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Quantum conversion or interface is one of the most prominent protocols inquantum information processing and quantum state engineering. We propose aphoton-phonon conversion protocol in a hybrid magnomechanical system comprisinga microwave optical mode, a driven magnon mode and a mechanical-vibrating mode.The microwave photons in the optical cavity are coupled to the magnons by themagnetic-dipole interaction, and the latter are coupled to the mechanicalphonons by the magnetostrictive interaction. With strong photon-magnoninteraction and strong driving on magnon, an effective Hamiltonian isconstructed to describe the conversion between photons and phonons nearby theirresonant point. The cavity-magnon system can then play the role of a quantummemory. Moreover, the faithfulness of the photon-phonon conversion is estimatedin terms of fidelities for state evolution and state-independent transfer. Theformer is discussed in the Lindblad master equation taking account the leakagesof photon, phonon and magnon into consideration. The latter is derived by theHeisenberg-Langevin equation considering the non-Markovian noise from thestructured environments for both optical and mechanical modes. Thestate-evolution fidelity is found to be robust to the weak leakage. Thetransfer fidelity can be maintained by the Ohmic and sub-Ohmic environments ofthe photons and is insensitive to the $1/f$ noise of the phonons. Our work thusprovides an interesting application for the magnon system as a photon-phononconverter in the microwave regime.

Magnon-assisted photon-phonon conversion in the presence of the structured environments