Anomalous Hall effect in the van der Waals bonded ferromagnet Fe3−xGeTe2

We report the anomalous Hall effect (AHE) in single crystals of a quasi-two-dimensional ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ ($x\ensuremath{\approx}0.36$) ferromagnet grown by the flux method which induces defects on the Fe site and bad metallic resistivity. Fe $K$-edge x-ray absorption spectroscopy was measured to provide information on the local atomic environment in such crystals. The dc and ac magnetic susceptibility measurements indicate a second-stage transition below 119 K in addition to the paramagnetic to ferromagnetic transition at 153 K. A linear scaling behavior between the modified anomalous Hall resistivity ${\ensuremath{\rho}}_{xy}/{\ensuremath{\mu}}_{0}{H}_{\mathrm{eff}}$ and longitudinal resistivity ${\ensuremath{\rho}}_{xx}^{2}M/{\ensuremath{\mu}}_{0}{H}_{\mathrm{eff}}$ implies that the AHE in ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ should be dominated by the intrinsic Karplus-Luttinger mechanism rather than the extrinsic skew-scattering and side-jump mechanisms. The observed deviation in the linear-$M$ Hall conductivity ${\ensuremath{\sigma}}_{xy}^{A}$ below 30 K is in line with its transport characteristic at low temperatures, implying the scattering of conduction electrons due to magnetic disorder and the evolution of the Fermi surface induced by a possible spin-reorientation transition.