The scaling relation of anomalous Hall effect in van der Waals ferromagnet Fe3GeTe2

According to the Mermin-Wagner theory, two-dimensional (2D) long-range magnetic order would be destroyed by thermal fluctuation at any nonzero temperature. Until 2017, magnetic 2D materials CrI3, Cr2Ge2Te6, and Fe3GeTe2 (FGT) were experimentally confirmed, which attributes to their strong magnetic anisotropy energy against the thermal fluctuation. Since then, the pursuit of high Curie temperature 2D magnets, such as FenGeTe2 (3 < n < 5, T_c=200∼400K) and Fe3GaTe2 (T_c~367 K), has emerged as a prominent research focus.
The vdWs ferromagnet FGT has recently been found to exhibit complex physics phenomena, including heavy fermions, Kondo lattice, and topological nodal lines. Here, we investigated the scaling relation of the anomalous Hall effect (AHE) in FGT nanoflakes by varying the flake thickness and the temperature. Our findings reveal that the scaling relation of the AHE in FGT falls within the cross-region between the intrinsic and dirty regimes, indicating both the intrinsic Berry curvature and hopping transport origin in the AHE of FGT. We observed that the scaling relation of AHE follows the relationship σ_AH ∝ σ_xx^γ, where γ ranges from 1.4 to 2 as temperature increases from 2 K to its Curie temperature ~200 K. Besides, the low-temperature anomaly of longitudinal (ρ_xx) and anomalous Hall resistivity (ρ_AH) are observed, which are interpreted as three-dimensional enhanced electron-electron interaction caused by Fe vacancies and its quantum correction to AHE, respectively.