⇦Chinese Physics Letters, 2023, Vol. 40, No. 11, Article code 117501Express Letter Giant 2D Skyrmion Topological Hall Effect with Ultrawide Temperature Window and Low-Current Manipulation in 2D Room-Temperature Ferromagnetic Crystals Gaojie Zhang (张高节)1,2, Qingyuan Luo (罗清源)3, Xiaokun Wen (文晓琨)1,2, Hao Wu (武浩)1,2*, Li Yang (杨丽)1,2, Wen Jin (靳雯)1,2, Luji Li (李路吉)1,2, Jia Zhang (张佳)4, Wenfeng Zhang (张文峰)1,2,5, Haibo Shu (舒海波)3*, and Haixin Chang (常海欣)1,2,5* Affiliations 1State Key Laboratory of Material Processing and Die & Mold Technology, School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2Wuhan National High Magnetic Field Center and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 3College of Optical and Electronic Technology, China Jiliang University, Hangzhou 310018, China 4School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China 5Shenzhen R&D Center of Huazhong University of Science and Technology, Shenzhen 518000, China Received 17 October 2023; accepted manuscript online 26 October 2023; published online 1 November 2023 *Corresponding authors. Email: hxchang@hust.edu.cn; h_wu@hust.edu.cn; shuhaibo@cjlu.edu.cn Citation Text: Zhang G J, Luo Q Y, Wen X K et al. 2023 Chin. Phys. Lett. 40 117501    Abstract The discovery and manipulation of topological Hall effect (THE), an abnormal magnetoelectric response mostly related to the Dzyaloshinskii–Moriya interaction (DMI), are promising for next-generation spintronic devices based on topological spin textures such as magnetic skyrmions. However, most skyrmions and THE are stabilized in a narrow temperature window either below or over room temperature with high critical current manipulation. It is still elusive and challenging to achieve large THE with both wide temperature window till room temperature and low critical current manipulation. Here, using controllable, naturally oxidized sub-20 and sub-10 nm 2D van der Waals room-temperature ferromagnetic Fe$_{3}$GaTe$_{2-x}$ crystals, we report robust 2D skyrmion THE with ultrawide temperature window ranging in three orders of magnitude from 2 to 300 K, in combination with giant THE of $\sim$ 5.4 $µ \Omega\cdot$cm at 10 K and $\sim$ 0.15 $µ \Omega\cdot$cm at 300 K, which is 1–3 orders of magnitude larger than that of all known room-temperature 2D skyrmion systems. Moreover, room-temperature current-controlled THE is also realized with a low critical current density of $\sim$ $6.2\times10^{5}$ A$\cdot$cm$^{-2}$. First-principles calculations unveil natural oxidation-induced highly enhanced 2D interfacial DMI reasonable for robust giant THE. This work paves the way to room-temperature electrically controlled 2D THE-based practical spintronic devices.
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 DOI:10.1088/0256-307X/40/11/117501 © 2023 Chinese Physics Society Article Text Over the past decade, realizing real-space topological spin textures at room temperature has attracted enormous attention for topological physics and spintronics.[1-7] Understanding the abnormal magnetoelectric transport behavior of carriers coupling with these topological spin textures is crucial for practical applications in spintronic devices. In general, topological spin textures with scalar spin chirality generate an effective magnetic field that results in the topological Hall effect (THE) when the carriers passing through it, thereby linking the local topological spin textures to an electrical response.[8-10] The THE appears as an antisymmetric spike in the magnetoelectric transport image, which has been observed in some magnetic systems with inversion symmetry breaking and strong spin-orbit coupling (SOC).[6,8-15] Up to date, THE has become an effective tool for electrical detection and manipulation of topological spin textures such as magnetic skyrmions.[6,8-10,16-18] However, most skyrmions and THE can only be stabilized in a narrow temperature window either below or over room temperature with high critical current manipulation.[6,10,16] It is still elusive and challenging to realize large THE with both wide temperature window till room temperature and low critical current manipulation. The THE-hosting magnetic systems mostly possess the appreciable Dzyaloshinskii–Moriya interaction (DMI), $H_{\rm DMI}=-D_{ij}\cdot(S_{i}\times S_{j}$), which implies an antisymmetric exchange interaction between two neighboring spins $S_{i}$ and $S_{j}$ with strength and direction determined by Moriya vector $D_{ij}$.