First-principles studies of spin-orbital physics in pyrochlore oxides

The pyrochlore oxides A2B2O7 exhibit a complex interplay between geometrical frustration, electronic correlations, and spin–orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B = Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA) + U and LDA + dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations