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Unconventional Hall effect and its variation with Co-doping in van der Waals Fe3GeTe2

Abstract

Two-dimensional (2D) van der Waals (vdW) magnetic materials have attracted a lot of attention owing to the stabilization of long range magnetic order down to atomic dimensions, and the prospect of novel spintronic devices with unique functionalities. The clarification of the magnetoresistive properties and its correlation to the underlying magnetic configurations is essential for 2D vdW-based spintronic devices. Here, the effect of Co-doping on the magnetic and magnetotransport properties of Fe3GeTe2 have been investigated. Magnetotransport measurements reveal an unusual Hall effect behavior whose strength was considerably modified by Co-doping and attributed to arise from the underlying complicated spin textures. The present results provide a clue to tailoring of the underlying interactions necessary for the realization of a variety of unconventional spin textures for 2D vdW FM-based spintronics.

Introduction

Two-dimensional (2D) van der Waals (vdW) materials have recently drawn considerable attention owing to their prospect for 2D magnetism, spintronic and magneto-optical applications1,2,3,4. The stabilization of a long-range ferromagnetic and/or antiferromagnetic order down to the atomic limit and its seamless flexibility with various elements and structures provide an exciting opportunity for exploring new physical properties and realization of novel electronic devices down to the 2D limit2,3,4. Among the family of layered vdW ferromagnets (FMs), quasi-2D metallic Fe3GeTe2 is a promising candidate owing to its relatively high Curie temperature (~ 220 K)5,6,7,8,9,10, large anomalous Hall effect (AHE)7,8,9,10,11, and significant uniaxial magnetic anisotropy12, down to the atomic limit. Figure 1a shows the crystal structure of Fe3GeTe2. It possesses a hexagonal structure (see Fig. 1b) (space group- P63/mmc)5,6, 13, where a Fe3Ge substructure containing inequivalent Fe atoms is sandwiched between two vdW-bonded Te layers. Previous investigations using single-crystals and nanometer-sized flakes have demonstrated that the competition between magnetic exchange and dipole–dipole interaction, relativistic band structure effects, and magnetic frustration originating from inequivalent Fe atoms manifest in topological nodal line-driven large anomalous Hall angle11, and formation of various domain structures including stripe domains14 and hexagonal lattice of skyrmion bubbles15, 16. Besides, an unconventional Hall effect anomaly has been reported9, 17,18, whose origin is heavily debated and attributed to a multitude of factors, including the formation of in-plane skyrmions17,19, non co-planar spin configurations9, or multi to single-domain transformations under applied magnetic field18. Thus, an understanding of the factors determining the origin of the unusual magnetotransport features and its possible correlation to the underlying domain or topological spin textures is essential for the subsequent development of 2D vdW FM-based spintronic devices. One of the possible ways to achieve this objective pertains to the chemical substitution of the magnetic (Fe) site by a different element, which is expected to modify the underlying interactions and enable understanding of the factors contributing to the unconventional magnetotransport behavior. Some previous studies have shown that the substitution of Fe site by Co results in substantial changes of the magnetic properties (e.g., ferromagnetic transition temperature)20, modification of magnetic anisotropy strength21, and the emergence of a hard-magnetic phase with strong domain-wall pinning effects20. However, the effect of Co-doping on the magnetoresistive properties and the associated variations in the underlying magnetic domain and/or topological spin textures have not been clarified yet. The presence of such an unique magnetoresistive response is expected to serve as a confirmatory signature enabling selection of materials for non-trivial spin texture based physics and applications.

Figure 1
figure1

(a) Crystal structure of Fe3GeTe2. The Co atoms (red circles) are distributed randomly at the Fe site (yellow circles). (b) Crystal structure as viewed from ab plane with the c-axis along out-of-the plane of the paper.

Here, we show the impact of Co-doping on the unconventional Hall effect in the uniaxial vdW FM Fe3GeTe2. Magnetotransport measurements demonstrate a substantial modification of an unconventional cusp-like behavior in Hall resistivity with Co-doping, tentatively attributed to underlying domain structures from complementary magneto-optical investigations. The obtained results demonstrate a possible route towards the tuning of the properties within the family of vdW FMs, prospective for topological magnetism, and for the realization of a variety of non-collinear spin textures at reduced dimensions.

