  We present a scheme to entangle two magnon modes in a cavity magnomechanical
system. The two magnon modes are embodied by collective motions of a large
number of spins in two macroscopic ferrimagnets, and couple to a single
microwave cavity mode via magnetic dipole interaction. We show that by
activating the nonlinear magnetostrictive interaction in one ferrimagnet,
realized by driving the magnon mode with a strong red-detuned microwave field,
the two magnon modes can be prepared in an entangled state. The entanglement is
achieved by exploiting the nonlinear magnon-phonon coupling and the linear
magnon-cavity coupling, and is in the steady state and robust against
temperature. The entangled magnon modes in two massive ferrimagnets represent
genuinely macroscopic quantum states, and may find applications in the study of
macroscopic quantum mechanics and quantum information processing based on
magnonics.
