  We investigate the magnetic and transport properties of the
$La_{1-x}Sr_{x}MnO_{3}$ (LSMO)/$Pr_{1-x}Ca_{x}MnO_{3}$ (PCMO) like
ferromagnetic/antiferromagnetic superlattices in three dimensions using a two
orbitals double exchange model incorporating the Jahn-Teller lattice
distortions, superexchange interactions and long-range Coulomb interactions. In
our simulations we primarily focus on periodic arrangement of $w_L$ planes of
ferromagnetic LSMO and $w_P$ planes of antiferromagnetic PCMO manganites, and
set $w_L$+$w_P$ = 10. The induced ferromagnetic correlations in the parent PCMO
layer decreases monotonically with increasing the PCMO layer width $w_P$ at
high temperatures for both half-doping ($n =0.5$) and off-half-doping ($n =
0.55$) scenarios. As we decrease the temperature further the induced
ferromagnetic moments in PCMO layer disappears or decreases considerably at
half-doping due to the onset of charge ordering in antiferromagnetic PCMO
layers. Overall, the magnetization in PCMO layer decreases at low temperatures
and the metal-insulator transition temperature of the LSMO/PCMO superlattices
increases with increase of the PCMO layer width $w_P$, similar to the
experiments. On the other hand, at off-half-doping, the induced ferromagnetic
moment survives even at low temperatures due to weakened charge ordering in
PCMO layer and interestingly, varies nonmonotonically with PCMO layer width, in
agreement with experiments. The nonmonotonic trend of the conductivity of the
superlattice with increase of the PCMO layer width $w_P$ shows an one-to-one
correspondence between conductivity of the superlattice and the induced
ferromagnetic moments in the PCMO layer. We highlight the key role of induced
ferromagnetic moment in PCMO layer in analyzing the magnetotransport properties
of the LSMO/PCMO superlattices.
