We present comprehensive neutron scattering studies of nonsuperconducting and superconducting electron-doped Pr0.88LaCe0.12CuO4(PLCCO). At zero field, the transition from antiferromagnetic (AF) as-grown PLCCO to superconductivity without static antiferromagnetism can be achieved by annealing the sample in pure Ar at different temperatures, which also induces an epitaxial (Pr,La,Ce)2O3 phase as an impurity. When the superconductivity first appears in PLCCO, a quasi-two-dimensional (2D) spin-density-wave (SDW) order is also induced, and both coexist with the residual three-dimensional (3D) AF state. A magnetic field applied along the [-1,1,0] direction parallel to the CuO2 plane induces a ``spin-flop transition, where the noncollinear AF spin structure of PLCCO is transformed into a collinear one. The spin-flop transition is continuous in semiconducting PLCCO, but gradually becomes sharp with increasing doping and the appearance of superconductivity. A c-axis aligned magnetic field that suppresses the superconductivity also enhances the quasi-2D SDW order at (0.5,0.5,0) for underdoped PLCCO. However, there is no effect on the 3D AF order in either superconducting or nonsuperconducting samples. Since the same field along the [-1,1,0] direction in the CuO2 plane has no (or little) effect on the superconductivity, (0.5,0.5,0) and (Pr,La,Ce)2O3 impurity positions, we conclude that the c-axis field-induced effect is intrinsic to PLCCO and arises from the suppression of superconductivity.
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