  We investigate coexistence of antiferromagnetic and superconducting
correlations in bilayered materials using a two-dimensional t-J model with
couplings across the layers using variational Monte Carlo calculations. It is
found that the underdoped regime supports a coexisting phase, beyond which the
(d-wave) superconducting state becomes stable. Further, the effects of
interplanar coupling parameters on the magnetic and superconducting
correlations as a function of hole doping are studied in details. The magnetic
correlations are found to diminish with increasing interplanar hopping away
from half filling, while the exchange across the layers strengthens interplanar
antiferromagnetic correlations both at and away from half filling. The
superconducting correlations show more interesting features where larger
interplanar hopping considerably reduces planar correlations at optimal doping,
while an opposite behaviour, i.e. stabilisation of the superconducting state is
realised in the overdoped regime, with the interplanar exchange all the while
playing a dormant role.
