Scaling relation and low-temperature anomaly of the anomalous Hall effect in the Van der Waals ferromagnet Fe3GeTe2

The van der Waals (vdW) ferromagnet ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ (FGT) has recently attracted much attention due to its fruitful physical phenomena. In this paper, by varying the thickness of FGT nanoflakes, the relationship between anomalous Hall conductivity (AHC) ${\ensuremath{\sigma}}_{\text{AH}}$ and the sheet electric conductivity ${\ensuremath{\sigma}}_{xx}$ in FGT is found to follow ${\ensuremath{\sigma}}_{\text{AH}}\ensuremath{\propto}{\ensuremath{\sigma}}_{xx}^{\ensuremath{\gamma}}$, where $\ensuremath{\gamma}$ varies from 1.4 to 2.2 as the temperature increases from 2 K to the Curie temperature of 200 K. The scaling relation is found to be near the transition between the intrinsic and dirty regimes, suggesting a dual origin involving the intrinsic Berry curvature and the strong scattering. Moreover, an upturn of the sheet resistivity 20 K is caused by the electron-electron interaction due to Fe vacancies and the quantum correction to the AHC is negligible. This paper is beneficial to the further understanding of the physics of the AHC in vdW ferromagnets.