[10-12] Compared with bulk DMI induced THE in chiral, kagome, and frustrated magnets,[8,19,20] interfacial DMI induced THE in 2D heterostructures or superlattices provides a broader platform for the miniaturization, integration, and controllability of 2D spintronic devices, which is more desirable in current microelectronic industry.[9-13] However, 2D interfacial DMI is mostly induced in conventional heavy-metal/ferromagnet ultrathin heterostructures so far,[2,10,12] and delicate control of 2D DMI for 2D THE manipulation at room temperature is still challenging. In this work, via natural oxidization of sub-20 and sub-10 nm 2D van der Waals (vdW) room-temperature ferromagnetic Fe$_{3}$GaTe$_{2-x}$ crystal (O-Fe$_{3}$GaTe$_{2-x}$), we demonstrate robust 2D THE with an ultrawide temperature window ranging in three orders of magnitude from 2 to 300 K in O-Fe$_{3}$GaTe$_{2-x}$/Fe$_{3}$GaTe$_{2-x}$ (O-FGaT/FGaT) heterostructures. Remarkably, 2D O-FGaT/FGaT exhibits giant THE with topological Hall resistivity ($\rho_{\rm TH}$) of $\sim$ 5.4 $µ \Omega \cdot$cm at 10 K and $\sim$ 0.15 $µ \Omega \cdot$cm at 300 K, which is 1–3 orders of magnitude better than that of all known room-temperature 2D skyrmion systems. Moreover, the current-controlled THE in 2D O-FGaT/FGaT at room temperature reveals a low critical current density of $\sim$ $6.2\times 10^{5}$ A$\cdot$cm$^{-2}$. Using first-principles calculations, we unveil that the surface natural oxidation induces O–Fe, O–Ga, O–Te orbital hybridization and surface charge transfer, which further induces enhancement by $\sim$ 8.2–26.3 times, sizeable interfacial DMI in 2D O-FGaT/FGaT, providing an opportunity to engineer 2D vdW heterostructures for robust large THE-based spin memory with low-critical-current tunability. Results—Characterizations of Pristine and Oxidized 2D vdW Room-Temperature Ferromagnetic Fe$_{3}$GaTe$_{2-x}$. The pristine vdW-stacked Fe$_{3}$GaTe$_{2-x}$ crystal is a layered metallic ferromagnet with $P6_{3}/mmc$ space group and some Te vacancies. As shown in Fig. 1(a), a Fe$_{3}$Ga heterometallic slab is sandwiched between two Te (or Te vacancies) layers, forming a monolayer Fe$_{3}$GaTe$_{2-x}$ stacked along the $c$-axis. The crystal structure of Fe$_{3}$GaTe$_{2-x}$ is basically similar to that of Fe$_{3}$GaTe$_{2}$[21,22] and confirmed by x-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), and energy-dispersive spectroscopy (EDS) (Figs. S1 and S2 in the Supplemental Material). The uniform elemental distribution of Fe, Ga, Te and atomic ratio of $3.12\!:\!0.95\!:\!1.70$ are identified, implying the existence of Te vacancies in the pristine Fe$_{3}$GaTe$_{2-x}$ crystal. This speculation is further verified by electron probe micro-analyzer (EPMA) with Te vacancy content of $\sim$ 15 at.% (Fig. S3). The naturally oxidized Fe$_{3}$GaTe$_{2-x}$ nanosheet is examined by a high-angle annular dark-field scanning transmission election microscopy (HAADF-STEM) along the [120] direction [Fig. 1(b)]. Figures 1(c)–1(e) clearly show the vdW-stacked structure and the presence of Te vacancies with atomic resolution in pristine Fe$_{3}$GaTe$_{2-x}$. The natural oxidation leads to the formation of O-FGaT/FGaT heterostructure with an oxidation layer thickness of $\sim$ 4.5 nm, which can be examined by EDS mappings [Fig. 1(f)]. Moreover, the 2D O-FGaT layer is also confirmed by the element line distribution along the depth direction [Fig. 1(g)] and Ar$^{+}$-etched x-ray photoelectron spectroscopy (XPS) (Fig. S4, more discussions in Note S1 of the Supplemental Material).
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Fig. 1. Crystal structure and TEM characterizations of 2D O-FGaT/FGaT heterostructure from natural oxidization. (a) Structural models of vdW Fe$_{3}$GaTe$_{2-x}$ along the [110] and [120] directions. (b) Cross-sectional HAADF-STEM image of vdW Fe$_{3}$GaTe$_{2-x}$ crystal along the [120] direction. (c) Atomic-resolution HAADF-STEM image and corresponded arrangement of the stacking structure of Te, Fe, and Ga atoms. [(d), (e)] Observation of Te vacancies and corresponded intensity profiles. The visibility and contrast between atoms were enhanced for identifying the Te vacancy. (f) Cross-sectional HAADF image and corresponded elemental mapping of an h-BN capped O-FGaT/FGaT. Note that only a little diluted scattered oxygen distribution imaged within Fe$_{3}$GaTe$_{2-x}$ comes from the temporary atmospheric exposure during the sample preparation by FIB. (g) Elemental line distribution along the depth direction.
