Evidence for Magnetic Skyrmions at the Interface of Ferromagnet

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Evidence for magnetic skyrmions at the interface of ferromagnet/topological-insulator heterostructures Junshu Chen, Linjing Wang, Meng Zhang, Liang Zhou, Runnan Zhang, Lipeng Jin, Xuesen Wang, Hailang Qin, Yang Qiu, Jiawei Mei, Fei Ye, Bin Xi, Hongtao He, Bin Li, and Gan Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b02191 • Publication Date (Web): 23 Aug 2019 Downloaded from pubs.acs.org on August 24, 2019

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Evidence for magnetic skyrmions at the interface of ferromagnet/topological-insulator heterostructures Junshu Chen†‡, Linjing Wang†, Meng Zhang†, Liang Zhou†, Runnan Zhang†, Lipeng Jin§, Xuesen Wang‡, Hailang Qin†, Yang Qiu#, Jiawei Mei†, Fei Ye†, Bin Xi§*, Hongtao He*†, Bin Li*†|| and Gan Wang*†|| † Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China ‡ Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551, Singapore § College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China # Materials Characterization and Preparation Center, Southern University of Science and Technology, Shenzhen 518055, China || Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China Emails and telephones of corresponding authors: *[email protected], 75588018288;

086-13810515112;

*[email protected],

*[email protected],

1

ACS Paragon Plus Environment

086-

086-75588018254;

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*[email protected], 086-75588018216

ABSTRACT The heterostructures of the ferromagnet (Cr2Te3) and topological insulator (Bi2Te3) have been grown by molecular beam epitaxy. The topological Hall effect as evidence of the existence of magnetic skyrmions has been observed in the samples in which Cr2Te3 was grown on top of Bi2Te3. Detailed structural characterizations have unambiguously revealed the presence of intercalated Bi bilayer nanosheets right at the interface of those samples. The atomistic spindynamics simulations have further confirmed the existence of magnetic skyrmions in such systems. The heterostructures of ferromagnet and topological insulator that host magnetic skyrmions may provide an important building block for next generation of spintronics devices.

KEYWORDS Bi nanosheets, Cr2Te3, Bi2Te3, heterostructures, topological Hall effect, magnetic skyrmions

Introduction Skyrmion, proposed by Skyrme in the field of high energy physics, is a topologically stable soliton in its mathematical form.1 Thereafter, the magnetic skyrmions have been demonstrated in condensed matter systems,2–4 such as

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MnSi,5 Cu2OSeO3,6 Fe1–xCoxSi,7 FeGe,8 Pt/Co/MgO nanostructures9 and Fe/Ir.10 The magnetic skyrmions are a kind of pseudo-particles formed by concentric gradual canting of electron spins, which have remarkable potential in the future application of spintronics and information storage.11–15 In recent studies, magnetic skyrmions have been observed in the magnetically doped topological insulator (TI) systems as evidenced by the topological Hall effect (THE).16,17 The hallmark of THE is a hump in the anomalous Hall conductivity, which is induced by the emergent magnetic field of the skyrmions.18–20 Rooted in the strong spin-orbital coupling (SOC), topological insulator hosts extraordinary electronic structure.21,22 Due to the bulk–surface correspondence, the electronic state at the boundary of such system exhibits a Dirac cone dispersion and the spin direction of an Dirac electron is perpendicular to its momentum. For 3D TI, such state is called the helical surface state. The closed point is the Dirac point (DP), which is protected by the time–reversal symmetry (TRS). Breaking TRS by introducing magnetism will result in novel electron behaviors. It has been proposed and demonstrated that the Dirac electrons in the surface state may mediate the coupling of magnetic moments, thus the magnetic order is able to form based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism.23–26 As a consequence of the breaking of inversion symmetry and strong SOC, the Dirac electrons in the surface state may also mediate the Dzyaloshinskii-Moriya (DM) interactions,24 which is necessary for the formation of magnetic skyrmions in the magnetically doped TIs. However,

