Competing magnetic orders and multipolar Weyl fermions in 227 pyrochlore iridates

Owing to comparably strong spin-orbit coupling and Hubbard interaction, iridium based 227 pyrochlore oxides harbor a rich confluence of competing magnetic orders and emergent multipolar Weyl quasiparticles. Here we show that this family of materials is predominantly susceptible toward the nucleation of electronic noncoplanar all-in all-out (AIAO) and three-in one-out (3I1O) orders, respectively transforming under the singlet $A_{2u}$ and triplet $T_{1u}$ representations, supporting octupolar and dipolar Weyl fermions, and favored by strong on-site Hubbard and nearest-neighbor ferromagnetic interaction. Furthermore, a coplanar magnetic order generically appears as an intermediate phase between them. This order transforms under the triplet $T_{2u}$ representation and also hosts octupolar Weyl fermions. With the AIAO and 3I1O phases possibly being realized in (Nd$_{1-x}$Pr$_{x}$)$_2$Ir$_2$O$_7$ when $x=0$ and 1, respectively, the intervening $T_{2u}$ order can in principle be found at an intermediate doping ($0<x<1$) or in pressured (hydrostatic) Nd$_2$Ir$_2$O$_7$.