  The effect of antiferromagnetic spin fluctuations on two-dimensional
quarter-filled systems is studied theoretically. An effective $t-J'-V$ model on
a square lattice which accounts for checkerboard charge fluctuations and
next-nearest-neighbors antiferromagnetic spin fluctuations is considered. From
calculations based on large-N theory on this model it is found that the
exchange interaction, $J'$, increases the attraction between electrons in the
d$_{xy}$ channel only, so that both charge and spin fluctuations work
cooperatively to produce d$_{xy}$ pairing.
