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By determining the lattice parameters as a function of temperature of thehexagonal van der Waals ferromagnet Fe$_{2.92(1)}$Ge$_{1.02(3)}$Te$_2$ weobtain the temperature dependence of the spontaneous in-plane magnetostrictionin the ferromagnetic and the linear thermal expansion coefficients in theparamagnetic state. The spontaneous magnetostriction is clearly seen in thetemperature dependence of the in-plane lattice parameter $a(T)$, but less wellpronounced perpendicular to the planes along $c$. Below $T_{\rm C}$ thespontaneous magnetostriction follows the square of the magnetization and leadsto an expansion of the hexagonal layers. Extrapolating to $T\rightarrow$ 0~K weobtain a spontaneous in-plane saturation magnetostriction of $\lambda_{{\rmsp},a}(T \rightarrow 0) \approx-220 ~\times~10^{-6}$. In the paramagnetic statethe linear thermal expansion coefficients amount to13.9(1)$\times$10$^{-6}$~K$^{-1}$ and to 23.2(2)$\times$10$^{-6}$~K$^{-1}$ forthe in-plane and out-of-plane direction, respectively, indicating a linearvolume thermal expansion coefficient of 50.8(4)$\times$10$^{-6}$K$^{-1}$ whichwe use to estimate the volume thermal expansion contribution to the heatcapacity determined at constant pressure. A Sommerfeld-type linear term in thelow-temperature heat capacities can be quantitatively ascribed to 2dimferromagnetic magnon excitations.

Thermal and Magnetoelastic Properties of the van der Waals Ferromagnet  Fe$_{3-\delta}$GeTe$_2$: Anisotropic Spontaneous Magnetostriction and  Ferromagnetic Magnon Excitations