  We use neutron scattering to demonstrate that electron-doped superconducting
Pr0.88LaCe0.12CuO4 in the underdoped regime is electronically phase separated
in the ground state, showing the coexistence of a superconducting phase with a
three-dimensional antiferromagnetically ordered phase and a
quasi-two-dimensional spin density wave modulation. The Neel temperature of
both antiferromagnetic phases decreases linearly with increasing
superconducting transition temperature (Tc) and vanishes when optimal
superconductivity is achieved. These results indicate that the electron-doped
copper oxides are close to a quantum critical point, where the delicate
energetic balance between different competing states leads to microscopic
heterogeneity.