Giant 2D THE with Ultrawide Temperature Window. The pristine bulk Fe$_{3}$GaTe$_{2-x}$ crystal and its 2D nanosheet host an above-room-temperature ferromagnetism (Curie temperature $T_{\rm C}\approx350$–360 K) and large perpendicular magnetic anisotropy (PMA)[21-23] (Figs. S5 and S6, more discussions in Note S2 of the Supplemental Material). Only typical anomalous Hall effect (AHE) exists in pristine Fe$_{3}$GaTe$_{2-x}$ 2D nanosheets and no THE is observed [Fig. S6(c)]. The anomalous Hall device geometry for O-FGaT/FGaT heterostructure is shown in Fig. 2(a), and the thickness of as-tested 2D O-FGaT/FGaT is ranged from 77 down to 9.8 nm (Fig. S7). As shown in Figs. 2(b) and 2(c), 77 and 30 nm O-FGaT/FGaT heterostructures exhibit obvious AHE hysteresis loops when the measured temperature is lower than $\sim$ 370 K. When the thickness of O-FGaT/FGaT is less than 20 nm, the unusual dips and peaks emerge around the coercivity ($H_{\rm C}$) and disappear at higher fields, indicating that the THE is induced when the magnetic moment starts to be reversed [Figs. 2(d) and 2(e) and Fig. S8(c)]. Note that the AHE and THE in the sub-20 nm O-FGaT/FGaT can remain up to room temperature, implying the coexistence of robust ferromagnetic order and topological spin textures in 2D scale at room temperature. Moreover, the normalized anomalous Hall resistivity ($\rho_{\rm AH}$) and $H_{\rm C}$ show a thickness dependence in these O-FGaT/FGaT with $T_{\rm C} \sim330$–370 K, decreasing with reducing thickness [Fig. 2(f), 2(g)].
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Fig. 2. Thickness-dependent magnetotransport of 2D room-temperature ferromagnetic O-FGaT/FGaT heterostructures. (a) Schematic illustration and measurement geometry of Hall devices. (b)–(e) Behavior of $\rho_{xy}$ versus $B$ for four 2D O-FGaT/FGaT nanosheets with different thicknesses at various temperatures. Insets show optical images of each Hall device. [(f), (g)] Temperature-dependent normalized $\rho_{\rm AH}$ and H$_{\rm C}$ extracted from (b)–(e). Error bars sd., $N=25$ for $\rho_{\rm AH}$ and $N=3$ for $H_{\rm C}$. The temperature at zero normalized $\rho_{\rm AH}$ is determined to be the $T_{\rm C}$. (h) Diagram of extracting the THE contribution in a typical 16 nm 2D O-FGaT/FGaT at 10 K. Contributions from AHE (red solid line) and THE term (light green area) are marked, where the AHE contributions are fitted by a step function.
Before discussing the 2D THE in sub-20 nm O-FGaT/FGaT, it is necessary to review some recent criticisms about the artifact “THE”.[24] Based on recently reported distinguishing methods,[25,26] the possibility of the artifact THE has been discussed and eliminated (see more discussions in Note S3 and Fig. S9 of the Supplemental Material), thereby implying that the observed 2D THE may originate from topologically nontrivial spin textures such as magnetic skyrmions.[11,14] Actually, the observed 2D THE in sub-20 nm O-FGaT/FGaT is most likely major induced by Néel-type skyrmions stabilized by interfacial DMI, similar with other Néel-type skyrmion systems such as CrTe$_{2}$/Bi$_{2}$Te$_{3}$,[13] WTe$_{2}$/Fe$_{3}$GeTe$_{2}$,[11] and O-Fe$_{3}$GeTe$_{2}$/Fe$_{3}$GeTe$_{2}$.[27,28] This deduction is confirmed by Lorentz-TEM at room temperature, as the skyrmion in 2D O-FGaT/FGaT is only visible at nonzero tilt angle while invisible at zero tilt and reverse its contrast when reversing the tilt angle or focus direction (Fig. S10 in the Supplemental Material), consistent with the nature of Néel-type skyrmions.