  Non-reciprocal propagation of sound, that is, the different transmission of
acoustic waves traveling along opposite directions, is a challenging
requirement for the realization of devices like acoustic isolators and
circulators. Here, we demonstrate the efficient non-reciprocal transmission of
surface acoustic waves (SAWs) propagating along opposite directions of a GaAs
substrate coated with an epitaxial Fe$_3$Si film. The non-reciprocity arises
from the acoustic attenuation induced by the magneto-elastic (ME) interaction
between the SAW strain field and spin waves in the ferromagnetic film, which
depends on the SAW propagation direction and can be controlled via the
amplitude and orientation of an external magnetic field. The acoustic
transmission non-reciprocity, defined as the difference between the transmitted
acoustic power for forward and backward propagation under ME resonance, reaches
values of up to 20%, which are, to our knowledge, the largest non-reciprocity
reported for SAWs traveling along a semiconducting piezoelectric substrate
covered by a ferromagnetic film. The experimental results are well accounted
for by a model for ME interaction, which also shows that non-reciprocity can be
further enhanced by optimization of the sample design. These results make
Fe$_3$Si/GaAs a promising platform for the realization of efficient
non-reciprocal SAW devices.
