High-temperature (high-T c ) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds. The evolution of the AF phase with doping and its spatial coexistence with superconductivity are governed by the nature of charge and spin correlations and provide clues to the mechanism of high-T c superconductivity. Here we use a combined neutron scattering and scanning tunneling spectroscopy (STS) to study the T c evolution of electron-doped superconducting Pr 0.88 LaCe 0.12 CuO 4- obtained through the oxygen annealing process. We find that spin excitations detected by neutron scattering have two distinct modes that evolve with T c in a remarkably similar fashion to the electron tunneling modes in STS. These results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometer length scales, and the dominant electron-boson coupling at low energies originates from the electron-spin excitations.High-temperature (high-T c ) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds 1,2 . The evolution of the AF phase with doping and its spatial coexistence with superconductivity are governed by the nature of charge and spin correlations and provide clues to the mechanism of high-T c superconductivity 3,4 . Electron correlation in hole-and electrondoped materials can be quite different 5 . While doped electrons reside in the Cu 3d orbitals with correlations involving primarily d-electrons 2 , doped holes form Zhang-Rice singlets moving in the background of Cu spins 1 and are subject to stronger correlations 1-7 . In electron-doped copper oxides, there are bulk signatures of coexisting AF and superconducting phases [8][9][10][11][12] . These measurements, however, cannot distinguish nanoscale spatial coexistence from larger scale phase segregation. Here we report advances made by a combined neutron scattering and scanning tunneling spectroscopy (STS) studies on nominally identical electron-doped superconducting Pr 0.88 LaCe 0.12 CuO 4- (PLCCO) samples with different T c 's obtained through the oxygen annealing process 13,14 . We find that spin excitations detected by neutron scattering 15,16 have two distinct modes that evolve with T c in a remarkably similar fashion to the electron tunneling modes 17 in STS. Spatial mapping of the modes shows nanoscale regions of coexisting AF and superconducting order in the lower T c samples. Since the annealing process is not expected to change lattice (phonon) properties 2,13,14,18 , these results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometer length scales, and the dominant electron-boson coupling at low energies originates from the electron-spin excitations 17 rather than electron-phonon interactions 19 .There is experimental and theoretical evidence suggesting that antiferromagnetism is a competing phase to superconductivity i...