Magnomechanically induced transparency in the ferrimagnetic bridge crystal of atom opto-magnomechanical system

We investigate the absorption and transmission properties of a weak probe field in an atom opto-magnomechanics system. The system comprises an assembly of two-level atoms and a magnon mode within a ferrimagnetic crystal, which directly interacts with an optical cavity mode through the crystal's deformation displacement. We observe optomechanically induced transparency (OMIT) via radiation pressure and a magnomechanically induced transparency (MMIT) due to the nonlinear magnon-phonon interaction. In addition, due to the coupling of the atom to the detected and signal light, the system's width transparency window is divided into two narrow windows. Additionally, we demonstrate that the group delay is contingent upon the tunability of the magnon-phonon coupling strength. Our solution possesses significant in the field of quantum precision measurement.