[11,27,28] A thinner 2D O-FGaT/FGaT shows a higher skyrmion density and the average skyrmion size of $\sim$ 65 nm at 150 Oe (Fig. S11). In contrast, no skyrmions are observed in the pristine non-oxidized thin 2D Fe$_{3}$GaTe$_{2-x}$ nanosheet (Fig. S12), implying the important role of surface oxidization for realizing Néel-type skyrmions in this 2D system. Hence, Hall effect can be decomposed into three terms, including ordinary Hall effect (OHE), AHE and THE (see more discussions in Note S4 of the Supplemental Material). In order to study the temperature and magnetic field dependence of THE, the linear fitting and a step function $M_{0}\tanh[\frac{B}{a_{0}}-H_{0}]$, where $M_{0}$, $a_{0}$, and $H_{0}$ are fitting parameters, are used to single out the OHE and AHE contributions[13] [Fig. 2(h) and Fig. S13]. The skyrmion phase diagrams for 9.8, 13, and 16 nm O-FGaT/FGaT are plotted based on temperature-dependent THE [Figs. 3(a)–3(d) and Fig. S14]. In certain $\rho_{\rm TH}$–$B$ curves, the occurrence of both positive and negative peaks near the $H_{\rm C}$ is attributed to the nucleation and pinning of skyrmions, similar to other skyrmion systems.[29] Moreover, as temperature increases, the 2D THE exists in a smaller magnetic field and gradually weakens but persists at room temperature. The large THE at low temperatures implies a stronger effective magnetic field ($B_{\rm eff}$) induced by magnetic skyrmions in real space.[9,13] For 19 nm O-FGaT/FGaT, the emergent THE exists in an ultrawide temperature window ranging in three orders of magnitude from 2 to 300 K [Fig. 3(e)], suggesting the robust skyrmions in these sub-20 nm O-FGaT/FGaT nanosheets. At room temperature, the variation of $\rho_{\rm TH}$ with magnetic field of this 19 nm O-FGaT/FGaT has a similar variation trend to that of skyrmions density with magnetic field of Lorentz-TEM thin sample mentioned above, which further confirms the correlation between THE and skyrmions to some extent (Fig. S15 in the Supplemental Material). Therefore, according to current results and analysis, the most likely major origin of THE in thin 2D O-FGaT/FGaT is the skyrmions. The magnitude of 2D THE presents some thickness dependence. Remarkably, the 13 nm O-FGaT/FGaT shows giant $\rho_{\rm TH}$ as large as $\sim$ 5.4 $µ \Omega \cdot$cm at 10 K and $\sim$ 0.15 $µ \Omega \cdot$cm at 300 K [Fig. 3(a), and Table S1 in the Supplemental Material], reflecting the large coupling strength between current and skyrmions.[19] Note that the room-temperature $\rho_{\rm TH}$ in 2D O-FGaT/FGaT is 1–3 orders of magnitude better as compared with all other 2D skyrmion systems such as [Ir/Fe/Co/Pt]$_{20}$ (0.03 $µ \Omega \cdot$cm),[12] Tm$_{3}$Fe$_{5}$O$_{12}$/Pt (0.0046 $µ \Omega \cdot$cm),[10] and [Co/Pt]$_{5}$ (0.01 $µ \Omega \cdot$cm)[30] [Fig. 3(f) and Table S2]. For 19, 16, and 13 nm O-FGaT/FGaT nanosheets, $\rho_{\rm TH}$ increases with reduced thickness (Table S1). However, $\rho_{\rm TH}$ of 9.8 nm O-FGaT/FGaT deteriorates with worst performance (Table S1), which may originate from the oxidation-induced structural degradation due to the fact that thin sample is more likely to be damaged by air oxidation compared with thicker one. Further, the THE-derived skyrmion size ($n_{\rm sk}^{-1/2}$) of four sub-20 nm O-FGaT/FGaT nanosheets are summarized in Table S1 (see more discussions in Note S4 in the Supplemental Material), and the 13 nm O-FGaT/FGaT shows skyrmion size of 1.2 and 12.3 nm at 10 and 300 K, respectively. Such extremely tiny THE-derived skyrmion size is the smallest one for 2D skyrmion systems[9,20] (Fig. S16). Note that the THE-derived skyrmion size is based on an ideal situation, so it can only provide an order of magnitude estimation of the skyrmion sizes and is different from the actual value measured in Lorentz-TEM. Overall, this robust 2D THE combining an ultrawide temperature window till room temperature and giant $\rho_{\rm TH}$ in 2D O-FGaT/FGaT is superior to that of all known 2D skyrmion systems [Fig. 3(g) and Table S2], which is essential for practical applications of 2D THE-based spintronic devices.
