A detailed study of electrical transport, magnetotransport, anomalous, and topological Hall effect behavior of van der Waals force bonded layered single-crystalline ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ ($x\approx 0.3$) have been performed. The single crystal of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$, grown by the chemical vapor transport method, crystallizes in hexagonal crystal structure with space group $\mathit{P}{6}_3/\mathit{mmc}$. Temperature ($T$)-dependent dc magnetic susceptibility of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ depicts a paramagnetic to ferromagnetic transition at $T\approx 180\mathrm{K}$ (${\mathit{T}}_{\mathrm{C}}$). Magnetic field variations of isothermal magnetization along the principal crystallographic directions in the magnetically ordered state at 5 K reveal soft ferromagnetic nature and significant magnetic anisotropy with the crystallographic $c$ axis being the easy axis of magnetization. Temperature-dependent study of linear electrical resistivity reveals the metallic nature of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$, exhibiting different scattering phenomena in three consecutive temperature regimes. The quadratic temperature dependence of linear electrical resistivity of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ below the magnetic ordering temperature gives a clear indication of the dominance of electron-magnon scattering. Magnetoresistance of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ along both the principal crystallographic directions are found to be negative and unsaturated with varying magnetic fields. The nature of the magnetic field dependence of magnetoresistance is very unusual, however exotic, revealing significant anisotropic behavior. Field-dependent magnetoresistance along the hard magnetization direction depicts quadratic magnetization dependence till the saturation magnetization field, which is reminiscent of the chiral spin texture of skyrmion host material. The study of Hall effect in ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ depicts an anomalous Hall behavior, as expected. In addition, Hall effect of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ depicts a signature revealing nontrivial topological spin texture when magnetic field and current were applied along the basal $ab$ plane, however perpendicular to each other. This type of topological Hall signature is expected for a candidate skyrmion host material like ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$.

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• Crystal phenomena
• Electrical conductivity
• Electrical properties
• Growth
• Hall effect
• Magnetic anisotropy
• Magnetic order
• Magnetic phase transitions
• Magnetic susceptibility
• Magnetic texture
• Magnetoresistance
• Magnetotransport
• Topological materials