Magnetic order in pyrochlore iridate Nd$_2$Ir$_2$O$_7$ probed by muon spin relaxation

Muon-spin relaxation results on the pyrochlore iridate Nd$_2$Ir$_2$O$_7$ are reported. Spontaneous coherent muon-spin precession below the metal-insulator transition (MIT) temperature of about 33 K is observed, indicating the appearance of a long-ranged magnetic ordering of Ir$^{4+}$ moments. With further decrease in temperature, the internal field at the muon site increases again below about 9 K. The second increase of internal field suggests the ordering of Nd$^{3+}$ moments, which is consistent with a previous neutron experiment. Our results suggest that the MIT and magnetic ordering of Ir$^{4+}$ moments have a close relationship and that the large spin-orbit coupling of Ir 5\textit{d} electrons plays a key role for both MIT and the mechanism of the magnetic ordering in pyrochlore iridates in the insulting ground state.