  We optimize the recording medium for heat-assisted magnetic recording by
using a high/low $T_{\mathrm{c}}$ bilayer structure to reduce AC and DC noise.
Compared to a former work, small Gilbert damping $\alpha=0.02$ is considered
for the FePt like hard magnetic material. Atomistic simulations are performed
for a cylindrical recording grain with diameter $d=5\,$nm and height $h=8\,$nm.
Different soft magnetic material compositions are tested and the amount of hard
and soft magnetic material is optimized. The results show that for a soft
magnetic material with $\alpha_{\mathrm{SM}}=0.1$ and
$J_{ij,\mathrm{SM}}=7.72\times 10^{-21}\,$J/link a composition with $50\%$ hard
and $50\%$ soft magnetic material leads to the best results. Additionally, we
analyse how much the areal density can be improved by using the optimized
bilayer structure compared to the pure hard magnetic recording material. It
turns out that the optimized bilayer design allows an areal density that is
$1\,$Tb/in$^2$ higher than that of the pure hard magnetic material while
obtaining the same SNR.
