in terms of the variation of the DW energy may not be general, as the pinning potential landscape may be strongly affected by the in-plane field.

In conclusion, we have shown that in Pt/Co/GdO$_x$ samples with different oxidation degrees of the Co/Gd interface the dependence of the DW velocity as a function of the in-plane field cannot be interpreted within the creep law relating the DW speed changes exclusively to the DW energy variations. Therefore in these samples, the $v(H_{x}$) curves fail to give information about the sign and the strength of the DM interaction. We have correlated the failure of the proposed creep law with the modification of the pinning potential landscape induced by the in-plane field. When by applying strong and ultrashort out-of-plane field pulses we change the dynamic regime of the DW propagation, the $v(H_{x}$) curves indicate that the chirality of the DDW is left-handed, and $D$ is of the order of $1.3$mJ/m$^{2}$ for $1$nm Co.

This work was supported by the Agence Nationale de la Recherche, project ANR 11 BS10 008 ESPERADO. SP acknowledges the support of E. Wagner and of the staff of the Nanofab facility in Institut Néel.

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A. 