Varying magnetism in the lattice distorted Y2NiIrO6 and La2NiIrO6

We investigate the electronic and magnetic properties of the synthesized double perovskites ${\mathrm{Y}}₂{\mathrm{NiIrO}}₆$ and ${\mathrm{La}}₂{\mathrm{NiIrO}}₆$, using density functional calculations, crystal field theory, superexchange pictures, and Monte Carlo simulations. We find that both systems are antiferromagnetic (AFM) Mott insulators, with the high-spin ${\mathrm{Ni}}²⁺\phantom{\rule{4pt}{0ex}}{t}_2g⁶{e}_g²$ ($S=1$) and the low-spin ${\mathrm{Ir}}⁴⁺\phantom{\rule{4pt}{0ex}}{t}_2g⁵$ ($S=1/2$) configurations. We address that their lattice distortion induces ${t}_2g\text{\ensuremath{-}}{e}_g$ orbital mixing and thus enables the normal ${\mathrm{Ni}}⁺\text{\ensuremath{-}}{\mathrm{Ir}}⁵⁺$ charge excitation with the electron hopping from the Ir `${t}<sub>2g</sub>$' to Ni `${e}_g$' orbitals, which promotes the AFM ${\mathrm{Ni}}²⁺\text{\ensuremath{-}}{\mathrm{Ir}}⁴⁺$ coupling. Therefore, the increasing ${t}_2g\text{\ensuremath{-}}{e}_g$ mixing accounts for the enhanced ${T}_{\mathrm{N}}$ from the less distorted ${\mathrm{La}}₂{\mathrm{NiIrO}}₆$ to the more distorted ${\mathrm{Y}}₂{\mathrm{NiIrO}}₆$. Moreover, our test calculations find that in the otherwise ideally cubic ${\mathrm{Y}}₂{\mathrm{NiIrO}}₆$, the ${\mathrm{Ni}}⁺\text{\ensuremath{-}}{\mathrm{Ir}}⁵⁺$ charge excitation is forbidden, and only the abnormal ${\mathrm{Ni}}³⁺\text{\ensuremath{-}}{\mathrm{Ir}}³⁺$ excitation gives a weakly ferromagnetic behavior. Furthermore, we find that, owing to the crystal field splitting, Hund exchange, and broad band formation in the highly coordinated fcc sublattice, ${\mathrm{Ir}}⁴⁺$ ions are not in the ${j}_{\mathrm{eff}}=1/2$ state but in the $S=1/2$ state carrying a finite orbital moment by spin-orbit coupling. This paper clarifies the varying magnetism in ${\mathrm{Y}}₂{\mathrm{NiIrO}}₆$ and ${\mathrm{La}}₂{\mathrm{NiIrO}}₆$ associated with the lattice distortions.