  We analyze resonant magneto-elastic interactions between standing
perpendicular spin wave modes (exchange magnons) and longitudinal acoustic
phonon modes in free-standing hybrid metal-ferromagnet bilayer and trilayer
structures. Whereas the ferromagnetic layer acts as a magnetic cavity, all
metal layers control the frequencies and eigenmodes of acoustic vibrations. The
here proposed design allows for achieving and tuning the spectral and spatial
modes overlap between phonons and magnons that results in their strong resonant
interaction. Realistic simulations for gold-nickel multilayers show that
sweeping the external magnetic field should allow for observing resonantly
enhanced interactions between individual magnon and phonon modes in a broad
range of frequencies spanning from tens of GHz up to several hundreds of GHz,
which can be finely tuned through the multilayer design. Our results would
enable the systematic study and the deep understanding of resonantly enhanced
magneto-elastic coupling between individual phonon and magnon modes up to
frequencies of great contemporary fundamental and applied interest.
