  We consider a two-dimensional opto-magnomechanical (OMM) system including two
optical cavity modes, a magnon mode, a phonon mode, and a collection of
two-level atoms. In this study, we demonstrate the methodology for generating
stationary entanglement between two-level atoms and magnons, which are
implemented using two optical cavities inside the setup. Additionally, we
investigate the efficiency of transforming entanglement from atom-phonon
entanglement to atom-magnon entanglement. The magnons are stimulated by both a
bias magnetic field and a microwave magnetic field, and they interact with
phonons through the mechanism of magnetostrictive interaction. This interaction
generates magnomechanical displacement, which couples to an optical cavity via
radiation pressure. We demonstrate that by carefully selecting the frequency
detuning of an optical cavity, it is possible to achieve an increase in
bipartite entanglements. Furthermore, this improvement is found to be resistant
to changes in temperature. The entanglement between atoms and magnons plays a
crucial role in the construction of hybrid quantum networks. Our modeling
approach exhibits potential applications in the field of magneto-optical trap
systems as well.
