  We construct a hybrid cavity magnomechanical system to transfer the bipartite
entanglements and achieve the strong microwave photon-phonon entanglement based
on the reservoir engineering approach. The magnon mode is coupled to the
microwave cavity mode via magnetic dipole interaction, and to the phonon mode
via magnetostrictive force (optomechanical-like). It is shown that the initial
magnon-phonon entanglement can be transferred to the photon-phonon subspace in
the case of these two interactions cooperating. In reservoir-engineering
parameter regime, the initial entanglement is directionally transferred to the
photon-phonon subsystem, so we obtain a strong bipartite entanglement in which
the magnon mode acts as the cold reservoir to effectively cooling the
Bogoliubov mode delocalized over the cavity and the mechanical deformation
mode. Moreover, as the dissipation ratio between the cold reservoir mode and
the target mode increases, we can achieve greater quantum entanglement and
better cooling effect. Our results indicate that the steady-state entanglement
is robust against temperature. The scheme may provides potential applications
for quantum information processing, and is expected to be extended to other
three-mode systems.