Results

Single-crystal growth and characterization

Single crystalline (CoxFe1−x)3GeTe2 (CoxFGT, hereafter) samples and a reference sample of Fe3GeTe2 (FGT, hereafter) were grown by chemical vapor transport (CVT) method. The various doping levels of 0, 0.05, 0.45, and 0.55 utilized in this study refer to the Co concentrations (x) determined using the atomic percentage ratios obtained from scanning electron microscope (SEM) energy-dispersive X-ray (EDX) spectroscopy measurements. X-ray diffraction (XRD) was carried out at room temperature with Cu-Kα radiation. Figure 2a shows the experimental results of out-of-plane XRD for undoped, slightly doped (Co0.05FGT), and significantly doped (Co0.45FGT) single-crystals. The observed Bragg peaks can be indexed with (00l) peaks, indicating that the sample surface corresponds to the ab plane with the c-axis along the out-of-plane direction.

Figure 2
figure2

(a) Out-of-plane X-ray diffraction pattern for Co0.05FGT (blue curve), Co0.45FGT (dark yellow curve), and FGT (red curve) single-crystalline samples at room temperature. The inset in (a) shows the optical micrograph of a cm sized FGT single-crystal utilized in this study. (b) Laue diffraction pattern of FGT single crystal. (c) Variation of c-axis lattice parameter versus Co-concentration (x) determined from energy dispersive X-ray (EDX) spectroscopy. (d)–(f) EDX spectra for Co0.05FGT, Co0.55FGT, and FGT, respectively.

Besides, any new peak corresponding to unreacted elements or peak shifts due to unintentional formation of other Co-Fe variants was not observed, indicating a homogenous mixing of Co and Fe. Laue diffraction pattern of the FGT crystal (see Fig. 2b) confirms the formation of high-quality single crystals. The obtained c-axis lattice parameter from XRD shows a monotonic decrease with increasing x (see Fig. 2c), consistent with earlier reports20. The EDX spectra of the samples, as shown in Fig. 2d–f confirms Co, Fe, Ge, and Te elements in the CoxFGT and FGT samples, respectively. The magnetic properties were characterized using a superconducting quantum interference device within the temperature range 5–300 K. Polar magneto-optical Kerr effect (MOKE) investigations were carried out on freshly cleaved ex-situ samples. Electrical and magnetotransport measurements were performed by a physical property measurement system using a conventional four-probe technique. To check the reproducibility of the observed results, similar experiments were repeated in separate single crystals of different sizes. Longitudinal (ρXX) and transverse (ρXY) resistivities were obtained as a function of both temperature and applied magnetic field (H).

