Electron interactions, spin-orbit coupling, intersite correlations in pyrochlore iridates

We perform combined density functional and dynamical mean-field calculations to study the pyrochlore iridates Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$ and Eu$_2$Ir$_2$O$_7$. Both single-site and cluster dynamical mean-field calculations are performed and spin-orbit coupling is included. Paramagnetic metallic phases, antiferromagnetic metallic phases with tilted Weyl cones and antiferromagnetic insulating phases are found. The magnetic phases display all-in/all-out magnetic ordering, consistent with previous studies. Unusually for electronically three dimensional materials, the single-site dynamical mean-field approximation fails to reproduce qualitative material trends, predicting in particular that the paramagnetic phase properties of Y$_2$Ir$_2$O$_7$ and Eu$_2$Ir$_2$O$_7$ are almost identical, although in experiments the Y compound has a much higher resistance than the Eu compound. This qualitative failure is attributed to the importance of intersite magnetic correlations in the physics of these materials.