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the magnetism comes from magnetic dopants within the bulk of the materials in such systems, thus it will raise a question that whether the similar picture can be applied to the system of a topological insulator interfacing with a magnet. In this letter, we report the observation of magnetic skyrmions in the undoped topological insulator (Bi2Te3)27,28 and a traditional magnet (Cr2Te3)29,30 heterostructure as evidenced by the THE in the transport experiments. The averaged magnetic moment per Cr ion is 1.98 B in Cr2Te3 and the Curie temperature (TC) of this material can reach as high as ~200 K,29–31 where B = 9.27  10-24 J T-1 is the Bohr magnetron. In this study, three different heterostructures have been prepared: Cr2Te3/Bi2Te3/Cr2Te3 (CT/BT/CT), Bi2Te3/Cr2Te3 (BT/CT) and Cr2Te3/Bi2Te3 (CT/BT). Interestingly, the THE signal is prominent only in CT/BT/CT and CT/BT structures, while it cannot be recognized in BT/CT structure. A closer examination of the cross-sectional atomic structure of CT/BT sample has revealed the existence of Bi bilayer nanosheets intercalated at the interface of the CT and BT, which has been found essential to the formation of magnetic skyrmions in this study. This is consistent with our recent observation that the black-phosphorus-like bismuth (BP-Bi) nanosheets embedded in the CT lattice plays the crucial role in the formation of magnetic skyrmions.32 The Bi bilayer has been demonstrated very robust in many material systems.33–35 With an atomic number of 83, Bi atoms host a strong SOC, which is the prerequisite for a significant DM interaction. The hybridization of Bi p-orbitals and Cr d-orbitals can greatly enhance the DM 4


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interaction, which is also confirmed by atomistic spin-dynamics simulations based on Landau–Lifshitz–Gilbert (LLG) equation to study the stability of the skyrmions formed in these systems.36–38 Moreover, two additional features will be underlined: 1) The majority carrier type can be tuned from n to p by manipulating the thickness of each film, which means the Fermi level can sweep the entire gap of the material. This is critical for the realization of the quantum anomalous Hall effect. 2) The ‘sign-reversal’ feature in the resistivity of anomalous Hall effect holds true for all three heterostructures, which provides more details on the magnetic order in these systems. The superiority of heterostructures is that the Bi bilayer nanosheets can be grown in a controlled way via an annealing procedure, which can be generalized to a broad range of FM/TI heterostructural systems, and hold the promise of realizing more extraordinary effects of magnetic skyrmions. Experimental details The growth of samples was conducted within a Createc molecular beam epitaxy (MBE) system connected with a SPECS Joule-Thomason scanning tunneling microscope (STM). The base pressure reached 10-10 mbar before the growth started. The elemental Cr, Te and Bi2Te3 compounds were evaporated from standard Knudsen cells held at 1110 °C, 320 °C, and 440 °C, respectively. All of the structures for transport measurement were grown on sapphire [Al2O3(0001)] substrates, except one CT/BT sample for in situ STM study which was grown on a conductive 0.7%-wt Nb-doped SrTiO3(001) substrate. The 5


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substrate temperature was first raised to 600 °C for about one hour to outgas, then decreased to 270 °C and 200 °C for the growth of CT and BT, respectively. The growth duration for CT (BT) was 30 min (20 min) with the growth rate of 0.67 nm/min (0.5 nm/min). Particularly for the growth of CT on top of BT, the sample was annealed at 270 °C after the growth of BT for about 20 mins to stabilize the formation of Bi bilayer nanosheets. The growth processes were monitored by the reflection high–energy electron diffraction (RHEED) operated at 25 kV. To study the magneto-transport properties, 6-terminal Hall bar devices were fabricated for all three samples. The devices were then measured in a Quantum Design 14 T PPMS system, with the base temperature of 2 K. A lock-in amplifier was applied to measure the magneto resistivity, with an AC current amplitude of 50 μA at 357 Hz. The cross-sectional atomic structures of samples were investigated with a scanning transmission electron microscope (STEM, model Thermal Fisher Titan 60–300 Cube). The high-resolution STEM images were acquired in the high-angle annular dark field (HAADF) imaging mode at 300 kV. HAADF contrast, also known as Z-contrast, can provide directly not only the location of atomic columns but also information on the elemental composition at atomic scale. STM topographic images were acquired at 77 K in constant-current mode, and

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dI/dV spectra were measured by a standard lock-in method with a modulation amplitude of about 10 - 20 mV at 998 Hz. Results and discussion Bi2Te3 has a rhombohedral lattice structure with R3𝑚 symmetry (lattice constants: a = b = 4.38 Å, c = 30.49 Å), while Cr2Te3 has a NiAs lattice structure with P31c symmetry and lattice constants of a = b = 6.8 Å, c = 12 Å (For details of the lattice structure, see Figure S1 in the supporting information).30 The inplane lattice constants of Al2O3(0001) are a = b = 4.74 Å. Therefore, the lattice mismatches across the CT/ Al2O3, BT/ Al2O3, and CT/BT interfaces are 21.5%, 8.2%, and 12.3%, respectively.