Magnetic properties of CoxFGT and FGT

To investigate the impact of doping on the magnetic properties, we measured the temperature (T) dependence of magnetization and magnetic hysteresis of the single crystals. Figure 3a shows the experimental results of field-cooled (FC) magnetic susceptibility (χ) vs. T, for CoxFGT and FGT, under an applied magnetic field µ0H = 0.5 T, parallel (out-of-plane) and perpendicular (in-plane) to c-axis (µ0 is the permeability in vacuum). For FGT, from the derivative of χ, we obtain an averaged Curie temperature (TC) ≈ 206 K (± 4 K), demonstrating the onset of ferromagnetic order. The introduction of Co results in a gradual decrease of ferromagnetic transition temperature (TC) to ≈ 184.5 K (± 0.5 K) for Co0.05FGT, ≈ 60 K (± 1 K) for Co0.45FGT, and ≈ 35 K (± 2 K) for Co0.55FGT (see Supplementary Fig. S1). Besides, an increase of x also results in a suppressed bifurcation of χ along H || c and H c-axes, representing a significant reduction of the anisotropic magnetic character. Figure 3b–i shows the magnetic hysteresis curves along the out-of-plane (H || c) and in-plane (H c) directions for CoxFGT and reference FGT. The M-H curves for H || c-axis show the magnetic easy-axis along the c-axis and a lowering of the spontaneous magnetic moment with increasing x. Furthermore, no noticeable changes originating from surface oxidation effects were observed in the magnetic behavior of the samples (see Supplementary Fig. S2). The observed suppression of TC and spontaneous magnetic moment is consistent with the previous experimental results on transition metal doped FGT single-crystals20,22. To clarify the influence of doping on magnetic anisotropy, M-H curves for H c-axis were utilized to determine first-order (K1) and second-order (K2) anisotropy constants (see Supplementary Fig. S3) by Sucksmith-Thompson method8,23. Figure 3j shows the Co concentration (x) dependence of K1 and K2 at 10 and 50 K (T < TC for all the samples). An increase of x results in a considerable weakening of K1 by more than an order of magnitude while still retaining a positive value, indicating the uniaxial character of the magnetic anisotropy. Furthermore, for both CoxFGT and FGT, the temperature dependence of anisotropy constants shows a monotonic decrease of K1 with a rise of temperature. On the other hand, no significant effect of doping or temperature on K2 was observed (see Fig. 3k). The observed trend of variation of K1 can be qualitatively explained to arise from sharp changes in the magnetic anisotropy energy associated with spin–orbit interaction induced changes of electronic structure with reduced Fe concentration21 and/or Co doping, while that for K2 indicates the presence of additional factors. Assuming K1 is equivalent to uniaxial anisotropy constant (KU), we determine the quality factor Q = 2KU/µ0MS2 (where MS is saturation magnetization). We obtain Q = 7.58, 7.21, 4.29 and 11.98 for Co0.05FGT, Co0.45FGT, Co0.55FGT, and FGT, respectively (at 10 K). The obtained values are lower than some previous reports8, 9, 18, indicating a relatively soft ferromagnetic nature with Co doping. The results from the magnetization measurements will be later used for the extraction of the unconventional Hall contribution from ρXY vs. magnetic field curves.

Figure 3
figure3

(a) Magnetic susceptibility (χ) versus temperature (T) under magnetic field µ0H = 0.5 T applied parallel to c-axis and perpendicular to c-axis for the doped (CoxFGT) and undoped (FGT) single-crystalline samples. (b), (c) Field (H) dependence of magnetization (M) for Co0.05FGT single-crystal at various temperatures with H || c-axis and H c-axis, respectively. (d), (e) H dependence of magnetization M for Co0.45FGT single-crystal at various temperatures with H || c-axis and H c-axis, respectively. (f), (g) H dependence of magnetization M for Co0.55FGT single-crystal at various temperatures with H || c-axis and H c-axis, respectively. (h), (i) M versus H for the reference FGT single-crystalline sample at indicated temperatures for H || c-axis and H c-axis, respectively. (j) Co-concentration (x) dependence of first-order (K1) and second-order (K2) anisotropy constants at T = 10 and 50 K. (k) T dependence of first-order (K1) and second-order (K2) anisotropy constants for CoxFGT and reference FGT single-crystalline samples.

