  Two-dimensional (2D) Heisenberg honeycomb ferromagnets are expected to have
interesting topological magnon effects as their magnon dispersion can have
Dirac points. The Dirac points are gapped with finite second nearest neighbor
Dzyaloshinskii-Moriya interaction, providing nontrivial Berry curvature with
finite magnon Hall effect. Yet, it is unknown how the topological properties
are affected by magnon damping. We report the thermal Hall effect in
Cr$_2$Ge$_2$Te$_6$, an insulating 2D honeycomb ferromagnet with a large Dirac
magnon gap and significant magnon damping. Interestingly, the thermal Hall
conductivity in Cr$_2$Ge$_2$Te$_6$ shows the coexisting phonon and magnon
contributions. Using an empirical two-component model, we successfully estimate
the magnon contribution separate from the phonon part, revealing that the
magnon Hall conductivity was 20 times smaller than the theoretical calculation.
Finally, we suggest that such considerable suppression in the magnon Hall
conductivity is due to the magnon damping effect in Cr$_2$Ge$_2$Te$_6$.
