Magnetic Phase Diagram of the electron-doped high-$T_{c}$ superconductor Nd$_{2-x}$Ce$_{x}$CuO$_{4}$

An intriguing issue in high-$T_{c}$ superconductivity is the phase diagram asymmetry with respect to electron and hole-doping. The antiferromagnetic phase extends further with electron doping and appears to overlap with superconductivity. Our prior results suggested that genuine long-range antiferromagnetic order and superconductivity do not co-exist in Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ [Motoyama \textit{et al.} Nature 445, 186 (2007)]. However, some uncertainty remained due to Ce concentration inhomogeneity in large single crystals. Here we report neutron scattering and $\mu $SR measurements on crystals with improved Ce homogeneity. Inelastic neutron scattering indicates that genuine long-range antiferromagnetic order indeed disappears within a small doping window around x =0.12. Meanwhile, $\mu $SR measurements show that static magnetic order persists up to x = 0.14, where bulk superconductivity first unambiguously appears. Our results suggest a possible first-order phase transition in a narrow region of the phase diagram, between x = 0.12 and x =0.14, characterized by clusters of short-range static magnetic order and traces of superconductivity.