  We report large nonreciprocity in the transmission of shear-horizontal
surface acoustic waves (SAWs) on LiTaO3 substrate coated with a FeCoSiB/NiFeCu
magnetoelastic bilayer. The large difference in saturation magnetization of the
two layers not only brings nonreciprocal spin waves (SWs), but also ensures the
phonon-magnon (SAWs-SWs) coupling at relatively low wavenumbers. It is found
that the angle between the magnetization and the wavevector play important
roles in determining the strength of magnetoelastic coupling and
nonreciprocity, simultaneously. A large nonreciprocal transmission of SAWs
about 30 dB (i.e. 60 dB/mm) is demonstrated at 2.33 GHz. In addition, the
dispersion relation between coupled SH-SAWs and nonreciprocal SWs is developed,
which provide a good insight into the observed phenomena. Our results offer a
convenient approach to implement nonreciprocal SAW isolators or circulators.
