Anomalous domain-wall conductance in pyrochlore-typeNd2Ir2O7on the verge of the metal-insulator transition

We have investigated the charge transport and low-energy dynamics originating from the antiferromagnetic (AF) domain wall (DW) in pyrochlore-type Nd${}_{2}$Ir${}_{2}$O${}_{7}$ with the all-in all-out type AF ground state by means of the magneto-resistance measurement and the terahertz time-domain spectroscopy. The resistivity is much lower in the multi-magnetic-domain state than in the nearly single-magnetic-domain one. Furthermore, the terahertz optical conductivity spectrum unravels a Drude-like response only in the multidomain state; the Drude-like absorption is strongly suppressed with increasing field and irreversibly disappears above 5 T. These observations suggest that the AF DW is highly conductive with a minimal damping constant of 2 meV, contrary to the fully-gapped (45 meV) AF insulating state of bulk. We discuss the nature of metallic states at AF DWs and their possible relevance to the gapless edge state inherent to the Weyl semimetal.