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We investigate the electronic and magnetic properties of the newlysynthesized double perovskites Y$_{2}$NiIrO$_{6}$ and La$_{2}$NiIrO$_{6}$,using density functional calculations, crystal field theory, superexchangepictures, and Monte Carlo simulations. We find that both systems areantiferromagnetic (AFM) Mott insulators, with the high-spin Ni$^{2+}$$t_{2g}$$^{6}e_{g}$$^{2}$ ($S=1$) and the low-spin Ir$^{4+}$ $t_{2g}$$^{5}$($S=1/2$) configurations. We address that their lattice distortion induces$t_{2g}$-$e_{g}$ orbital mixing and thus enables the normal Ni$^{+}$-Ir$^{5+}$charge excitation with the electron hopping from the Ir `$t_{2g}$' to Ni`$e_g$' orbitals, which promotes the AFM Ni$^{2+}$-Ir$^{4+}$ coupling.Therefore, the increasing $t_{2g}$-$e_{g}$ mixing accounts for the enhanced$T_{\rm N}$ from the less distorted La$_{2}$NiIrO$_{6}$ to the more distortedY$_{2}$NiIrO$_{6}$. Moreover, our test calculations find that in the otherwiseideally cubic Y$_{2}$NiIrO$_{6}$, the Ni$^{+}$-Ir$^{5+}$ charge excitation isforbidden, and only the abnormal Ni$^{3+}$-Ir$^{3+}$ excitation gives a weaklyferromagnetic (FM) behavior. Furthermore, we find that owing to the crystalfield splitting, Hund exchange, and broad band formation in the highlycoordinated fcc sublattice, Ir$^{4+}$ ions are not in the $j_{\rm eff}=1/2$state but in the $S=1/2$ state carrying a finite orbital moment by spin-orbitcoupling (SOC). This work clarifies the varying magnetism in Y$_{2}$NiIrO$_{6}$and La$_{2}$NiIrO$_{6}$ associated with the lattice distortions.

Varying magnetism in the lattice distorted Y2NiIrO6 and La2NiIrO6