Unconventional Hall effect and its modification with Co-doping in FGT

Until now, most of the studies concerning the formation of topological spin textures have focused on the utilization of relativistic chiral Dzyaloshinskii-Moriya interaction (DMI)24,25, either originating from crystallographic lattice lacking inversion symmetry in single-layered FMs26,27,28,29,30,31,32,33 or due to broken space inversion symmetry in ferromagnetic multilayers34,35,36,37. Owing to the non-trivial nature of the spin structures, a traversing electron experiences a continuous precession of its spin magnetic moment, equivalent to a virtual (or emergent) magnetic field. Conventionally, the effect of this emergent field manifests as an additional contribution to Hall resistivity and serves as an electrical signature of the existence of topological spin textures, commonly referred to as topological Hall effect (THE)27,38,39,40,41,42. On the other hand, the possibility of utilization of centrosymmetric FMs as topological spin texture hosting materials was completely neglected owing to symmetry requirements, which dictates the absence of DMI in these systems. Recent experimental results have demonstrated the formation of topological skyrmion lattice and/or chiral structures in single-crystalline bulk FGT15,43, exfoliated nanoflakes16,44, and formation of Néel-type skyrmions in FGT-based heterostructures44,45,46. However, the experimental results from the magnetoresistive measurements9,17,18 cannot be solely interpreted to arise from submicron skyrmion bubble-like textures, demonstrated by magnetic imaging techniques15. In a practical scenario, doping of the Fe site by Co might modify the underlying magnetic microstructure and stabilize or destabilize topological spin textures by additional symmetry-breaking interactions44, enabling a resolution of the previous experimental results and tuning of topological spin structures in this material system. Figure 4a shows the schematic diagram of the measurement geometry utilized in this work. An applied dc I ( c-axis) of magnitude 10 mA was passed through the single-crystals along the x-direction (i.e., along crystal ab plane). The resulting change in ρXY under simultaneous application of external H (along z or x directions) and I was obtained by measuring voltage drop along the y-direction. For applied HZ (|| c-axis), we have observed a sizable Hall resistance, which can be attributed to the anomalous Hall effect (AHE)9,10,18, possibly originating from topological nodal lines in the band structure with the magnetization pointing along the easy axis11 (see Fig. 4b). The magnitude of AHE decreases with the increase of x, owing to the reduction of spontaneous magnetization with increasing Co-concentration (see Fig. 3b,d,f,h), while no characteristic features of THE were observed in ρXY vs. HZ. Furthermore, ρXY measurements also manifest in low magnitudes of the coercive field and remanence to saturation ratios, confirming the soft ferromagnetic nature. On the other hand, for the applied field along x-direction (HX || I c-axis), we have observed a reduction of ρXY magnitude along with the emergence of a prominent cusp-like feature (see Fig. 4c). The position of the cusp-like feature is independent of the in-plane field direction (HX or HY) (see Supplementary Fig. S5), shows negligible variation among different crystals with fixed x (see Supplementary Fig. S4), and shifts towards lower field values with increasing x. To further examine the origin of the observed features, we have also measured ρXY as a function of the angle θ for various applied field magnitudes (θ is defined as the angle subtended by H with respect to the out-of-plane z-direction) (see Fig. 4d–i). For applied µ0HX ≤ 2 T, ρXY sharply deviates from the usual cosine θ relation expected from conventional Hall effect47, hinting towards a different origin of the observed magnetotransport behavior (see Fig. 4d,e,g,h). An increase of H (µ0HX = 3 T) resulted in a gradual transition towards the conventional harmonic nature for Co0.05FGT, Co0.45FGT, and FGT, possibly due to a transition towards a single-domain behavior. A further increase of H is expected to result in a cosine θ behavior, where the magnetization follows the rotating H. This situation is observed for Co0.55FGT (see Fig. 4i), where ρXY follows a harmonic behavior. Interestingly, the cusp-like feature and its variation with Co-doping cannot be explained by Stoner-Wohlfarth model17 or due to planar Hall effect under applied H. Furthermore, owing to the stabilization of pining-type hard magnetic phases in CoxFGT and FGT at much higher temperatures20,48, the observed behavior is also unlikely to be related to the possibility of incoherent dynamics originating from nucleation and/or motion of magnetic domain walls. Thus, our experimental observations from ρXY vs. HX and peculiar angular dependencies over the entire range of Co-doping with varying magnetic properties are a strong indication of the existence of an unconventional magnetoresistive feature when H is applied perpendicular to the magnetic easy-axis of the vdW FM.

Figure 4
figure4

(a) Schematic representation of the measurement configuration utilized in this work. The angle (θ) is defined as the angle subtended by the applied magnetic field (H) with respect to the crystallographic c-axis (out-of-plane) of the single-crystalline samples. Applied current (I) for measurement is along X-direction. (b) Hall resistivity (ρXY) versus H (|| c-axis) for Co0.05FGT, FGT at 100 K and Co0.45FGT, Co0.55FGT at 10 K. (c) ρXY versus H ( c || I) for Co0.05FGT, FGT at 100 K and Co0.45FGT, Co0.55FGT at 10 K. The arrows in the figure denotes the position of maximum in ρXY for the single crystals investigated in this study. (d), (e), (f) θ dependence of ρXY for Co0.05FGT and FGT under applied µ0H = 1, 2 and 3 T at 100 K. (g), (h), (i) Experimental results for similar measurements on Co0.45FGT and Co0.55FGT under applied µ0H = 0.1, 1 and 3 T at 10 K. Solid lines in (i) denotes the fitting of the experimental data with the harmonic cosine θ dependence.

