  Surface Acoustic Waves (SAW) have been used frequently in spintronic
applications, mostly to decrease the magnetic field or the electric current
required to move magnetic domain walls (DW). Because the SAW cannot achieve
magnetic switching without the assistance of a magnetic field or a current, for
a marginal improvement in the energy required for the magnetic switching, the
device gains in complexity, making it impractical. In this work, we report a
mechanism that allows a transfer of linear momentum from the acoustic wave to
the magnetic domain wall. Experimentally we show that, using the appropriate
dimensions of the magnetic strip, the SAW can move the DW in the same direction
as the traveling SAW. With the help of micromagnetic simulations, we reveal a
complex yet direct mechanism that allows the SAW to push the DW in the same
direction of its travel, even without any external field or currents. The DW
can reach velocities in the range of 100 m/s and at a very small energetic
cost, equivalent to using a current density of $\sim 5 \cdot 10^4 A/cm^2$ if
the movement was triggered by spin transfer. This new mechanism opens the door
to designing innovative spintronic devices where the magnetization can be
controlled exclusively by an acoustic wave.