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Fig. 3. Giant 2D THE in sub-20 and sub-10 nm 2D room-temperature ferromagnetic O-FGaT/FGaT heterostructures. (a) Curves of $\rho_{\rm TH}$–$B$ for a 13 nm O-FGaT/FGaT at different temperatures. Inset: the scheme of skyrmion-based THE. (b)–(d) Skyrmion phase diagrams from the THE versus temperature and magnetic field for 9.8, 13, and 16 nm O-FGaT/FGaT nanosheets. The color bar indicates the value of $\rho_{\rm TH}$. Interpolation is performed at each experimental data point. (e) Curves of $\rho_{\rm TH}$–$B$ for 19 nm O-FGaT/FGaT at different temperatures ranging from 2 to 300 K. (f) Comparison of the high-temperature ($\ge$ 300 K) $\rho_{\rm TH}$ with those of other 2D skyrmion systems. (g) Comparison of the maximum $\rho_{\rm TH}$ and THE temperature window with those of other 2D skyrmion systems. See reported data and references in Table S2 in the Supplemental Material.
Room-Temperature Low-Current Manipulation of THE. So far, current-controlled THE has been studied theoretically and experimentally in many skyrmion systems, which provides a potential possibility for electrical detection of skyrmion motion.[6,16-18,31] Hence, we perform the current-density dependence of 2D THE in 19 and 13 nm O-FGaT/FGaT at room temperature (Fig. 4). Prior to this, the influence of joule heating effect is evaluated by $\rho_{xx}$ and saturated $\rho_{\rm AH}$ at each current density (Fig. S17, more discussions in Note S5 of the Supplemental Material). With the increase of current density, the $\rho_{\rm TH}$ of 19 and 13 nm O-FGaT/FGaT first remains unchanged and then gradually decreases, as shown in Figs. 4(a) and 4(b). In order to confirm whether the decrease of $\rho_{\rm TH}$ is due to the skyrmions motion, we use some formulas to analyze these THE data. In the system of current-driven skyrmion motion, the current-density dependence of the $\rho_{\rm TH}$ follows the formula[16] $\rho _{\rm {TH}}(j)=\rho _{\rm {TH}}(j\leqslant j_{\rm c})[1-A(1-j_{\rm c}/j)]$, where $\rho _{\rm {TH}}(j\leqslant j_{\rm c})=PR_{0}B_{\rm{eff}}=PR_{0}n_{\rm {sk}}\varPhi_{0}$, which has been mentioned in Note S4 of the Supplemental Material, $A$ is an introducing coefficient, and $j_{\rm c}$ is the critical current density. After nonlinear fitting, the current-density dependent $\rho_{\rm TH}$ data are in good agreement with the relation $\rho_{\rm TH}(j>j_{\rm c})\propto 1/j$ [upper panels in Figs. 4(c) and 4(d)], which implies that the reduction of $\rho_{\rm TH}$ may be attributed to the skyrmion motion. Actually, since skyrmions have been proved to induce exactly one quantum of emergent magnetic flux per skyrmion,[32] a moving skyrmion will produce an emergent electric field perpendicular to the direction of the skyrmion motion according to Faraday's law of induction. This emergent electric field opposes to the topological Hall field arising from the static skyrmions, thereby suppressing the $\rho_{\rm TH}$.[16,31] Meanwhile, the $j_{\rm c}$ for current-controlled THE in 19 and 13 nm O-FGaT/FGaT are $\sim$ $6.2\times 10^{5}$ A$\cdot$cm$^{-2}$ and $\sim$ $7.82\times 10^{5}$ A$\cdot$cm$^{-2}$, respectively, 1–2 orders of magnitude lower than those of most room-temperature 2D skyrmion systems[33-35] (Table S3 in the Supplemental Material).
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Fig. 4. Room-temperature current-controlled 2D THE by low critical current density ($j_{\rm c}$) in 2D O-FGaT/FGaT heterostructures. [(a), (b)] Curves of $\rho_{\rm TH}$–$B$ of 19 and 13 nm O-FGaT/FGaT at 300 K under increasing current densities. [(c), (d)] Current density ($j$) dependence of the $\rho_{\rm TH}$ and $v_{\rm d}$ for 19 and 13 nm O-FGaT/FGaT. The red lines are fitted curves. Error bars: standard deviation, with sample size $N=25$. (e) Room-temperature $j_{\rm c}$ and maximum $v_{\rm d}$ comparison for various 2D skyrmion systems with vdW structures (solid symbols) and non-vdW structures (open symbols). See reported data and references in Table S3 in the Supplemental Material.
