Disorder driven crossover between anomalous Hall regimes in Fe$_3$GaTe$_2$

Abstract: The large anomalous Hall conductivity (AHC) of the Fe$3$(Ge,Ga)Te$_2$ compounds has attracted considerable attention. Here, we expose the intrinsic nature of AHC in Fe$_3$GaTe$_2$ crystals characterized by high conductivities, which show disorder-independent AHC with a pronounced value $\sigma{xy}^{\text{c}}\approx$ 420 $\Omega^{-1}$cm$^{-1}$. In the low conductivity regime, we observe the scaling relation $\sigma_{xy}\propto\sigma_{xx}^{1.6}$, which crosses over to $\sigma_{xy} \simeq \sigma_{xy}^{\text{c}}$ as $\sigma_{xx}$ increases. Disorder in low-conductivity crystals is confirmed by the broadening of a first-order transition between ferromagnetism and the ferrimagnetic ground state. Through density functional theory (DFT) calculations, we reveal that the dominant sources of Berry curvature are located a few hundred meV below the Fermi energy around the $\Gamma$-point. Therefore, Fe$_3$GaTe$_2$ clearly exposes the disorder-induced crossover among distinct AHC regimes, previously inferred from measurements on different ferromagnets located in either side of the crossover region.