  The recently developed hybrid magnonics provides new opportunities for
advances in both the study of magnetism and the development of quantum
information processing. However, engineering coherent quantum state transfer
between magnons and specific information carriers, in particular, mechanical
oscillators and solid-state spins, remains challenging due to the intrinsically
weak interactions and the frequency mismatch between diffrent components. Here,
we show how to strongly couple the magnon modes in a nanomagnet to the
quantized mechanical motion (phonons) of a micromechanical cantilever in a
hybrid tripartite system. The coherent and enhanced magnon-phonon coupling is
engineered by introducing the quantum parametric amplifiation of the mechanical
motion. With experimentally feasible parameters, we show that the mechanical
parametric drive can be adjusted to drive the system into the strong-coupling
regime and even the ultrastrong-coupling regime. Furthermore, we show the
coherent state transfer between the nanomagnet and a nitrogen-vacancy center in
the dispersive-coupling regime, with the magnon-spin interaction mediated by
the virtually-excited squeezed phonons. The amplifid mechanical noise can
hardly interrupt the coherent dynamics of the system even for low mechanical
quality factors, which removes the requirement of applying additional
engineered-reservoir techniques. Our work opens up prospects for developing
novel quantum transducers, quantum memories and high-precision measurements.
