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