cycles do not exhibit any exchange bias indicating that no CoO is formed at the top Co interface.

![\[fig:VSM\] VSM-SQUID measurements carried out from 10K to 300K for an out-of-plane field up to 1T. Left: in sample (C), the shift of the cycle at low temperature is an indication of the presence of CoO at the top Co/Gd interface. Right: in sample (D), the cycle does not exhibit a shift, sign of the absence of relevant oxidation. Note the factor 10 difference in the field scale.](CreepDMI-Fig5-new.pdf){width="9cm"}

The anomalous behaviour of the $v(H_{x}$) curves in the creep regime seems therefore to be related to the presence of Co oxide at the top Co interface, and the details of the curves to the different degree of oxidation. Although the CoO is paramagnetic at the room temperature, it exhibits a magnetic susceptibility in the $x$-direction [@Ambrose1996]. We speculate that the CoO magnetic moments induced in the $x$ direction by the in-plane field may act as an extra pinning potential acting on the DWs. Since the magnetic susceptibility may depend on the CoO thickness, this could explain why different samples exhibit maximum velocity for different $H_{x}$ fields. The description of the creep law simply 