  We present a scheme to entangle two microwave fields by using the nonlinear
magnetostrictive interaction in a ferrimagnet. The magnetostrictive interaction
enables the coupling between a magnon mode (spin wave) and a mechanical mode in
the ferrimagnet, and the magnon mode simultaneously couples to two microwave
cavity fields via the magnetic dipole interaction. The magnon-phonon coupling
is enhanced by directly driving the ferrimagnet with a strong red-detuned
microwave field, and the driving photons are scattered onto two sidebands
induced by the mechanical motion. We show that two cavity fields can be
prepared in a stationary entangled state if they are respectively resonant with
two mechanical sidebands. The present scheme illustrates a new mechanism for
creating entangled states of optical fields, and enables potential applications
in quantum information science and quantum tasks that require entangled
microwave fields.
