  In this paper, the spin transfer between two ferromagnetic insulators is
studied. There is a narrow gap between the ferromagnetic insulators so that
they are weakly interacting with each other. One of the ferromagnetic
insulators is moving at a constant speed while the other is at rest; hence, the
system is out of equilibrium. In the presence of the shearing motion, the
interaction amplitude is periodically modulated at the Doppler frequency. A
unitary transformation allows us to regard the periodic modulation of the
interaction amplitude as an effective potential, which drives the spin
transfer. The amount of the spin current is controlled by the spectral overlap
and the carrier population difference between the two ferromagnetic media. If
the spectra of the two ferromagnets are moderately broadened, the overlap in
the spectral domain increases, enlarging the spin current. However, too much
broadening spoils the spectral overlap and, hence, the spin current. This
implies that there is an optimal condition for maximising the spin transfer.
