Magnetic transition phenomena in cubic chiral antiferromagnet EuPtSi with $T_{rm N}$=4.0~K were investigated by means of single crystal neutron diffraction. At 0.3~K in the ground state, magnetic peaks emerge at positions represented by an ordering vector ${q}_{1}$=$(0.2, 0.3, 0)$ and its cyclic permutation. Upon heating, an additional magnetic peak splitting with hysteresis was uncovered at around $T^*_{rm N}{sim}$2.5~K, indicating the presence of a first-order commensurate-incommensurate transition with ${q}^*_{1}$=$(0.2, 0.3, {delta})$ (${delta}_{rm max}{simeq}$0.04) at $T^*_{rm N}$. A half-polarized neutron scattering experiment for polarization parallel to the scattering vector revealed that polarization antiparallel to the scattering vector has stronger intensity in both magnetic phases. This feature clarifies the single chiral character of the helical structure with moments lying perpendicular to the ordering vector in both ordered states. Under a vertical magnetic field of 1.2~T for ${B}{parallel}$[1,1,1] at 1.9~K entering into the so-called $A$ phase, magnetic peaks form characteristic hexagonal patterns in the equatorial scattering plane around nuclear peaks. An ordering vector ${q}_{A}{simeq}({pm}0.09, {pm}0.20, {mp}0.28)$ of the $A$-phase has similar periodic length as $q_{1}$, and could be the hallmark of a formation of skyrmion lattice in EuPtSi.
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