  We numerically study the acoustic parametric amplification of spin waves
using surface acoustic waves (SAW) in a magnetic thin film. First, we
illustrate how the process of parametric spin-wave generation using short-waved
SAWs with a fixed frequency allows to tune frequencies of the generated spin
waves by the applied magnetic field. We further present the amplification of
microwave driven spin waves using this method. The decay length and the
amplitude of the driven spin waves can be amplified up to approximately 2.5 and
10 times compared to the reference signal, respectively. More importantly, the
proposed design can be used as a frequency converter, in which a low (high)
frequency spin-wave mode stimulates the excitation of a high (low) frequency
mode. Our results pave the way in designing highly flexible and efficient
hybrid magnonic device architectures for microwave data transport and
processing.
