Impact of spin-orbit coupling on the magnetism of Sr3MIrO6 (M = Ni, Co)

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Using density functional calculations, we demonstrate that the spin-orbit coupling (SOC) of the Ir4+ ion plays an essential role in determining the antiferromagnetism of the hexagonal spin-chain system Sr3MIrO6 (M = Ni, Co) by tuning the crystal-field level sequence and altering the Ir-M inter-orbital interactions. The SOC splits the e'g doublet of the octahedral Ir4+ ion (t₂g⁵) in a trigonal crystal field, and the single t₂g hole resides on the e'g upper branch and gives rise to the antiferromagnetic superexchange. In absence of the SOC, however, the single t₂g hole would occupy the a₁g singlet instead, which would mediate an unreal ferromagnetic exchange due to a direct a₁g hopping along the Ir-M chain. We also find that the Ni2+ and Co2+ ions are both in a high-spin state and moreover the Co2+ ion carries a huge orbital moment. This work well accounts for the recent experiments and magnifies again the significance of the SOC in iridates.