To examine the temperature-magnetic field phase space evolution of the unconventional Hall effect and to establish a clear picture, we have examined the temperature dependence of ρXY vs. HX. Figure 5a–c shows the results for Co0.05FGT, Co0.45FGT, and Co0.55FGT, respectively. For all the single-crystals, the cusp-like behavior persists over the entire temperature range (up to TC), indicating a magnetic origin of the observed features. An increase of x has a two-fold response; monotonic reduction of ρXY amplitude and reduction of the magnetic field strength corresponding to maximum ρXY, possibly reflecting the changes in the underlying interactions as a function of doping. To extract the unconventional contribution from total Hall resistivity (ρXY), we consider

$$\rho _{{{\text{XY}}}} = \mu _{0} R_{0} H + S_{{\text{A}}} \rho _{{{\text{XX}}}}^{2} M + \rho _{{{\text{XY}}}}^{{\text{U}}} ,$$
(1)

where ρXX is the longitudinal resistivity of the single crystal, SA is the field independent coefficient to the anomalous Hall resistivity determined from fitting (see Supplementary Fig. S6), and R0 is the ordinary Hall coefficient, determined from the slope of ρXY vs. HZ measurements. In this convention, the first term of Eq. (1) corresponds to the ordinary Hall effect (OHE), the second term corresponds to AHE, and ρXYU corresponds to the unconventional Hall effect comprising THE and magnetoresistive contributions from topologically trivial and non-trivial underlying spin configurations. Figure 5d,e shows the extracted unconventional Hall resistivity (ρXYU) from ρXY and in-plane magnetization curves (see Fig. 3c,e,g,i) for Co0.05FGT, FGT at 100 K and Co0.45FGT, Co0.55FGT at 10 K, respectively. These experimental results were then utilized to constitute the phase diagram of ρXYU over a wide temperature range for all the single crystals (see Fig. 5f–i). For Co0.05FGT and reference FGT, a significant strength of ρXYU is obtained, larger than THE strength either in vdW material9,18 or other potential skyrmionic FMs19,26,27,28,29,30,31,32,48,49. An increase in x results in a reduction of ρXYU over the entire temperature range, indicating its sensitivity to the underlying interactions. The magnitude of the in-plane field at which ρXYU attains a maximum is considered to be a measure of a possible internal emergent magnetic field (He), and its strength monotonically decreases with increasing x. These results of an unconventional Hall effect and the ability to control the internal emergent magnetic field by doping deepens our understanding of magnetoresistive effects in 2D vdW FMs.

Figure 5
figure5

(a), (b), (c) Hall resistivity (ρXY) versus applied HX ( c-axis || I) for Co0.05FGT, Co0.45FGT, and Co0.55FGT single-crystal, respectively, at various temperatures. (d) Experimental data for ρXY versus applied HX ( c-axis || I) for Co0.05FGT (red-rimmed circle) and FGT (black-rimmed circle) at 100 K, and extracted unconventional Hall contribution (ρXYU) to ρXY for Co-FGT (solid red circle) and FGT (solid black circle), respectively at 100 K. (e) Experimental results of similar measurements for Co0.45FGT (dark yellow-rimmed circle) and Co0.55FGT (blue-rimmed circle) at 10 K. (f), (g), (h), (i) Contour mapping of extracted ρXYU as a function of the applied magnetic field (H) and temperature (T) for reference FGT, Co0.05FGT, Co0.45FGT, and Co0.55FGT, respectively. Yellow lines in (f)–(i) correspond to the internal emergent magnetic field (He) for the single-crystals at various temperatures.

