The 3$d$-5$d$ based double perovskites offer an ideal playground to study the interplay between electron correlation ($U$) and spin-orbit coupling (SOC) effect, showing exotic physics. The Sr$_2$FeIrO$_6$ is an interesting member in this family with ionic distribution of Fe$^{3+}$ (3$d^5$) and Ir$^{5+}$ (5$d^4$) where the later is believed to be nonmagnetic under the picture of strong SOC. Here, we report detailed investigation of structural, magnetic and electronic transport properties along with electronic structure calculations in (Sr$_{1-x}$Ca$_x$)$_2$FeIrO$_6$ series with $x$ from 0 to 1. While the basic interactions such as, $U$ and SOC are unlikely to be modified but a structural modification is expected due to ionic size difference between Sr$^{2+}$ and Ca$^{2+}$ which would influence other properties such as crystal field effect and band widths. While a nonmonotonic changes in lattice parameters are observed across the series, the spectroscopic investigations reveal that 3+/5+ charge state of Fe/Ir continue till end of the series. An analysis of magnetic data suggests similar nonmonotonic evolution of magnetic parameters with doping. Temperature dependent crystal structure as well as low temperature (5 K) magnetic structure have been determined from neutron powder diffraction measurements. The whole series shows insulating behavior. The electronic structure calculations show, SOC enhanced, a noncollinear antiferromagnetic and Mott-type insulating state is the stable ground state for present series with a substantial amount of orbital moment, but less than the spin magnetic moment, at the Ir site and the magnetocrystalline anisotropy. The obtained results imply that the Ca$^{2+}$ has large influence on the magnetic and transport properties, further showing a large agreement between experimental results as well as theoretical calculations.
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