Cavity magnomechanics has become an ideal platform to explore macroscopic
quantum effects. Bringing together magnons, phonons, and photons in a single
physical system, it opens many opportunities for quantum technologies. It was
conventionally realized by a yttrium iron garnet, which exhibits a linear
magnon-phonon coupling m^†m^(b^†+b^), with
m^ and b^ being the magnon and phonon modes. Inspired by the
recent realization of two-dimensional (2D) magnets, we propose a new cavity
magnomechanical system with one of the cavity mirror formed by a 2D magnetic
material. Its anisotropic magnetostrictive interaction induces a unique
nonlinear phonon-magnon coupling m^†m^(b^†+b^)2.
It is found that 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.Comment: 7 pages and 3 figures in the main text. 3 pages in the supplemental
materia