Modification of unconventional Hall effect with doping at the nonmagnetic site in a two-dimensional van der Waals ferromagnet

Two-dimensional (2D) van der Waals (vdW) magnets have garnered considerable attention owing to the existence of magnetic order down to atomic dimensions, flexibility towards interface engineering and unconventional magnetoresistive properties, offering an attractive platform to explore novel phenomena and functionalities, prospective for spintronic or quantum information devices. Among the promising candidates, vdW ferromagnet (FM) ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ shows an unusual magnetotransport behavior, tunable by doping at the magnetic (Fe) site, and tentatively arising from complicated underlying spin texture configurations. In this work, we explore an alternative route towards manipulation of magnetotransport properties without directly affecting the magnetic site i.e., by doping at the nonmagnetic (Ge) site of ${\mathrm{Fe}}_3\left(\mathrm{Ge},\mathrm{As}\right){\mathrm{Te}}_2$. Interestingly, doping at the non-magnetic (Ge) site results in an unconventional Hall effect whose strength was considerably modified by increasing As concentration, tentatively attributed to underlying emergent electromagnetic behavior, demonstrating an alternate direction towards tailoring of underlying interactions without perturbing the magnetic (Fe) site in 2D vdW magnetic materials.

Figure 1

(a) Crystal structure of ${\mathrm{Fe}}_3\left({\mathrm{Ge}}_{1-x}{\mathrm{As}}_x\right){\mathrm{Te}}_2$ (${\mathrm{As}}_x\mathrm{FGT}$). The As atoms (yellow circles) are distributed randomly at the Ge site (blue circles). The dashed rectangular area denotes one monolayer of ${\mathrm{Fe}}_3\left({\mathrm{Ge}}_{1-x}{\mathrm{As}}_x\right){\mathrm{Te}}_2$. (b) Crystal structure as viewed from $ab$ plane with the $c$ axis along out of the plane of the paper. (c) Optical micrograph of ${\mathrm{As}}_{0.20}\mathrm{FGT}$ single-crystal, utilized in this study. (d) Out-of-plane x-ray diffraction pattern for ${\mathrm{As}}_{0.20}\mathrm{FGT}$, ${\mathrm{As}}_{0.40}\mathrm{FGT}$, and FGT single-crystalline samples at room temperature. (e) X-ray diffraction of ${\mathrm{As}}_{0.40}\mathrm{FGT}$ sample with Le Bail fit. (f) Laue diffraction pattern of FGT single crystal. (g), (h) Energy dispersive x-ray analysis (EDX) spectra for ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and ${\mathrm{As}}_{0.40}\mathrm{FGT}$, respectively.

Figure 2

(a) Magnetic susceptibility (χ) versus temperature ($T$) under magnetic field ${\mu }_{0}H=0.5\mathrm{T}$, applied parallel to $c$ axis or perpendicular to $c$ axis for ${\mathrm{As}}_x\mathrm{FGT}$ and FGT. (b), (c) Field ($H$) dependence of magnetization ($M$) for ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and parent FGT single-crystals at various temperature with $H\left|\right|$ $c$ axis and $H$ ⊥ $c$ axis, respectively. (d), (e) $M$ versus $H$ for ${\mathrm{As}}_{0.40}\mathrm{FGT}$ single-crystal at indicated temperatures for $H\left|\right|$ $c$ axis and $H$ ⊥ $c$ axis, respectively. (f) $T$ dependence of effective anisotropy constant ($K_{\mathrm{eff}}$) with/without As doping.

Figure 3

(a)–(c) Differential p-MOKE image of remnant magnetic state for ${\mathrm{As}}_{0.20}\mathrm{FGT}$, ${\mathrm{As}}_{0.40}\mathrm{FGT}$, and FGT respectively at 120, 50, and 100 K. Black (grey) areas correspond to magnetization pointing in parallel (antiparallel) direction with respect to $c$ axis (out-of-plane of paper). The scale bar for the p-MOKE images of ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and ${\mathrm{As}}_{0.40}\mathrm{FGT}$ corresponds to the one above (a), while that for FGT is above (c).

Figure 4

(a) Hall resistivity $\left({\rho }_{XY}\right)$ versus applied $H_X$ ($\perp \mathrm{c}$ axis || $I$) for ${\mathrm{As}}_x\mathrm{FGT}$ single-crystal at various temperatures. (b), (c) Temperature dependence of transverse resistivity (${\rho }_{XY}$) versus $H_{\mathrm{Z}}$ (|| $c$ axis) for ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and ${\mathrm{As}}_{0.40}\mathrm{FGT}$, respectively. (d), (e) Temperature dependence of ${\rho }_{XY}$ versus $H_X$ ($\mathbf{\perp }c$ axis) for ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and ${\mathrm{As}}_{0.40}\mathrm{FGT}$, respectively. Solid lines in (d), (e) indicate the total contributions from ordinary and anomalous Hall effect contributions, calculated using Eq. (1). (f), (g) Contour mapping of extracted unconventional Hall effect contribution (${\rho }_{XY}^{\mathrm{U}}$) as a function of applied magnetic field ($H$) and temperature ($T$) ${\mathrm{As}}_{0.20}\mathrm{FGT}$ and ${\mathrm{As}}_{0.40}\mathrm{FGT}$, respectively, respectively. Yellow solid lines in (f), (g) corresponds to the magnetic field strength where a maximum in ${\rho }_{XY}^{\mathrm{U}}$ was obtained at a fixed $T$.

Figure 5

Three-dimensional temperature ($T$), unconventional Hall resistivity (${\rho }_{XY}^{\mathrm{U}}$), and effective emergent magnetic field $\left(B_Z^{\mathrm{eff}}\right)$ phase diagram for reference FGT doping at the magnetic site (Fe) of FGT [26], and doping at the nonmagnetic (Ge) site (this work).

Figure 6

(a) Differential p-MOKE image of remnant magnetic state for FGT, respectively at 100 K. Black (grey) areas correspond to magnetization pointing in parallel (antiparallel) direction with respect to $c$ axis (out of the plane of paper). The test lines A and B (yellow lines) were drawn to evaluate the domain period. (b) Pixel intensity versus test line length for the yellow lines in (a). The minimum pixel intensity (∼0) correspond to the regions with the magnetization orienting antiparallel to the $c$ axis while the maximum pixel intensity (∼255) correspond to the magnetization along the $c$ axis.

Figure 7

Anomalous Hall conductivity (${\sigma }_{XY}$) versus longitudinal conductivity (${\sigma }_{XX}$) for Fe single crystals [44], Gd thin film [44], chiral magnet MnSi [45], ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ [46], ferromagnetic semiconductor GaMnAs [47], magnetite ${\mathrm{Fe}}_{2.5}{\mathrm{Zn}}_{0.5}{\mathrm{O}}_4$ [48], van der Waals ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ [26], and As-doped FGT (this work). The black horizontal and vertical line denotes the expected value for quantum Hall effect per atomic layer $\left(e^2/h\right)$ ($e$ = electronic charge, $h$ is Planck's constant).

Figure 8

Longitudinal resistivity (${\rho }_{XX}$) versus temperature ($T$) for ${\mathrm{As}}_{0.20}\mathrm{FGT}$, ${\mathrm{As}}_{0.40}\mathrm{FGT}$, and parent FGT single-crystalline samples.