energy is maximum. From equation \[speed\] it then follows that the DW velocity should exhibit a minimum for $H_{x}=-H{_\mathrm{DMI}}$. This is indeed observed for sample (D). Note that the left-handed DW chirality deduced from the measurement agrees with the results of the current-induced measurements.

![\[fig:speed\_Hcreep\] Domain wall speed *vs.* $H_{x}$ field measured in the thermally activated regime for bubble domains in Pt/Co/GdO$_x$ samples (A) to (D), for the DW propagating along the $x$-axis direction. ](CreepDMI-Fig3-new.pdf){width="15cm"}

The speed *vs.* $H_{x}$ curves obtained for samples (A-C) show a different behaviour. For sample (A) the speed asymmetry is the same as for sample (D), but the velocity of the down/up DW increases for negative fields and decreases up to a critical field for positive fields. In sample (B) the speed asymmetry practically disappears and the speeds of the up/down and down/up DWs continuously decrease with both positive and negative $H_{x}$ fields. In sample (C) the asymmetry is switched for down/up and up/down DW, with respect to sample (D). Therefore in these three samples the $v(H_{x})$ curves do not follow the variation of the DW energy. Curves deviating from the expected behaviour have also been recently reported in the literature [@Lavrijsen2015].

Note that the 