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We present an analysis of the electronic structure of perovskite-relatediridates, 5d electron compounds where a subtle interplay between spin-orbitcoupling, tetragonal distortions and electron correlations determines theelectronic structure properties. We suggest via electronic structurecalculations that a non-collinear calculation is required to obtain solutionsclose to the usually quoted $j_{eff}$ = 1/2 state to describe the $t_{2g}$ holein the $Ir^{4+} :d^5$ cation, while a collinear calculation yields a differentsolution, the hole is in a simpler xz/yz complex combination with a smaller$L_z /S_z$ ratio. We describe what the implications of this are in terms of theelectronic structure; surprisingly, both solutions barely differ in terms oftheir band structure, and are similar to the one obtained by a tight bindingmodel involving $t_{2g}$ orbitals with mean field interactions. We also analyzehow the electronic structure and magnetism evolve with strain, with thespin-orbit coupling strength and with the on-site Coulomb repulsion, suggestthe way the band structure gets modified and draw some comparisons withavailable experimental observations.

Non-collinear vs collinear description of the Ir-based one-$t_{2g}$ -hole perovskite-related compounds: SrIrO$_3$ and Sr$_2$IrO$_4$