Figure 1. The growth process and cross-sectional topographies of BT/CT and CT/BT characterized by STEM. (a_i-a_iv) of (a) are RHEED patterns of the growth of CT/BT/CT structure at different stages as labeled at each left bottom corner, corresponding to the schematic drawing of the CT/BT/CT structure in (b). (c) and (d) are the HAADF STEM images of BT/CT and CT/BT interfaces in the area marked by the orange and green rectangles in (b), with the black

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solid lines indicating the interfaces. The Bi bilayer has been clearly observed at CT/BT interface in (d). The inset atomic model demonstrates the lattice structure of CT, BT and Bi bilayer, respectively. The growth process of CT/BT/CT sample was monitored with RHEED (Figure 1a_i-a_iv). The sample structure is sketched in Figure 1b. The surface of Al2O3 substrate was charged initially after outgassing (Figure 1a_i). After the growth of the first CT layer at 270 °C, the RHEED pattern of CT could be observed (see Figure 1a_ii). Due to the large lattice mismatch between CT and Al2O3, the bottom CT layer tended to be in polycrystalline form at the very initial stage (as manifested by the slight ‘ring’ pattern). However, this changed rapidly upon further growth. When the thickness reached 20 nm, the overall RHEED pattern was streaky, indicating a high-quality thin film. The successive growth of BT layer facilitated the quasi-van der Waals (vdW) epitaxy (Figure 1a_iii) at 200 °C.39 The streaky RHEED pattern became brighter and sharper than that from the bottom CT, reflecting an improved crystal quality of BT despite of the large lattice mismatch between BT and CT. The growth of top CT layer adopted the same substrate temperature during the growth of the first CT layer, which required the temperature to be raised from 200 °C to 270 °C as described above. The ultimate top CT layer had a much better quality comparing with the bottom one as revealed by the RHEED patterns (see Figure 1a_iv vs. 1a_i) with bright and sharp streaks and no 'ring' pattern had emerged. A 22 reconstruction had been observed from this CT layer. To figure out the exact difference of the two 8


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heterointerfaces, STEM in HAADF mode was employed to characterize the BT/CT and CT/BT interfacial structures (see Figure 1c-d). The BT/CT interface shown in Figure 1c is sharp and of quasi-vdW type. The STEM image of the CT/BT interface atomic structures is displayed in Figure 1d.34,40 In contrast to the BT/CT interface, the Bi bilayer nanosheets have been observed at such interface. The color scale corresponds to the intensity which is related to the scattering power of the elements, which can unambiguously illustrate that an intercalation Bi bilayer nanosheet exists between the upper CT and lower BT layers. An atomic model has been superimposed on the STEM image. It can be seen that CT and BT match their supposed structure very well.

Figure 2. STM images of Bi bilayer on BT and further CT growth. (a) Surface morphology of BT after annealing. The 0.4 nm step height indicates that a Bi (111) bilayer has formed. (b) The nucleation of CT islands after 20 s deposition of Cr and Te. (c-h) Surface morphologies during further CT growth. (c), (e) and (g) are surface morphologies of CT after 7 min, 17 min and 67 min growth. (d), (f) and (h) are the zoom-in images of the red-square areas as marked in (c), (e)