Furthermore, the skyrmions drift velocity ($v_{\rm d}$) is linearly fitted by using formula[6,16] $v_{\rm d}=jR_{0}[1-\rho _{\rm{TH}}(j)/\rho _{\rm{TH}}(j\leqslant j_{\rm c})]$ and also shows good fitting quality [lower panels in Figs. 4(c) and 4(d)]. For 19 and 13 nm O-FGaT/FGaT, the typical $v_{\rm d}$ are calculated as $\sim$ $0.54$ and $\sim$ $0.82$ m$\cdot$s$^{-1}$, four orders of magnitude larger than those of some heavy metal/ferromagnet heterostructures such as Ta/CoFeB/TaO$_{x}$ ($v_{\rm d}=2.5\times 10^{-5}$ m$\cdot$s$^{-1})$.[2] Remarkably, 2D O-FGaT/FGaT exhibits low $j_{\rm c}$ and moderate $v_{\rm d}$ at room temperature compared with other 2D skyrmion systems, which are crucial for practical application of 2D skyrmion-based logic and memory devices [Fig. 4(e)]. Also, the combination of low current and THE measurements offers fundamental insights into the emergent electrodynamics of skyrmions motion, which will be important for practical applications in the long term.[17,31] Nevertheless, given the complexity and challenge of fully identifying the underlying physical nature behind the electrically controlled THE and skyrmions, more studies in these promising 2D room-temperature ferromagnetic crystals are necessary in the future. First-Principles Calculations of DMI. The first-principles calculations are used to qualitatively reveal the surface oxidation effect on DMI in O-FGaT/FGaT (see the experimental section in the following). Fe$_{3}$GaTe$_{2-x}$ shows higher activity and affinity to incorporate with oxygen than perfect Fe$_{3}$GaTe$_{2}$ under ambient condition, confirming the possibility to induce the formation of a uniform oxide layer on the surface of Fe$_{3}$GaTe$_{2-x}$ by the exposure to air (Table S4). The DMIs in bulk Fe$_{3}$GaTe$_{2-x}$ and bilayer Fe$_{3}$GaTe$_{2-x}$ with/without surface oxidization are obtained by calculating the layer-resolved SOC energy difference ($\Delta E_{\rm SOC}$), microscopic and micromagnetic DMI parameters ($d$ and $D$) (Fig. 5 and Fig. S18). In all cases, non-zero total DMI energies ($|D|\ne0$) are attributed to asymmetric crystal structure caused by Te vacancies and/or surface oxidization. However, the THE-hosting magnetic systems usually present an appreciable $|D|$ up to $\sim$ 1–2 mJ$\cdot$m$^{-2}$, such as WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ and Tm$_{3}$Fe$_{5}$O$_{12}$/Pt.[10,11] Given that the bulk transport is dominant in thick O-FGaT/FGaT samples, we evaluate the DMI in the bulk Fe$_{3}$GaTe$_{2-x}$ and find a weak $|D|$ of $\sim$ 0.379 mJ$\cdot$m$^{-2}$ [Fig. 5(a)], which is difficult to generate the detectable THE. This result also supports the absence of THE in O-FGaT/FGaT with thickness over 30 nm. For pristine bilayer Fe$_{3}$GaTe$_{2-x}$, a slight crystal asymmetry caused by Te vacancies produces a weak $|D|$ of $\sim$ 0.28 mJ$\cdot$m$^{-2}$, resembling to the magnitude of that of bulk Fe$_{3}$GaTe$_{2-x}$ [Fig. 5(b)]. In contrast, an additional large DMI contribution is recognized when introducing the surface O atoms on the bilayer Fe$_{3}$GaTe$_{2-x}$ [Figs. 5(c) and 5(d)]. The oxidation-induced large $|D|$ for the O-substituted and O-interstitial bilayer Fe$_{3}$GaTe$_{2-x}$ reaches $\sim$ 7.354 and $\sim$ 2.301 mJ$\cdot$m$^{-2}$, which are $\sim$ 26.3 and $\sim$ 8.2 times that of pristine case, respectively [Fig. 5(e)]. The significant enhancement of DMI in bilayer Fe$_{3}$GaTe$_{2-x}$ with surface oxidation supports the existence of robust THE in 2D O-FGaT/FGaT heterostructures. Further calculations show that introducing surface O atoms in 2D Fe$_{3}$GaTe$_{2-x}$ crystals will cause the shift of total, Fe $3d$, Ga $4p$, Te $5p$ states toward the low-energy direction (Fig. S19) and the obvious charge transfer from other adjacent atoms into O atoms (Table S5). These results imply that the orbital hybridization between O $2p$ and other atoms (including Fe $3d$, Ga $4p$, Te $5p$) and surface charge transfer play an essential role in sizeable DMI of 2D O-FGaT/FGaT heterostructures.[36-38]
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Fig. 5. First-principles calculations of DMI in pristine and oxidized Fe$_{3}$GaTe$_{2-x}$. (a) Atomic model, layer-resolved SOC energy difference ($\Delta E_{\rm SOC}$), and DMI parameter ($d$) in pristine bulk Fe$_{3}$GaTe$_{2-x}$. (b)–(d) Atomic models, layer-resolved $\Delta E_{\rm SOC}$, and $d$ in pristine (b), O-substituted (c) and O-interstitial (d) bilayer Fe$_{3}$GaTe$_{2-x}$. The inserted values in the following each case show total microscopic and micromagnetic DMI parameters ($d$ and $D$). (e) Comparison of DMI energies ($|D|$) for bilayer and bulk Fe$_{3}$GaTe$_{2-x}$ with and/or without oxidization.
