these conditions the speed *vs.* $H_{x}$ curves all acquire the trend expected for chiral Néel walls in the flow regime [@Jue2015].

![\[fig:speed\_H\_flow\] Domain wall speed *vs.* $H_{x}$ field measured for bubble domains in Pt/Co/GdO$_x$ for samples (A) to (D) for 20ns-long $H_{z}$ field pulses varying between 70mT and 200mT. For samples (B) to (D) the curves were measured for two $H_{z}$ field values (empty symbols correspond to the scale to the right). The trends of the normalised speed curves are the same for each field value. For sample (D) the speeds are larger, as the depinning of the DWs occurs for lower fields. ](CreepDMI-Fig4-new.pdf){width="15cm"}

In the high field regime, the stationary DW velocity is given by $v=\gamma_{0}\Delta_{T} H_{z}/\alpha m_{z0}$, where $\Delta_{T}$ is the Thiele domain wall width [@Thiele1974] and $m_{z0}$ is the easy-axis magnetisation within the domains. The speed variation with $H_{x}$ is mainly related to the modification of the Thiele DW width with the in-plane field (see Suppl. Information). In all the samples, the down/up DWs propagate faster than the up/down DWs for positive $H_{x}$ fields, confirming once again that the DW chirality is the same (left handed) in agreement with the current-induced measurements and the field-induced (creep) measurements 