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and (g), correspondingly. The bright spots in (d) and (f) represent the quasihexagonal-periodic Moiré pattern. The distance between the two spots has been measured as 2.8 nm, as marked in (f). The black arrow in (h) indicates the point defects. (i, j) Simulations of the Moiré patterns based on two models: CT grown on Bi(111) bilayer (i) and BT (j), with the quasi-period labeled for each model. To further investigate the lateral atomic arrangement of the CT/BT interface, STM imaging was performed in situ during the growth of CT on BT. The surface morphological evolution of CT characterized by STM could provide more information on the growth process as well as atomic environment of the interface. The step height measured on the BT surface after annealing in Figure 2a matches that of hexagonal Bi(111) bilayer, i.e. 0.4 nm,34,41 clearly different from that of Bi2Te3 (~1 nm). Cr and Te were then deposited on such surface. After 20 sec, small CT islands emerged as shown in Figure 2b. Importantly, after 7 min growth of CT, the surface shown in Figure 2c had been fully covered by CT islands. A periodic bright ‘spotty pattern’ had been observed on such surface (see the zoom-in image in Figure 2d, corresponding to the red-square area in Figure 2c). This pattern persisted even up to 17 min growth (Figure 2e and 2f), which will be discussed later in details. The CT growth was completed at 67 min with a nominal thickness around 20 nm. The final morphology is shown in Figure 2g. The surface was covered with multi-stage triangular islands, which is determined by the CT lattice symmetry. A closer look has revealed a 10


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number of point defects (see Figure 2h). Now come back to the ‘spotty pattern’ mentioned above. The distance between two nearest spots is 2.8 nm (Figure 2f). This feature is quite likely to be the ‘Moiré pattern’.42 Two atomic models have been constructed to verify this assumption. The model in Figure 4i is the superposition of Te layer from CT (each monolayer can represent the periodicity of CT because of its symmetry) and a Bi bilayer nanosheet. The periodicity induced by the simulated lattice stacking is close to 2.8 nm, agreeing well with the experimental results. On the other hand, the periodicity of Moiré pattern resulted from the superposition of Te layer from CT and Te layer from BT (the same circumstance with CT) is 3.5 nm, far from the experimental value. Therefore, it has been confirmed that the periodic feature in STM is the Moiré pattern produced by CT overlapping on Bi bilayer nanosheets created by annealing procedure. This observation supports that the Bi bilayer nanosheets existing at CT/BT interface, consistent with our STEM characterizations shown in Figure 1d.

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Figure 3. Magneto-transport measurements. (a-c) Temperature–dependent Hall measurements of the CT/BT/CT, BT/CT, CT/BT samples, respectively. THE peaks have been marked by green and black arrows. (d) Normalized THE signal extracted from the total Hall resistivity. (e) Magneto-resistivity (MR) measurements along the longitude direction at 2 K. The humps corresponding to the THE have also been marked by arrows. The fitted dashed black lines are guide to eyes on the MR curve. To study the impact on the transport properties brought by the Bi bilayer nanosheets, two heterostructures of CT/BT and BT/CT had been fabricated for comparison and temperature-dependent double-sweep Hall measurements had been performed for the CT/BT/CT, BT/CT, CT/BT samples. The results are plotted in Figure 3. The Hall resistivity curve of CT/BT/CT sample displayed in Figure 3a can be divided into three parts. At higher field, the Hall resistivity has a linear dependence on the applied magnetic field, which is of ordinary Hall effect (OHE). At lower field, a hysteresis loop has been observed unambiguously. The maximum coercivity is about 1 T at 2 K. This part can be attributed to the anomalous Hall effect (AHE). The ‘sign-reversal’ transition has been observed in this sample at 25 K when the AHE vanished. There are several mechanisms including the extrinsic (skew scattering, side jump) and intrinsic (Berry phase) that could cause the AHE.43 Those mechanisms will compete with each other, leading to the ‘sign-reversal’ feature. Nevertheless, the above two Hall resistivities are not the main concern in this letter. 12


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Remarkably, near the coercive field, there exist abnormal Hall resistivities in a range of temperatures, as manifested by humps on the shoulder of AHE loops, which will be assigned to the topological Hall effect (THE) in the following analysis. The Hall measurements on the CT/BT and BT/CT samples can provide the information of the contributions to the Hall resistivity brought by the two interfaces of the CT/BT/CT structure. First, for the BT/CT sample (see Figure 3b), only OHE and AHE have been observed (and the ‘sign-reversal’ feature as well). In contrast, on the CT/BT sample, all OHE, AHE and THE have been observed. For quantitatively comparison, the normalized THE signal has been extracted (see Method in the supporting information) from the total Hall resistivity at the temperatures where AHE disappears for each sample (Figure 3d). The intensities of THE signals of BT/CT (blue curve) and CT/BT (pink curve) are radically different. Remarkably, the magneto-resistance (MR) anomaly has also been demonstrated in Figure 3e. There are two extra humps superimposed on the MR curves for CT/BT/CT and CT/BT structures, peaked near the coercive fields. The THE together with magneto-resistance anomaly strongly indicate there may exist the emergent magnetic field induced by magnetic skyrmions. Noticeably, the formation of magnetic skyrmions requires the DM interaction. At the interface of CT/Al2O3, only the inversion symmetry is broken but the SOC

