Microscopic Evidence of Direct Coupling between Magnetic and Superconducting Order Parameters in BaFe$_2$(As$_{1-x}$P$_x$)$_2$

The coexistence of magnetism and superconductivity in the isovalent-P-substituted BaFe$_2$(As$_{1-x}$P$_x$)$_2$ has been investigated microscopically by $^{31}$P-NMR measurements. We found that superconducting (SC) transition occurs in a magnetic region with static ordered moments and that the moments are reduced below the SC transition temperature $T_{\rm c}$ in the samples near the phase boundary of magnetism and superconductivity. Our results indicate that magnetism and superconductivity coexist spatially but compete with each other on the same Fermi surfaces. The coexistence state is qualitatively different from that observed in other unconventional superconductors and gives a strict constraint on the theoretical model for superconductivity in BaFe$_2$(As$_{1-x}$P$_x$)$_2$.