  Cavity magnomechanics has become an ideal platform to explore macroscopic
quantum effects. Bringing together magnons, phonons, and photons in a system,
it opens many opportunities for quantum technologies. It was conventionally
realized by an yttrium iron garnet, which exhibits a parametric magnon-phonon
coupling $\hat{m}^\dag\hat{m}(\hat{b}^\dag+\hat{b})$, with $\hat{m}$ and
$\hat{b}$ being the magnon and phonon modes. Inspired by the recent realization
of two-dimensional (2D) magnets, we propose a cavity magnomechanical system
using a 2D magnetic material with both optical and magnetic drivings. It
features the coexisting photon-phonon radiation-pressure coupling and quadratic
magnon-phonon coupling $\hat{m}^\dag\hat{m}(\hat{b}^\dag+\hat{b})^2$ induced by
the magnetostrictive interaction. A stable squeezing of the phonon and bi- and
tri-partite entanglements among the three modes are generated in the regimes
with a suppressed phonon number. Compared with previous schemes, ours does not
require any extra nonlinear interaction and reservoir engineering and is robust
against the thermal fluctuation. Enriching the realization of cavity
magnomechanics, our system exhibits its superiority in quantum-state
engineering due to the versatile interactions enabled by its 2D feature.
