  CePtSi2 was reported to exhibit an antiferromagnetic order below T*=1.8 K at
ambient pressure, a valence state change at ~1.2 GPa, and superconductivity in
the range between 1.4 and 2.1 GPa with the maximum transition temperature of
0.14 K [T. Nakano et al., Phys. Rev. B 79, 172507 (2009)]. We have performed
polycrystalline and single crystal neutron diffraction experiments to determine
the magnetic structure under ambient and high pressures. We found that
incommensurate magnetic peaks with the magnetic propagation vector of (0.32, 0,
0.11) at ambient pressure below T_{SDW}~1.25 K. Those magnetic peaks which
originate from a spin-density-wave order with the easy axis along the c axis
and an averaged ordered moment of 0.45(5) mu_B, suggesting that there may be an
intermediate phase between T* and T_{SDW}. Applying pressures, the magnetic
propagation vector shows no change and the magnetic order disappears around 1.0
GPa, which is much lower than the critical pressure for the superconducting
phase. The results suggest that other than magnetic fluctuations may play a
primary role in the superconducting pairing mechanism.