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is not strong enough. Moreover, the previous reports on Cr2Te3 grown on Al2O3 also have not observed any sign of skyrmions.44 Therefore, magnetic skyrmions cannot originate from this interface. One may note that the coercive field of CT/BT/Al2O3 (~0.5 T) is smaller than that of BT/CT/Al2O3 (~1 T). This may due to the influence of sublayer of CT. Usually the grain volume is an important factor for coercive field: the larger grain volume will cause the smaller coercive field.45 CT grown on Al2O3 tended to be in polycrystalline form at the very initial state (Figure 1a_ii), indicating the grain size of CT on Al2O3 would be smaller than CT on BT (cf. Figure 1a_iv), which may contribute to the larger coercive field. Additionally, the THE signal did not show up for BT/CT sample (Figure 3b) although its coercive field was close to CT/BT/CT sample (Figure 3a), while the THE signal did rise for CT/BT sample (Figure 3c) despite of smaller coercive field. Hence, these modifications in magnetic properties by different stacking orders could not contribute to the formation of magnetic skyrmions. Recall the STEM and STM results above, at CT/BT interface, there exists intercalated Bi(111) bilayer nanosheets. The Bi bilayer on top of BT hosts larger on-site SOC together with nontrivial topological electronic states33,41. It is reported in [32] that magnetic skyrmions can emerge near the BP-Bi bilayer nanosheets embedded in the CT lattice since the DM interaction can be enhanced by the coupling between the p-orbital of Bi and d-orbital of Cr. This picture is also applicable to the samples in this work. In comparison with CT/BT sample, there is no Bi bilayer nanosheets at the interface of BT/CT samples, thus no THE

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signal rises. The MR anomaly can then be attributed to the scattering of transmission charge carriers due to emergent magnetic field of skyrmions.32,46 The growth method described here is a controllable route for the manipulation of magnetic skyrmions than the doping via the heterointerface engineering. This stands on two aspects: (a) The form of Bi bilayer can vary depending on the annealing temperature.34 (b) For doing method, the dopants usually distribute randomly in the material. However, the Bi bilayer nanosheet is right at the interface for the heterointerface engineering, which enables the possibility of constructing the superlattice structure and is beneficial for the fabrication of spintronic devices. It is worthy to note that the Bi bilayer in Ref. [32] is in black phosphorus phase. The Bi bilayer nanosheets here are in hexagonal phase (refer to Figure 1e). This indicates that the intrinsic strong SOC of Bi plays the most essential role despite of different lattices of Bi bilayer nanosheets. Importantly, in the heterostructures, the thickness of TI is not relevant, which significantly lowers the obstacle of technical applications. In magnetically doped TIs, the ferromagnetism and THE signal commonly survive below 10 K.16,17 Outstandingly, in such heterostructure samples, the Curie temperature of ferromagnetism reaches 175 K rooting from the merit of the traditional ferromagnetic CT (see Figure S2 in the supporting information), and THE originated from the ferromagnetic phase has also been observed up to 40 K, which is close to the liquid nitrogen temperature (See Figure S5 in the

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supporting information for detailed discussion). Therefore, the heterostructure (CT/BT/CT) demonstrates a promising route to realize room temperature THE by replacing CT with other ferromagnetic layers of higher Curie temperature. Back to Figure 3a, and 3c, the carrier types are opposite for CT/BT/CT (n-type) and CT/BT (p-type) structures. The as-grown CT layer usually contains mainly p-type carriers.32 The holes are from the unoccupied d-orbitals of Cr. On the other hand, BT usually shows n-type.47–49 However, as mentioned above, during the annealing process, BT decomposed, and the film will become thinner. Therefore, holes from CT will outnumber the electrons in BT, leading to the overall p-type for the CT/BT junction. For the CT/BT/CT structure. It is found that the CT grown on Al2O3 tends to exhibit n-type due to the interdiffusion of Al.50 Then the bottom CT may provide more electrons that overwhelm holes from the upper part, and the overall carrier type is n-type. It is noticed that the sign of THE remain the same although the carrier types have changed. This would indicate that the spin-exchange interaction between localized spins and itinerant electrons at the interface in our case may involve more mechanisms beyond the commonly used double-exchange model, and it is open for more theoretical inputs. It is discernable that the overall THE signal in the CT/BT/CT structure is stronger than that of CT/BT structure (see Figure 3d). Additionally, the THE signal of CT/BT/CT structure could be unambiguously distinguished at ~40 K,

