  It is assumed that heat-assisted magnetic recording (HAMR) is the recording
technique of the future. For pure hard magnetic grains in high density media
with an average diameter of $5$nm and a height of $10$nm the switching
probability is not sufficiently high for the use in bit-patterned media. Using
a bilayer structure with 50$\%$ hard magnetic material with low Curie
temperature and 50$\%$ soft magnetic material with high Curie temperature to
obtain more than 99.2$\%$ switching probability, leads to very large jitter. We
propose an optimized material composition to reach a switching probability of
$P_{\mathrm{switch}}>99.2\%$ and simultaneously achieve the narrow transition
jitter of pure hard magnetic material. Simulations with a continuous laser spot
were performed with the atomistic simulation program VAMPIRE for a single
cylindrical recording grain with a diameter of 5nm and a height of 10nm.
Different configurations of soft magnetic material and different amounts of
hard and soft magnetic material were tested and discussed. Within our analysis,
a composition with 20$\%$ soft magnetic and $80\%$ hard magnetic material
reaches the best results with a switching probability
$P_{\mathrm{switch}}>99.2\%$, an off-track jitter parameter
$\sigma_{\mathrm{off},80/20}=14.2$K and a down-track jitter parameter
$\sigma_{\mathrm{down},80/20}=0.49$nm.
