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 $J_{ij,mathrm{SM}}=7.72times 10^{-21},$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.
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