Electronic and magnetic structures of a mixed triple perovskite: ${\mathrm{Ba}}_3{\mathrm{NiRuIrO}}_9$

In search of spin-orbit coupling driven nonmagnetic $J=0$ ground state and excitonic magnetism, various pentavalent iridates have been studied in recent years. However, a finite moment was observed in most of the cases due to solid state effects. In this work, we investigate the electronic and magnetic structure of $6H$ hexagonal compound ${\mathrm{Ba}}_3{\mathrm{NiRuIrO}}_9$, where ${\mathrm{Ir}}^{5+}$ is present along with magnetic ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ru}}^{5+}$ ions. Magnetic susceptibility measurements and neutron powder diffraction (NPD) experiments demonstrate the appearance of short-range magnetic ordering below 170 K and a long-range antiferromagnetic ordering below 80 K. The refinement of the NPD pattern further shows that the Ru and Ir moments interact antiferromagnetically within the dimer and interact ferromagnetically with the Ni sublattice. These experimental findings have been complemented by first-principles density functional theory calculations incorporating spin-orbit coupling effects and electronic correlations for the transitional metal $d$ states. The computed magnetocrystalline anisotropy is also found to be significant and the crystallographic $c$ axis comes out to be the easy axis of magnetization, consistent with the spin alignment direction found from NPD. This study shows that the mixed ruthenate iridate triple perovskite series is a promising family to study the interplay among spin-orbit coupling, electron correlation, and electron filling as a variety of ${\mathrm{Ba}}_{3}M{\mathrm{RuIrO}}_9$ with $M$ as a transition metal ion, rare-earth ion, and alkali metal ions can be synthesized.