Spin stiffness and spin excitation gap of van der Waals ferromagneticFe3+δGeTe2.

Fe3+δGeTe2(FGT) has proved to be an interesting van der Waals (vdW) ferromagnetic compound with a tunable Curie temperature (TC). However, the underlying mechanism for varyingTCremains elusive. Here, we systematically investigate and compare low-temperature magnetic properties of single crystalline FGT samples that exhibitTCs ranging from 160 K to 205 K. Spin stiffness ( D ) and spin excitation gap (Δ) are extracted using Bloch's theory for crystals with varying Fe content. Compared to Cr-based vdW ferromagnets, FGT compounds have higher spin stiffness values but lower spin wave excitation gaps. We discuss the implication of these relationships in Fe-Fe ion magnetic interactions in FGT unit cells. The itinerancy of magnetic electrons is measured and discussed under the Rhodes-Wohlfarth ratio (RWR) and the Takahashi theory.