  We present a comprehensive study of the magnetic properties of
Sr$_{3-x}$Y$_{x}$(Fe$_{1.25}$Ni$_{0.75}$)O$_{7-\delta}$ ($0 \leq x \leq 0.75$).
Experimentally, the magnetic properties are investigated using superconducting
quantum interference device (SQUID) magnetometry and neutron powder diffraction
(NPD). This is complemented by the theoretical study based on density
functional theory as well as the Heisenberg exchange parameters. Experimental
results show an increase in the N\'eel temperature ($T_N$) with the increase of
Y concentrations and O occupancy. The NPD data reveals all samples are
antiferromagnetically ordered at low temperatures, which has been confirmed by
our theoretical simulations for the selected samples. Our first-principles
calculations suggest that the 3D magnetic order is stabilized due to finite
inter-layer exchange couplings. The latter give rise to a finite inter-layer
spin correlations which disappear above the $T_N$.
