  Cavity magnomechanics has recently become a new platform for studying
macroscopic quantum phenomena. The magnetostriction induced vibration mode of a
large-size ferromagnet or ferrimagnet reaching its ground state represents a
genuine macroscopic quantum state. Here we study the ground-state cooling of
the mechanical vibration mode in a cavity magnomechanical system, and focus on
the role of magnon squeezing in improving the cooling efficiency. The magnon
squeezing is obtained by exploiting the magnon self-Kerr nonlinearity. We find
that the magnon squeezing can significantly and even completely suppress the
magnomechanical Stokes scattering. It thus becomes particularly useful in
realizing ground-state cooling in the unresolved-sideband regime, where the
conventional sideband cooling protocols become inefficient. We also find that
the coupling to the microwave cavity plays only an adverse effect in mechanical
cooling. This makes essentially the two-mode magnomechanical system (without
involving the microwave cavity) a preferred system for cooling the mechanical
motion, in which the magnon mode is established by a uniform bias magnetic
field and a microwave drive field.
