Anomalous temperature dependence of uniaxial magnetocrystalline anisotropy in the van der Waals ferromagnet ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$

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 ($T_C$). 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 $T_C$. Here, we experimentally unveil the anomalous temperature dependence of the UMA constant $K_{u1}$($T$) in the vdW ferromagnet ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$. Surprisingly, the $K_{u1}$($T$) first anomalously increases and then slowly decreases. We found that the anomalous $K_{u1}$($T$) 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 $K_{u1}$($T$). We propose that the complex competition between the two-ion mechanism and the itinerant-electron mechanism leads to the anomalous behavior of $K_{u1}$($T$) 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.