the creep regime respectively. Right: Differential Kerr image showing an example of the displacement of DWs in nanostrips.](CreepDMI-Fig2-new.pdf){width="15cm"}

The speed variation as a function of in-plane field $H_{x}$ is similar to that shown by other authors in strips of DMI materials [@Ryu2013; @Emori2013; @Ryu2014]. In all the curves, the speed of the down/up DWs increases for positive $H_{x}$ fields and decreases for negative fields. The symmetric curve is found for the up/down domain walls, as expected for chiral Néel walls. If we neglect the rotation of the magnetisation within the domains, the domain wall speed driven by the current $J$ *via* the SHE-SOT can be expressed as [@Thiaville2012] : $$\label{DW_speed_vs_J}
v = \gamma_{0}\frac{\Delta}{\alpha}\frac{\pi}{2}\chi M_{s}\cos \psi$$ where $\gamma_{0}$ is the gyromagnetic ratio, $\alpha$ is the damping parameter, $\Delta$ is the domain wall width, $\psi$ is the angle of the DW magnetisation with respect to the $x$-axis, and $\chi=\hbar \theta_{H} J / (2e\mu_{0} M_{s}^{2} t)$ where $\theta_{H}$ is the Spin Hall angle and $t$ the magnetic layer thickness. It can be shown (see Suppl. Information) that for our samples the variation of $\cos \psi$ with $H_{x}$ is negligible except around $H_{x}=-H_{\mathrm{DMI}}$ where it changes sign, so that the $v(H_{x})$ shape is mainly 