Electronic and magnetic properties of double-perovskite (La$_{1-x}$Sr$_{x})_{2}$CuIrO$_{6}$ compounds

Double perovskite oxides that combine 3d and 5d transition metal elements offer a model system to study novel electronic and magnetic states arising from the interplay of strong electron correlations and spin-orbit couplings (SOCs). In this work, we studied the electronic and magnetic properties of a double perovskite iridate La$_{2}$CuIrO$_{6}$ and its hole-doped compounds (La$_{1-x}$Sr$_{x})_{2}$CuIrO$_{6}$. Magnetic susceptibility measurements suggest that the Ir sublattice and the Cu sublattice both form antiferromagnetic order but at two different temperatures. Two-dimensional magnetism that was reported in many other Cu-based double-perovskites is not observed in our samples, indicating the existence of Cu-Ir interaction despite a weak orbital mixing. Sr-doping is shown to decrease the magnetic ordering temperatures and enhance the electrical conductivity. Density functional theory (GGA$+$SOC$+$U) calculations suggest that an isolated band is generated above the Fermi level as a result of strong SOC and U. The exchange coupling constants between transition metal ions are estimated by calculating the total energies for various magnetic ground states with expanded unit cells.