$H_{x}$, along $\pm
x$, which tunes the stability of the DDW internal structure. With such amplitudes of the $H_{z}$ field, DW speeds are of the order of some 0.1mm/s, the dynamics is thermally activated and described by the so-called creep regime.

![\[fig:images\] Left: Expansion by DW propagation of an up (black contrast) and a down (white contrast) domain in samples (A), (B), (C), (D). The Gd thickness increases from 2nm to 5nm going from (A) to (D). The DW displacements are obtained by an $H_{z}$ field pulse with amplitude $\sim$10mT and duration $\sim$20-100ms and a continuous in-plane field $H_{x}=+200$mT. Right: schematic view of a bubble domain expansion: the red arrows represent the equilibrium orientation of the magnetisation at the center of the DWs.](CreepDMI-Fig1-new.pdf){width="15cm"}

Starting from (down or up) saturation, a bubble domain was created by applying an up or a down $H_{z}$ pulse. The image of the domain was saved as a reference image. An $H_{z}$ pulse was then applied to enlarge the domain by DW propagation, and the new image was acquired. The difference between the two images gives the domain wall displacement that occurred during the field pulse. A black (white) contrast in the images corresponds to the 