Magneto-optical imaging of domain structures

To clarify the contribution of the underlying magnetic configuration towards the observed magnetotransport behavior, temperature-dependent MOKE measurements were carried out on the single crystals. First, a reference image was taken at 250 K, well above TC of the single crystals. Then, the samples were cooled down to low temperatures (~ 50 K) in the absence of an applied magnetic field. Subsequently, images were acquired at several temperatures in the warming cycle. To enhance the signal-to-noise ratio, the difference between these MOKE images and the reference image was obtained. Note that no domain patterns were observed for Co0.45FGT and Co0.55FGT samples, indicating that the domain period is smaller than the resolution of our MOKE microscope (~ 1 µm). Thus, we restrict the experimental results of this section to that for Co0.05FGT and FGT single-crystals. Figure 6a,b shows the zero-field cooled (ZFC) MOKE images for Co0.05FGT and reference FGT at 100 K. For both the single-crystals, below TC, a spontaneous generation of stripe-like surface domain patterns was observed with alternating contrast corresponding to the magnetization being parallel or antiparallel to the out-of-plane direction (i.e., (00l) axis). Rows of circular domains or skyrmion bubble-like features with opposite magnetization orientation are embedded within this stripe domain background, as has been observed for FGT using other techniques, as well8,15,43. On the other hand, a remarkable transformation of the ZFC domain pattern was observed under a magnetic field H ( c-axis) applied perpendicular to the easy axis. For this measurement, after acquiring a reference image at 250 K, the samples were cooled to 50 K in the presence of an applied magnetic field µ0H ( c-axis) = 20 mT (see inset of Fig. 6c) (maximum applicable magnetic field of our set-up). Subsequently, the field was turned off and MOKE images were acquired in the remnant state at several temperatures. Figure 6c,d shows the zero-field MOKE images for Co0.05FGT and FGT, respectively, obtained in the warming cycle after field cooling. As opposed to the stripe-like domain background in the ZFC condition, the observed domain patterns for this case can be considered as a combination of magnetic domain walls connected in rings consisting of a collection of dense circular domains or skyrmion-like bubbles15,16. Note that the size of the bubble-like features in our single-crystalline samples are much larger than the hexagonal skyrmion lattices observed in other studies15,16. Once these unconventional spin structures are generated by H ( c-axis), the structure remains unchanged over the entire temperature range. An increase of temperature, up to TC, only results in a weakening of the magnetic contrast due to decreased magnetization and enhanced thermal effects. Besides, these textures in our Co0.05FGT and FGT vdW materials show remarkable stability up to much higher temperatures (~ TC), unlike previous studies, which reported the existence of skyrmion-lattice phases confined within small ranges of temperature and magnetic field for chiral MnSi29,39, Cu2OSeO328, and (Ca,Ce)MnO339,48,49 magnets or Gd2PdSi330 centrosymmetric frustrated magnets.

Figure 6
figure6

(a), (b) Differential p-MOKE image of remnant magnetic state for Co0.05FGT and FGT, respectively at 100 K. (c), (d) Differential p-MOKE image of remnant magnetic state for Co0.05FGT and FGT, respectively at 100 K, obtained after field cooling under applied µ0H = 20 mT (H c-axis). The inset in (a) denotes the direction of the cooling field H relative to the c-axis of the crystal. Black (grey) areas in (a)–(d) correspond to magnetization pointing in parallel (antiparallel) direction with respect to c-axis (out of the plane of paper).

