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Recently, an anomalous temperature evolution of spin wave excitations hasbeen observed in a van der Waals metallic ferromagnet Fe$_3$GeTe$_2$ (FGT) [S.Bao, et al., Phys. Rev. X 12, 011022 (2022)], whose theoretical understandingyet remains elusive. Here we study the spin dynamics of a ferromagneticKondo-Heisenberg lattice model at finite temperature, and propose a mechanismof magnon damping that explains the intriguing experimental results. Inparticular, we find the magnon damping rate $\gamma(T)$ firstly decreases astemperature lowers, due to the reduced magnon-magnon scatterings. It thenreaches a minimum at $T_{\rm d}^*$, and rises up again following a logarithmicscaling $\gamma(T) \sim \ln{(T_0/T)}$ (with $T_0$ a constant) for $T < T_{\rmd}^*$, which can be attributed to electron-magnon scatterings of spin-fliptype. Moreover, we obtain the phase diagram containing the ferromagnetic andKondo insulator phases by varying the Kondo coupling, which may be relevant forexperiments on pressured FGT. The presence of a magnon damping minimum andlogarithmic scaling at low temperature indicates the emergence of the Kondoeffect reflected in the collective excitations of local moments in a Kondolattice system.

Magnon Damping Minimum and Logarithmic Scaling in a Kondo-Heisenberg Model