Magnetic-field control of topological charge-transport properties in Nd$_{2}$Ir$_{2}$O$_{7}$

Weyl semimetal is a novel quantum phase with topological properties where the linear-dispersive band with a surface Fermi arc state is realized in a three-dimensional bulk. Pyrochlore-type $R_{2}$Ir$_{2}$O$_{7}$ is one of the promising candidates for realization of the Weyl semimetal. In this system, the magnetic ordering pattern is predicted to play a key role for characterizing its electronic band structure. We report the magneto-transport properties in Nd$_{2}$Ir$_{2}$O$_{7}$ single crystals for several magnetic field directions. We reveal that all-in all-out type magnetic domain walls, at which the conductive mode inherent to the surface state of Weyl semimetal may be preserved, are finely controlled by an applied field along [111] direction showing unique hysteresis in resistivity. With applied field along [001] direction, the Nd-4$f$ moment forms 2-in 2-out configuration that turns the insulating state into the anomalous metallic one near the Weyl (semi-)metal phase. A mean-field calculation consistent with our experimental findings suggests that there are a plenty of exotic states in pyrochlore iridates as functions of electron correlation and external magnetic field that tunes Ir-5$d$ spin texture.