We have studied the interfacial Dzyaloshinskii-Moriya interaction (DMI) in a series of Pt/Co/MOx (M=Al, Gd) trilayers in which the degree of oxidation of the top Co interface is varied. To access to reliable values of the DMI strength, we have used a method based on the measurement of the saturation velocity of field driven chiral N'eel domain walls. We show that the effective DMI strength in the Pt/Co/MOx trilayers varies with the oxidation degree of the Co/MOx interface. This strongly suggests that the Co/MOx interface gives a distinct contribution to the total DMI, adding to that of the Pt/Co interface. The DMI presents a maximum for the oxygen coverage maximizing also the interface magnetic anisotropy energy Ks. This calls for common microscopic origins for the contributions of the Co/MOx interface to DMI and Ks.

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