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 ${({\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Pr}}_x)}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$ 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) ${\mathrm{Nd}}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$.