  We present a proposal to test Bell inequality in the emerging field of cavity
optomagnonics, where a sphere of ferromagnetic crystal supports two optical
whispering gallery modes and one magnon mode. The two optical modes are driven
by two laser pulses, respectively. Entanglement between magnon mode and one of
the two optical modes will be generated by the first pulse, and the state of
magnon mode is subsequently mapped into another optical mode via the second
pulse. Hence correlated photon-photon pairs is created out of the cavity. A
Bell test can be implemented using these pairs, which enables us to test local
hidden-variable models at macroscopic optomagnonical system. Our results show
that a significant violation of Bell inequality can be obtained in the
experimentally relevant weak-coupling regime. The violation of Bell inequality
not only verifies the entanglement between magnons and photons, but also
implies that cavity optomagnonics is a promising platform for quantum
information processing tasks.
