Analysis of Charge-spin-orbital Fluctuations by Ab Initio Calculation and Random Phase Approximation: Application to Non-coplanar Antiferromagnet Cd2Os2O7

We present a systematic analysis on the basis of ab initio calculations and many-body perturbation theory for clarifying the dominant fluctuation in complex charge-spin-orbital coupled systems. For a tight-binding multiband model obtained from the maximally-localized Wannier function analysis of the band structure by the local density approximation, we take into account electron correlations at the level of random phase approximation. To identify the dominant fluctuation, we carry out the eigenmode analysis of the generalized susceptibility that includes all the multiple degrees of freedom: charge, spin, and orbital. We apply this method to the paramagnetic metallic phase of a pyrochlore oxide Cd$_2$Os$_2$O$_7$, which shows a metal-insulator transition accompanied by a peculiar noncoplanar antiferromagnetic order of all-in all-out type. We find that the corresponding spin fluctuation is dominantly enhanced by the on-site Coulomb repulsions in the presence of strong spin-orbit coupling and trigonal crystal field splitting. Our results indicate that the combined method offers an effective tool for the systematic analysis of potential instabilities in strongly correlated electron materials.