In summary, with reliable naturally oxidized interfaces and highly enhanced large 2D DMI, the robust and giant 2D THE with ultrawide temperature window ranging in 2–300 K and low $j_{\rm c}$ for room-temperature current-controlled THE is reported in down to sub-20 and sub-10 nm 2D vdW room-temperature ferromagnet-based heterostructures. This 2D THE-hosting room-temperature ferromagnetic system has the unique advantage of balance in giant $\rho_{\rm TH}$, ultrawide temperature window till room temperature and low $j_{\rm c}$, which shows great potential in the real practical room-temperature applications of 2D skyrmion systems. Natural surface oxidization compatible with industrial semiconductor processing may provide general methodology to tune 2D DMI for spin transport control in 2D ferromagnetic crystals. This work not only proves that the earth-abundant light element of oxygen can induce giant 2D THE much better than that from heavy metals and strong SOC compounds, but also paves the avenue to electrical control of room-temperature 2D THE and skyrmions for 2D topological and spintronic devices. Experimental—Crystal Growth, Natural Oxidization and Device Fabrication. Fe$_{3}$GaTe$_{2-x}$ single crystals were grown by a self-flux method similar to a previous report.[21] The laser direct writing machine (MicroWriter ML3, DMO) and e-beam evaporation (PD-500 S, PDVACUUM) were used to fabricate the Hall bar electrodes (Cr/Au: 8/17 nm) on the SiO$_{2}$/Si substrate. A mechanically exfoliated Fe$_{3}$GaTe$_{2-x}$ nanosheet was transferred onto the Hall bar electrodes through the polydimethylsiloxane (PDMS)-assisted dry transfer method in an argon-filled glove box (H$_{2}$O, O$_{2} < 1$ ppm). To realize natural oxidization in exfoliated Fe$_{3}$GaTe$_{2-x}$ single nanosheets, the nanosheets were naturally oxidized in air for 20–30 min, forming the O-FGaT/FGaT heterostructures. Crystal Characterizations. The morphology, thickness, structure and elements of Fe$_{3}$GaTe$_{2-x}$ crystals were characterized at room temperature by optical microscopy (OM, MV6100), powder x-ray diffraction (XRD, Smartlab SE, Rigaku Corporation) with Cu $K_\alpha$ radiation ($\lambda =0.154$ nm), atomic force microscopy (AFM, Dimension EDGE, Bruker), x-ray photoelectron spectroscopy (XPS, AXIS SUPRA+, Shimadzu), electron probe micro-analyzer (EPMA, 8050 G, Shimadzu), field-emission transmission electron microscopy (FTEM, Tecnai G2 F30, FEI), and spherical aberration correction transmission electron spectroscopy (ACTEM, Themis Z, FEI) equipped with energy-dispersive spectroscopy (EDS). Cross-sectional ACTEM specimens were prepared on the h-BN/O-FGaT/FGaT heterostructures, using a focused ion beam instrument (FIB, Helios 5 CX, FEI). To protect the surface from ion beam damage, the platinum layer before milling was deposited. The magnetic properties of Fe$_{3}$GaTe$_{2-x}$ crystals were measured by a vibrating sample magnetometer (VSM) module in a physical property measurement system (PPMS DynaCool, Quantum Design, USA). Magneto-Transport Measurements. The magneto-transport measurements were performed in a physical property measurement system (PPMS, DynaCool, Quantum Design). The magnetic field was applied perpendicular to the sample unless otherwise stated. Specially, the magnetic field was changed with the interval of 20–100 Oe around the dips and peaks regime. Each data was tested 25 times in $R$–$T$ and $R$–$B$ curves for an average with the constant current mode. The constant current for measurement was set at 1–10 µA depending on the resistance of devices. Additional millisecond current pulses were used to test the current-controlled 2D THE at room temperature. Waiting several seconds after each pulse and then read the resistance. Lorentz-TEM Measurements. The as-tested O-FGaT/FGaT and pristine non-oxidized Fe$_{3}$GaTe$_{2-x}$ nanosheets were placed on a 50 nm amorphous silicon nitride substrate and capped with the 8 nm Au film to avoid further oxidization. Then, the in situ skyrmions and magnetic domains imaging at room temperature were carried out by using a 200 kV TEM (Talos F200X, FEI) equipped with Lorentz mode. First-Principles Calculations. The first-principles calculations were performed within the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).