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In heavy-fermion systems with $f$ electrons, there is an intricate interplaybetween Kondo screening and magnetic correlations, which can give rise tovarious exotic phases. Recently, similar interplay appears to also occur in$d$-electron systems, but the underlying mechanism remains elusive. Here, usinginelastic neutron scattering, we investigate the temperature evolution of thelow-energy spin waves in a metallic van der Waals ferromagnetFe$_{3-x}$GeTe$_{2}$ (Curie temperature $T_{\rm C}\sim160$ K), where theKondo-lattice behavior emerges in the ferromagnetic phase below acharacteristic temperature $T^*\sim90$ K. We observe that the magnon dampingconstant diverges at both low and high temperatures, exhibiting a minimumcoincidentally around $T^*$. Such an observation is analogous to theresistivity minimum as due to the single-impurity Kondo effect. This unusualbehavior is described by a formula that combines logarithmic and power terms,representing the dominant contributions from Kondo screening and thermalfluctuations, respectively. Furthermore, we find that the magnon dampingincreases with momentum below $T_{\rm C}$. These findings can be explained byconsidering spin-flip electron-magnon scattering, which serves as a magnonicanalog of the Kondo-impurity scattering, and thus provides a measure of theKondo coupling through magnons. Our results provide critical insights into howKondo coupling manifests itself in a system with magnetic ordering and shedlight on the coexistence of and interplay between magnetic order and Kondoeffect in itinerant 3$d$-electron systems.

Observation of Magnon Damping Minimum Induced by Kondo Coupling in a van der Waals Ferromagnet Fe$_{3-x}$GeTe$_{2}$