  Using the microscopic three temperature model, we simulate single-pulse
all-optical switching (AOS) in alloys and bilayers consisting of Co and Gd. In
particular, we investigate its dependence on the spin-flip probability of Gd
$a_\mathrm{sf,Gd}$, a material parameter describing the strength of spin-phonon
coupling. We do so to elucidate the mechanisms behind all-optical switching in
systems where Co is coupled to heavy rare-earth elements with higher damping
such as Tb. In alloys, our observations are twofold. First, an increase of
$a_\mathrm{sf,Gd}$ leads to a broadening of the range of compositions for which
AOS is observed. Second, the ideal Co content is decreased as
$a_\mathrm{sf,Gd}$ is varied. For bilayers, our analysis indicates that
switching is most efficient when $a_\mathrm{sf,Gd}$ takes on small values.
Conversely, increasing the value of $a_\mathrm{sf,Gd}$ leads to a general
suppression of AOS. Comparing alloys to bilayers, we find that AOS in alloys
exhibits greater resilience to variations in $a_\mathrm{sf,Gd}$ than it does in
bilayers.
