of $M_{s}$ and $A$ used for sample (D), and the measured in plane saturation field $\mu_{0}H_{K}=1.6$T giving rise to $\Delta=4.7$nm, we obtain a value of $D=1.31$mJ/m$^{2}$. We estimate that the uncertainty associated to the value of the exchange parameter A, together with the error associated to the definition of the $H_{x}$ field where the DW velocity is minimum, allow the determination of $D$ with a precision not better than $\pm0.2\,$mJ/m$^{2}$. The similar $D$ values found for the two samples indicate that the DMI strength is homogeneous along the wedge sample and that it is mainly arising from the Pt/Co interface.

As a consequence, the anomalous $v(H_{x}$) curves in the creep regime do not bear any information about the sign and strength of the DMI. In Figure \[fig:speed\_Hcreep\], the value for which the speed is maximum in samples (A) and (C) is not related to the $D$ value, and the absence of speed asymmetry for sample (B) is not a signature of a vanishing $D$. Since the anomalous behaviour of the $v(H_{x}$) curves is observed only in the creep regime and for samples (A) to (C), we conclude that this feature may be related to modifications of the domain wall pinning 