  We study the interaction of surface acoustic waves with spin waves in
ultra-thin CoFeB/Pt bilayers. Due to the interfacial Dzyaloshinskii-Moriya
interaction (DMI), the spin wave dispersion is non-degenerate for oppositely
propagating spin waves in CoFeB/Pt. In combination with the additional
nonreciprocity of the magnetoacoustic coupling itself, highly nonreciprocal
acoustic wave transmission through the magnetic film is observed. We
systematically characterize the magnetoacoustic wave propagation in a thickness
series of CoFeB($d$)/Pt samples as a function of magnetic field magnitude and
direction, and at frequencies up to 7 GHz. We quantitatively model our results
to extract the strength of the DMI and magnetoacoustic driving fields.