Discussion

Here, the possible scenarios contributing to the observation of an unconventional Hall effect and its correlation to the complicated domain configurations from MOKE are discussed. As stated before, the occurrence of a cusp-like feature in ρXY for applied H deviating from the (00l) direction is an unresolved issue attributed either to THE from the emergent magnetic field of underlying spin textures9,18, or to the effect of multi-domain to single-domain transformations under perpendicular magnetic anisotropy (PMA)17. The former is supported by the observation of submicrometer scale skyrmion lattice structure15,16, while, for the latter, the experimental results from FGT were compared with similar experiments and micromagnetic simulations on Ta/CoFeB/MgO multilayers17. The present experimental results with Co-doping reveals subtle differences, which enables the identification of the dominant contribution towards this unconventional magnetoresistive feature. Our temperature-dependent magnetization demonstrates a monotonic reduction of TC (TC ~ 200 K for FGT to ~ 35 K for Co0.55FGT), and a significant reduction of PMA with increasing x. Under the scenario of multi-to-single domain transformations17, stronger PMA results in a complete disappearance of the cusp-like behavior and ρXY magnitude under applied H ( c-axis). This is expected since PMA aligns the magnetization towards the easy-axis and hinders the formation of multi-domain magnetic configurations. On the other hand, our experimental results follow an opposite behavior (µ0He ≈ 3.5 T in FGT to ≈ 0.3 T in Co0.55FGT), ruling out the possibility of multi-to-single domain transformations as the dominant factor governing the ρXY versus H behavior. Complementary MOKE measurements also reveal a complicated spontaneous magnetic domain pattern consisting of bubble-like features which was converted into an unconventional ring-like structure with applied H perpendicular to the (00l) easy directions. We attribute these ring-like structures to an aggregate of connected topological skyrmion bubble-like or lattice structures and magnetic domain walls along with possible existence of trivial circular and/or stripe domains. Under this scenario, assuming that the ring-like patterns are composed of sub-micrometer sized bubble-like structures, the position of the cusp-like feature in our magnetotransport measurements corresponds to the emergent field from the underlying spin textures, attributed to the total flux quantum contained in these structures. The substitution of Fe by Co results in a modification of magnetic exchange and anisotropy, along with the introduction of symmetry-breaking interactions in the bulk44, leading to a modification of the spin configurations and associated flux quanta manifesting in significant depreciation of the internal emergent magnetic field. Future experimental investigations on imaging of the magnetic configurations at higher H and/or theoretical investigations on magnetic textures in vdW FMs would provide significant insights required for further understanding of the complicated spin structures in vdW FMs. We believe that these results provide a deeper understanding of magnetoresistive responses originating from complicated non-coplanar spin configurations in 2D vdW magnets and are a crucial step towards the development of vdW materials with engineered properties. The present study offer a route towards the realization of new-concept spin textures in vdW FMs, promising for non-collinear spin texture based physics and spintronic devices.

Method

Single-crystal growth

The single crystals of CoxFGT and reference FGT were grown by CVT method with I2 as a transport agent. Starting from a mixture of pure elements Fe (5 N), Ge (5 N), Te (5 N) and Co (5 N), the mixture was sealed in an evacuated quartz tube and heated in a two-zone furnace with a temperature gradient 750/700 °C for one week. Large crystals of sizes up to ~ 12 × 8 mm2 were obtained, cleavable in the ab plane.

Sample preparation for electrical measurements

From the synthesized single crystals with/without Co-doping, several mm-sized plate-like single crystals were selected. The selected samples were cut into rectangular shapes with typical sizes of ~ 5–6 × 3–5 mm2. Before electrode fabrication, the surface of these samples was freshly cleaved in an inert atmosphere. Current and voltage electrodes were fabricated in situ by connecting Au wires on the samples by silver epoxy.

Data availability

The data which support the findings of this work are available from the corresponding authors upon reasonable request.

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Acknowledgements

The authors thank Dr. Takaaki Dohi for discussions. RRC acknowledges Department of Science and Technology (DST), Government of India, for financial support (Grant no. DST/INSPIRE/04/2018/001755). RPS acknowledges Science and Engineering Research Board (SERB), Government of India, for Core Research Grant CRG/2019/001028. A portion of this work was supported by JSPS Kakenhi 19H05622, 20K15155 and RIEC International Cooperative Research Projects, Tohoku University. O.A.T. acknowledges the support by the Australian Research Council (Grant No. DP200101027) and NCMAS grant.

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R.R.C. and R.P.S. planned the study. RRC synthesized the single-crystal samples and carried out structural and magnetic characterizations. R.R.C. and S.D. performed the electrical and magneto-optical measurements and analyzed the data with inputs from O.A.T. R.R.C. and S.D. wrote the manuscript with input from all the authors. All authors discussed the results.

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Correspondence to Rajeswari Roy Chowdhury, Samik DuttaGupta or Ravi Prakash Singh.

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Chowdhury, R.R., DuttaGupta, S., Patra, C. et al. Unconventional Hall effect and its variation with Co-doping in van der Waals Fe3GeTe2. Sci Rep 11, 14121 (2021). https://doi.org/10.1038/s41598-021-93402-6

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