We study the phase of the coupling between magnons and surface acoustic wave (SAW) phonons in magnetic thin films. The coupling constant changes from a real to a complex number as the external magnetic field is reduced. Below a transition field, the imaginary coupling constant allows SAW phonons to couple to overdamped magnons whose resonance frequency is close to zero and far from the SAW resonance. The strength of the imaginary coupling constant and the magnitude of the transition field both scale with magnetic damping. We find the coupling produces a broad, pronounced minimum in the SAW transmittance spectrum near zero magnetic field in a Ni/Ru/Ni synthetic antiferromagnet with large magnetic damping. These results demonstrate that the phase of the complex magnon-phonon coupling constant can be tuned via magnetic field in strongly damped magnets, offering a platform to explore novel regimes of magnon-phonon interactions.

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• Acoustic phonons
• Magnetoacoustic effect
• Magnetoelastic effect
• Magnons
• Quasiparticles & collective excitations
• Spin dynamics
• Spin waves