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which is also higher than that of CT/BT structure (~20 K). As mentioned earlier, the BT decomposed into Bi bilayer nanosheets during the annealing process. Therefore, it can be inferred that the decomposition would not only occur at the top of the BT, but in the entire BT. This had been proved by the STEM images in Figure S3 (supporting information). Therefore, bilayer Bi may also exist at the bottom surfaces of BT after annealing. Although DM vectors could be antiparallel to each other at two interfaces in CT/BT/CT structure, the vorticity (skyrmion number) m does not change in these two cases, while DM vectors indeed affect the helicity γ of skyrmion (see supporting information for details). Therefore, two interfaces may both contribute to the THE signal. This gives a reasonable explanation for the stronger THE in CT/BT/CT sample. In order to testify the probability of the formation and energetical stability of magnetic skyrmion, the atomistic spin-dynamics simulations have been conducted. To simulate the magnetization reversal process of the heterostructure, we consider an effective two-dimensional Heisenberg spin system in a triangle lattice with Cr2Te3 lattice parameter a = 6.82 Å. The Hamiltonian reads as follows:

ℋ =―

∑[𝐽𝑆 ⋅ 𝑆 + 𝐷 𝑖

𝑗

𝑖𝑗

⋅ (𝑆𝑖 × 𝑆𝑗)] ―

〈𝑖,𝑗〉

∑[𝐾(𝑆 )

𝑧 2 𝑖

+ 𝜇𝑠𝐻𝑆𝑧𝑖],

(1)

𝑖

where 𝑆𝑖 is the unit vector in the total spin direction of atom at site 𝑖, and 𝜇𝑠  3 𝜇𝐵 is the magnetic moment of a Cr atom. The first two terms are the ferromagnetic exchange interaction and DM interaction, respectively, among all 17


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nearest-neighbor Cr atoms denoting with index 𝑗 on the triangle lattice. Since at the interface the inversion symmetry is broken along the axis perpendicular to the nanosheet, DM vector 𝐷𝑖𝑗 is supposed to lie in the plane anticlockwise and perpendicular to the directional vector 𝑟𝑖𝑗. The last two terms are the uniaxial anisotropy energy and Zeeman energy. The atomistic spin-dynamics simulations have been performed on a hexagonal sheet with the side length L = 200 CT lattice spacings. To simulate the edge deformations of islands shown in the images of surface morphologies in Figure 2, we first randomly put some triangle areas in the sheet, the side length of which is about 40 CT lattice spacings. Since Bi atoms are closer to Cr atoms at the edge of islands, we increase |𝐷𝑖𝑗| by 50% for those sites on triangle edges. The spin dynamics is described by LLG equation:51,52 ∂𝑆𝑖 ∂𝑡

=―

𝛾

𝛼𝛾

𝑖

(1 + 𝛼2)

(𝑆𝑖 × 𝐻𝑒𝑓𝑓) ―

(1 + 𝛼2)

(2)

𝑖

𝑆𝑖 × (𝑆𝑖 × 𝐻𝑒𝑓𝑓),

which can be solved numerically by Heun method53 with 𝑖

𝐻𝑒𝑓𝑓 =

∑ 𝐽𝑆 + ∑ 𝑆 × 𝐷 𝑗

𝑗

𝑖𝑗

(3)

+ 2𝐾𝑆𝑧𝑖 + 𝜇𝑠𝐻𝑒𝑧,

the effective field felt by spin 𝑆𝑖. We adopt the LLG parameters of Cr2Te3 as:54 𝐽 = 1.19 × 10 ―21 J, 𝐾 = 8.82 × 10 ―23 J, 𝜇𝑠 ≈ 3 𝜇𝐵, 𝛾 = 1.76 × 1011 (T ⋅ s) ―1. The

damping

parameter

α

is

demonstrated to be curial to the generation of skyrmion,55 and is in the range

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0.05–0.2 for materials with large anisotropy.56 We have chosen α = 0.05 since the coercive force for Cr2Te3 is about 0.5 T32 (different values of the damping coefficient have also been tested, see Figure S6). Hence, H is in the unit of

