Effect of longer-range lattice anisotropy on the electronic structure and magnetism of spin-orbit-coupled 5$d$ transition-metal oxides

Our detailed quantum chemistry calculations provide magnetic $g$ factors and exchange interactions for the quasi two-dimensional iridates Sr$_2$IrO$_4$ and Ba$_2$IrO$_4$. While canonical ligand-field considerations predict $g_{||}$-factors $<2$ for the positive tetragonal distortions present in Sr$_2$IrO$_4$, we find $g_{||} > 2$. This implies that the $d$ levels in Sr$_2$IrO$_4$ are inverted with respect to the ordering deduced from the local ligand distortions, whereas we find them in Ba$_2$IrO$_4$ to be instead normally ordered. Electron spin resonance measurements confirm the level inversion in Sr$_2$IrO$_4$. This $d$-level switching is driven by the specific ionic charge distribution within adjacent IrO$_2$ and SrO layers. Since polar discontinuities and the associated complications do not arise for such layers, our results highlight the tetravalent $d$-metal 214 oxides as ideal platforms to explore $d$-level reconstruction and engineering in the context of oxide heterostructures.