Theory of metal-insulator transition in the family of perovskite iridium oxides

Perovskite iridium oxides Srn+1IrnO3n+1 exhibit fascinating phenomena due to the combined effects of spin-orbit coupling (SOC) and electronic interactions. It was suggested that electronic correlation amplified via the strong SOC leads to a spin-orbit Mott insulator for n = 1 and 2, while three-dimensional (3D) SrIrO3 remains metallic because of the large bandwidth from the 3D structure. However, this bandwidth-controlled metal-insulator transition (MIT) is only valid when SOC is large enough to split J(eff) = 1/2 and 3/2 bands, while the mixing of 1/2 and 3/2 bands is conspicuous among the occupied bands. Here, we investigate the MIT as a function of n using weak-coupling theory. In this approach, the magnetic instability is determined by the states near the Fermi level rather than the entire band structure. Starting from t(2g) tight-binding models for n = 1, 2, and infinity, the states near the Fermi level are found to be predominantly J(eff) = 1/2 allowing an effective single-band model. Supplementing this effective J(eff) = 1/2 model with Hubbard-type interactions, transitions from a metal to magnetically ordered states are obtained. Strong-coupling spin models are derived to compare the magnetic ordering patterns obtained in the weak- and strong-coupling limits. We find that they are identical, indicating that these iridates are likely in an intermediate-coupling regime.