  We use a surface acoustic wave (SAW) cavity resonator to study the coupling
of acoustic magnons in a synthetic antiferromagnet (SAF) and the phonons
carried by SAWs. The SAF is composed of a CoFeB/Ru/CoFeB trilayer and the
scattering matrix of the SAW resonator is studied to assess the coupling. We
find that the spectral linewidth of the SAW resonator is modulated when the
frequency of the excited magnons approaches the SAW resonance frequency.
Moreover, the linewidth modulation varies with the magnitude and orientation of
the external magnetic field. Such change in the spectral linewidth can be well
reproduced using macrospin-like model calculations. From the model analyses, we
estimate the magnon-phonon coupling strength to be $\sim$15.6 MHz at a SAW
resonance frequency of 1.8 GHz: the corresponding magnomechanical cooperativity
is $\sim$0.66. As the spectral shape hardly changes in a CoFeB single layer
reference sample under the same experimental condition, these results show that
SAF provides an ideal platform to study magnon-phonon coupling in a SAW cavity
resonator.
