  The modulation of charge density and spin order in
(LaMnO$_3$)$_{2n}$/(SrMnO$_3$)$_n$ ($n$=1-4) superlattices is studied via Monte
Carlo simulations of the double-exchange model. G-type antiferromagnetic
barriers in the SrMnO$_{3}$ regions with low charge density are found to
separate ferromagnetic LaMnO$_{3}$ layers with high charge density. The
recently experimentally observed metal-insulator transition with increasing $n$
is reproduced in our studies, and $n=3$ is found to be the critical value.
