out current-induced DW dynamics measurements. For this purpose, the samples were patterned into $1\,\upmu$m wide strips by e-beam lithography and the DW dynamics was studied for a fixed value of the current-density $J=1.2 \times 10^{12}\,$A/m$^{2}$ and variable values of $H_{x}$. The results show that for all samples (note that sample (C) could not be measured, due to deterioration during the patterning process) the domain walls move in the same direction, opposite to the electron flow. Since in these systems the direction of the DW displacement is determined by the sign of the Spin-Hall angle in Pt (which is the same for samples (A) to (D)) and by the chirality of the DDW [@Thiaville2012; @Ryu2013; @Emori2013], this results is a strong indication that the domain walls in all the samples have the same chirality and therefore the sign of the DMI is sample independent. The results of the current-driven DW speed *vs.* $H_{x}$ field curves for samples (A) and (B) are shown in Figure \[fig:speed\_J\].

![\[fig:speed\_J\] Left: Domain wall speed *vs.* $H_{x}$ curves measured with constant current density $J=1.2 \times 10^{12}\,$A/m$^{2}$ for samples (A) and (B), for which a large and a vanishing field-induced domain wall speed asymmetry are found in 