  We demonstrate here that ultrathin ferromagnetic Pt/Co/Pt films with
perpendicular magnetic anisotropy exhibit a sizeable Dzyaloshinskii-Moriya
interaction (DMI) effect. Such a DMI effect modifies the domain-wall (DW)
energy density and consequently, results in an asymmetric DW expansion driven
by an out-of-plane magnetic field under an in-plane magnetic field bias. From
an analysis of the asymmetry, the DMI effect is estimated to be strong enough
for the DW to remain in the N\'eel-type configuration in contrast to the
general expectations of these materials. Our findings emphasize the critical
role of the DMI effect on the DW dynamics as the underlying physics of the
asymmetries that are often observed in spin-transfer-related phenomena.
