Magnetic properties of Sr$_{3-x}$Y$_{x}$(Fe$_{1.25}$Ni$_{0.75}$)O$_{7-\delta}$: A combined experimental and theoretical investigation

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 $T_N$.