Temperature and thickness dependence of the thermal conductivity in 2D ferromagnet Fe$_3$GeTe$_2$

The emergence of symmetry-breaking orders such as ferromagnetism and the weak interlayer bonding in van der Waals materials, offers a unique platform to engineer novel heterostructures and tune transport properties like thermal conductivity. Here, we report the experimental and theoretical study of the cross-plane thermal conductivity, $\kappa_\perp$, of the van der Waals 2D ferromagnet Fe$_3$GeTe$_2$. We observe a non-monotonic increase of $\kappa_\perp$ with the thickness and a large suppression in artificially-stacked layers, indicating a diffusive transport regime with ballistic contributions. These results are supported by the theoretical analyses of the accumulated thermal conductivity, which show an important contribution of phonons with mean free paths between 10 and 200 nm. Moreover, our experiments show a reduction of the $\kappa_\perp$ in the low-temperature ferromagnetic phase occurring at the magnetic transition. The calculations show that this reduction in $\kappa_\perp$ is associated with a decrease in the group velocities of the acoustic phonons and an increase in the phonon-phonon scattering of the Raman modes that couple to the magnetic phase. These results demonstrate the potential of van der Waals ferromagnets for thermal transport engineering.