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We have studied in detail the electronic structure of IrO$_2$ includingspin-orbit coupling (SOC) and electron-electron interaction, both within theGGA+U and GGA+DMFT approximations. Our calculations reveal that the Ir t$_{2g}$states at the Fermi level largely retain the J$_{\rm eff}$ = $\frac{1}{2}$character, suggesting that this complex spin-orbit entangled state may berobust even in metallic IrO$_2$. We have calculated the phase diagram for theground state of IrO$_2$ as a function of $U$ and find a metal insulatortransition that coincides with a magnetic phase change, where the effect of SOCis only to reduce the critical values of $U$ necessary for the transition. Wealso find that dynamic correlations, as given by the GGA+DMFT calculations,tend to suppress the spin-splitting, yielding a Pauli paramagnetic metal formoderate values of the Hubbard $U$. Our calculated optical spectra andphotoemission spectra including SOC are in good agreement with experimentdemonstrating the importance of SOC in IrO$_2$.

Effect of spin orbit coupling and Hubbard $U$ on the electronic structure of IrO$_2$