𝐽 𝜇𝑠

𝜇𝑠

≈ 50 T and τ = 𝛼𝛾𝐽 ≈ 0.88 ps in this simulation. We iterated 105 times per step for numerical simulations. As shown in Figure 4b, one can find the calculated ‘hedgehog’ spin configuration of single magnetic skyrmion. As shown in the subpanels in Figure 4c-4f, skyrmions emerge near the triangle edges of Bi bilayer nanosheets, where sites with larger DM interaction act as the nucleation centers of skyrmion (the detail dynamic of magnetic skyrmions can be found in Figure S4), which can further support our explanation of THE based on Bi nanosheets induced strong DM interaction at the interfaces. The hysteresis loop and skyrmion density are presented in Figure S9 in the supporting information, which may indicate the magnitude of THE are closely related to the density of skyrmion.

Figure 4. Atomistic spin-dynamics simulations of magnetic skyrmions 19


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generation. (a) Lattice setup of the model described by equation (1), where the red triangles mimic the islands in the STM images. The side lengths are 40 lattice spacings for triangles, and 200 for hexagonal sheet. (b) Simulated spin configuration of a skyrmion generated at the interface of CT/BT. (c-d) Snapshots of spin configurations at H = ―0.035, ― 0.075 in the left part of hysteresis loop. (e-f) Snapshots of spin configurations at H = 0.035, 0.075 in the right part of hysteresis loop. Conclusions In summary, three structures of CT/BT/CT, CT/BT, BT/CT have been constructed and compared. The THE signals have been observed in the CT/BT/CT and CT/BT structures, while no such signal in the BT/CT structure. The major structural difference revealed by STEM between these samples is that there exists Bi bilayer nanosheets intercalated at the interface when CT is grown on top of BT. The Bi bilayer nanosheets are formed during the annealing procedure as evidenced by the in-situ STM characterizations. The magnetization reversal process simulations based on the LLG equation have confirmed the possibility of existence of the magnetic skyrmions induced by the DM interaction at the interface. Our research demonstrates a potential way for the future skyrmion spintronics based on Bi bilayer nanosheets intercalated interfaces. ASSOCIATED CONTENT

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Supporting Information The details of lattice structure; the curves of resistance vs temperature; additional STEM images; the simulated skyrmion distribution at the interface; the stability of skyrmion against thermal fluctuations; the magnetic dynamics under different Gilbert damping constants; the discussion of the vorticity (skyrmion number); Magnetization and density of skyrmion versus with applied field; the method of the extraction of the THE signal. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected] Funding Sources This work was supported by the National Natural Science Foundation of China (No. 61734008, No. 11804143, No. 11774300, No. 11574129 and No. 11774143), the National Key Research and Development Program of China (No. 2018YFA0307100, and No. 2016YFA0301703), the Natural Science Foundation

of

Guangdong

Province

(No.

2015A030313840,

No.

2017A030313033 and No. 2017ZT07C062), the State Key Laboratory of Low-

21


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Dimensional Quantum Physics (No. KF201602), Technology and Innovation Commission of Shenzhen Municipality (No. ZDSYS20170303165926217, No. JCYJ20170412152334605 and No. KQJSCX20170727090712763). Notes The authors declare no competing financial interest. REFERENCES (1)

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Figure 1. The growth process structure and cross-sectional topography of CT/BT/CT characterized by STEM. (a_i-a_iv) of (a) are The RHEED patterns of the growth of CT/BT/CT structure at different stages as labeled at each left corner, corresponding to the schematic drawing of the CT/BT/CT structure in (b). (c) and (d) are the HAADF STEM images of BT/CT and CT/BT interfaces in the area marked by the orange and green rectangles in (b) respectively, with the black solid lines indicating the interfaces. The Bi bilayer has been clearly observed at CT/BT interface in (d). The inset atomic model demonstrates the lattice structure of CT, BT and Bi bilayer, respectively. 272x93mm (150 x 150 DPI)


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Evidence for Magnetic Skyrmions at the Interface of Ferromagnet

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