  Motivated by recent experiments, we investigate the nonreciprocal
magnetoelastic interaction between the surface acoustic phonons of dielectric
non-magnetic substrates and magnons of proximity nanomagnets. The magnetization
dynamics exerts rotating forces at the edges of the nanomagnet that causes the
nonreciprocal interaction with surface phonons due to its rotation-momentum
locking. This coupling induces the nonreciprocity of the surface phonon
transmission and a nearly complete phonon diode effect by several (tens of)
magnetic nanowires of high (ordinary) magnetic quality. Phase-sensitive
microwave transmission is also nonreciprocal that can pick up clear signals of
the coherent phonons excited by magnetization dynamics. Nonreciprocal pumping
of phonons by precessing magnetization is predicted using Landauer-B\"uttiker
formalism.
