Anomalous temperature dependence of uniaxial magnetocrystalline anisotropy in the van der Waals ferromagnet Fe3GeTe2

Uniaxial magnetocrystalline anisotropy (UMA) is vital for fundamental research, such as maintaining two-dimensional ferromagnetic order and realizing topological phases. However, in most cases, UMA rapidly decreases with increasing temperature and finally vanishes approaching the Curie temperature (${T}_{\mathrm{C}}$). The increasing UMA with increasing temperature is very rare in almost all traditional ferromagnetic materials and in emerging van der Waals (vdW) ferromagnets, which generally have relatively low ${T}_{\mathrm{C}}$. Here, we experimentally unveil the anomalous temperature dependence of the UMA constant ${K}_{\mathrm{u}1}$($T$) in the vdW ferromagnet ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$. Surprisingly, the ${K}_{\mathrm{u}1}$($T$) first anomalously increases and then slowly decreases. We found that the anomalous ${K}_{\mathrm{u}1}$($T$) can be perfectly fitted by Carr's model. Further analysis and temperature-dependent x-ray diffraction measurements suggest that the partial localization of $3d$ electrons and considerable lattice expansion are crucial for anomalous ${K}_{\mathrm{u}1}$($T$). We propose that the complex competition between the two-ion mechanism and the itinerant-electron mechanism leads to the anomalous behavior of ${K}_{\mathrm{u}1}$($T$) in ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$. Our findings from this unusual case help deepen the understanding of the temperature dependence of UMA.