We investigate the electronic and magnetic properties of the newly synthesized double perovskites Y$_{ 2}$NiIrO$_{ 6}$ and La$_{ 2}$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 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 distorted Y$_{ 2}$NiIrO$_{ 6}$. Moreover, our test calculations find that in the otherwise ideally cubic Y$_{ 2}$NiIrO$_{ 6}$, the Ni$^{ +}$-Ir$^{ 5+}$ charge excitation is forbidden, and only the abnormal Ni$^{ 3+}$-Ir$^{ 3+}$ excitation gives a weakly ferromagnetic (FM) behavior. Furthermore, we find that owing to the crystal field splitting, Hund exchange, and broad band formation in the highly coordinated 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-orbit coupling (SOC). This work clarifies the varying magnetism in Y$_{ 2}$NiIrO$_{ 6}$ and La$_{ 2}$NiIrO$_{ 6}$ associated with the lattice distortions.
Categories: cond-mat.mtrl-sci cond-mat.str-el