[39] The interaction between valence and core electrons was treated by the projector augmented wave (PAW) method.[40] The spin-polarized generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof version was used to describe exchange-correlation energy.[41] Since the GGA functional fails to treat partially occupied $3d$ electrons of transition metal elements, we employed the GGA+$U$ method with an effective $U = 3$ eV for Fe element as reported in the previous studies.[42,43] The interlayer van der Waals (vdW) interactions of bulk and bilayer Fe$_{3}$GaTe$_{2-x}$ ($x=0.25$) were described with the DFT-D3 correction in Grimme's scheme.[44] A kinetic cutoff energy of 450 eV was used for the plane-wave expansion. The $k$-point sampling in the Brillouin zone was implemented using the Monkhorst–Pack scheme[45] with a grid of $3 \times 12\times 1$ for pristine and oxidized bilayer Fe$_{3}$GaTe$_{2-x}$ and $2 \times 8\times 2$ for pristine bulk Fe$_{3}$GaTe$_{2-x}$, respectively. All the structures were fully relaxed until the force acting on each atom was less than 0.01 eV$\cdot$Å$^{-1}$. The Bader charge analysis[46] was carried out to examine the charge transfers among O dopants, Fe, Ga, and Te atoms in the oxidized bilayer Fe$_{3}$GaTe$_{2-x}$. We used the chirality-dependent total energy difference approach to obtain the DMI strength.[47,48] The DMI energy between normalized spins restricted to the nearest neighbors can be determined by \begin{align} E_{\rm DMI}=\sum\limits_{\langle i,j\rangle} \boldsymbol{d}_{ij} \cdot(\boldsymbol{S}_{j}\times \boldsymbol{S}_{j}), \tag {1} \end{align} where ${\boldsymbol{d}}_{ij}$ is summed by considering two types of pairs inside a given layer L, and interlayer pairs between a layer L and layers above or below. From the Moriya symmetry rule,[49] the DMI vector for the layer L can be written as \begin{align} \mathrm{\boldsymbol{d}}_{ij}^{\scriptscriptstyle{\rm L}}=d^{\scriptscriptstyle{\rm L}}(\hat{z}\times \hat{u}_{ij}), \tag {2} \end{align} where $\hat{z}$ and $\hat{u}_{ij}$ are unit vectors pointing along $z$ and from site $i$ to site $j$. The total DMI strength $d^{\rm tot}$ is derived by identifying the difference between the DFT energies $E_{\rm CW}$ and $E_{\rm ACW}$ for opposite-chirality-spin configuration (Fig. S18 in the Supplemental Material) with the corresponding energy differences calculated by \begin{align} d^{\rm tot}=(E_{\rm CW}-E_{\rm ACW})/m, \tag {3} \end{align} where the number $m$ depends on the length of cycloidal unit cell. For example, $m$ is 12 for the cycloid unit cell with $n = 4$ ($n$ is primitive cell number along the cycloid direction), as shown in Fig. S18. It is necessarily emphasized that $d^{\rm tot}$ is the DMI strength in a single atomic layer and produces an equivalent effect. The global effect on the bilayer or multilayer can also be expressed by the micromagnetic energy per volume unit of the magnetic film. Statistical Analysis. (i) The intensities in Fig. 2(f) and Fig. S1 are normalized. (ii) The error bars in Figs. 2(f), 2(g), 4(c) 4(d) and Figs. S3(e), S5(f), S6(d), S6(e), S15, S17 in the Supplemental Material are presented by mean $\pm$ standard deviation. (iii) The sample sizes ($N$) are presented in the caption of Fig. 4. Microsoft Office Excel, Origin and MATLAB are used for statistical analysis. Acknowledgements. This work was supported by the National Key Research and Development Program of China (Grant No. 2022YFE0134600), the National Natural Science Foundation of China (Grant Nos. 52272152, 61674063, and 62074061), Shenzhen Science and Technology Innovation Committee (Grant No. JCYJ20210324142010030), the Natural Science Foundation of Hubei Province (Grant No. 2022CFA031), and Interdisciplinary Research Program of Huazhong University of Science and Technology (Grant No. 5003110122). The Analytical and Testing Center in Huazhong University of Science and Technology for EPMA and XPS tests are acknowledged. 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