that it cannot always be described simply in terms of the variation of DW energy with $H_{x}$. Our measurements on Pt/Co/GdO$_x$ films suggest that modifications of the pinning barrier landscape upon application of the in-plane field also contribute to the trend of the $v(H_{x})$ curves.

A Pt(5nm)/Co(1nm)/Gd($t$) stack with varying Gd thickness ($t=2-5\,$nm) was grown on a Si/SiO$_{2}$ substrate by magnetron sputtering in the shape of a wedge, and oxidised by O$_{2}$ plasma for 35 seconds. Consequently 2nm of Al were deposited on top of the stack to protect it from further oxidation. The varying thickness of the Gd layer is at the origin of a gradient in the oxygen content at the Co/Gd interface, which varies the interfacial anisotropy [@Manchon2008a]. All the samples present a well defined PMA, with in-plane saturation fields varying between 1.6T (for 2nm Gd) and 0.6T (for 5nm Gd). Domain wall dynamics was studied at room temperature by wide-field Magneto-Optical Kerr microscopy, using a combination of easy-axis and in-plane magnetic fields. $H_{z}$ pulses of amplitude $\sim$10mT and duration $\sim$20-100ms were obtained using a conventional, uncooled coil. The $H_{z}$ pulses, driving the displacement of the DWs, were applied in the presence of a continuous in-plane field 