya interaction. These results make the Au/CoFeB/Au multilayer a compelling subject for further analysis and as a potential material for future applications within magnonics.