  Chiral domain walls in ultrathin perpendicularly magnetised layers have a
N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that
is generated at the interface between the ferromagnet and a heavy metal.
Different heavy metals are required above and below a ferromagnetic film in
order to generate the structural inversion asymmetry needed to ensure that the
DMI arising at the two interfaces does not cancel. Here we report on the
magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by
sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0
to 1 a structural inversion asymmetry is generated. We characterise the
epilayer structure with x-ray diffraction and cross-sectional transmission
electron microscopy, revealing (111) stacking. The saturation magnetization
falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular
magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$
was determined using the bubble expansion technique and also rises from a
negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning
field at which field-driven domain wall motion crosses from the creep to the
depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater
spatial fluctuations of the domain wall energy with increasing Au
concentration. Meanwhile, the increase in DMI causes the Walker field to rise
from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the
steady flow regime accessible. The full dependence of domain wall velocity on
driving field bears little resemblance to the prediction of a simple
one-dimensional model, but can be described very well using micromagnetic
simulations with a realistic model of disorder. These reveal a rise in Gilbert
damping as $x$ increases.
