Weiming Lv

Zhiyan Jia

Xin Luo

Yuan Lu

Bochong Wang

Zhongming Zeng

Zhongyuan Liu

Electric-field control of spin-orbit torques in WS2/permalloy bilayers

Transition metal dichalcogenides (TMDs) have drawn great attention owing to their potential for electronic, optoelectronic and spintronics applications. In TMDS/ferromagnetic bilayers, efficient spin current can be generated by the TMDs for the manipulation of magnetic moment in the ferromagnetic layer. In this work, we report on the electric-field modulated spin-orbit torques (SOT) in WS2/NiFe (Py) bilayers by spintorque ferromagnetic resonance technique (ST-FMR). It is found that the RF current can induce a spin accumulation at WS2/Py interface due to the interfacial Rashaba-Edelstein effect. More importantly, the SOT ratio between field-like torque and anti-damping-like torque can be effectively controlled by applying back-gate voltage in WS2/ NiFe bilayers.

These results provide a strategy for controlling spin-orbit torque with field-effect by using semiconducting TMDs. KEYWORDS : spintronics, spin-orbit torques, transition metal dichalcogenides, Rashba-Edelstein effect, electric-field With the development of modern magnetic memory and logic devices, the exploration of efficient and low energy consumption mechanisms to change the magnetization states has become a key issue. [START_REF] Katine | Device Implications of Spin-Transfer Torques[END_REF][START_REF] Hoffmann | Opportunities at the Frontiers of Spintronics[END_REF] An effective way is utilizing the strong spin-orbit interactions (SOIs) [START_REF] Slonczewski | Current-Driven Excitation of Magnetic Multilayers[END_REF][START_REF] Brataas | Current-Induced Torques in Magnetic Materials[END_REF] to induce spin current which can be used to exert spin-orbit torques (SOT) on adjacent magnetic layer for realizing the manipulation and switching of magnetization. [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF][START_REF] Garello | Ultrafast Magnetization Switching by Spin-Orbit Torques[END_REF] Previous studies have confirmed the influence of SOIs in layered heavy metal/ferromagnet bilayers through the spin Hall effect in heavy metal, such as Pt, [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF][START_REF] Miron | Perpendicular Switching of a Single Ferromagnetic Layer Induced by In-plane Current Injection[END_REF] Ta, [START_REF] Liu | Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum[END_REF][START_REF] Emori | Current-driven Dynamics of Chiral Ferromagnetic Domain Walls[END_REF] and W [START_REF] Pai | Spin Transfer Torque Devices Utilizing the Giant Spin Hall Effect of Tungsten[END_REF] , and other interface spin-orbit effect [START_REF] Sklenar | Perspective: Interface Generation of Spin-Orbit Torques[END_REF] in ferromagnet, such as Rashba-Edelstein effect, [START_REF] Shao | Strong Rashba-Edelstein Effect-Induced Spin-Orbit Torques in Monolayer Transition Metal Dichalcogenide/Ferromagnet Bilayers[END_REF][START_REF] Sanchez | Spin-To-Charge Conversion Using Rashba Coupling at the Interface Between Non-Magnetic Materials[END_REF][START_REF] Zhang | Spin Pumping and Inverse Rashba-Edelstein Effect in NiFe/Ag/Bi and NiFe/Ag/Sb[END_REF][START_REF] Isasa | Origin of Inverse Rashba-Edelstein Effect Detected at the Cu/Bi Interface Using Lateral Spin Valves[END_REF][START_REF] Fan | Quantifying Interface and Bulk Contributions to Spin-Orbit Torque in Magnetic Bilayers[END_REF][START_REF] Sangiao | Control of the Spin to Charge Conversion Using the Inverse Rashba-Edelstein Effect[END_REF] which can produce strong current-driven torques on the magnetic layer. Recent experiments in the material search for providing more efficient spin-orbit-induced torques have demonstrated that a large SOT can exist in topological insulators [START_REF] Mellnik | Spin-Transfer Torque Generated by A Topological Insulator[END_REF][START_REF] Fan | Magnetization Switching Through Giant Spin-Orbit Torque in a Magnetically Doped Topological Insulator Heterostructure[END_REF] and two-dimensional (2D) materials. [START_REF] Wang | Strong Interface-Induced Spin-Orbit Interaction in Graphene on WS2[END_REF][START_REF] Kormányos | Spin-Orbit Coupling, Quantum Dots, and Qubits in Monolayer Transition Metal Dichalcogenides[END_REF] Transition metal dichalcogenides (TMDs) as one kind of 2D materials, [START_REF] Shao | Strong Rashba-Edelstein Effect-Induced Spin-Orbit Torques in Monolayer Transition Metal Dichalcogenide/Ferromagnet Bilayers[END_REF][START_REF] Wang | Strong Interface-Induced Spin-Orbit Interaction in Graphene on WS2[END_REF][START_REF] Neal | Two-Dimensional TaSe2 Metallic Crystals: Spin-Orbit Scattering Length and Breakdown Current Density[END_REF][START_REF] Kosmider | Large Spin Splitting in The Conduction Band of Transition Metal Dichalcogenide Monolayers[END_REF][START_REF] Li | Strong Spin-Orbit Splitting and Magnetism of Point Defect States in Monolayer WS2[END_REF] such as MX2 (M =Mo, W; X = S, Se, Te), have been extensively studied in the electronic and optoelectronic field due to their layered structure and unique band structure depending on thickness. [START_REF] Wang | Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides[END_REF][START_REF] Klein | Electronic Properties of WS2 Monolayer Films[END_REF] Moreover, the strong SOC effect and the breaking of inversion symmetry for monolayer TMDs also promote the research works on their spintronic applications, especially for the generation of SOT. [START_REF] Xiao | Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides[END_REF][START_REF] Zhu | Giant Spin-Orbit-Induced Spin Splitting in Two-Dimensional Transition-Metal Dichalcogenide Semiconductors[END_REF][START_REF] Náfrádi | Electron Spin Dynamics of Two-Dimensional Layered Materials[END_REF] Current induced field-like and damping-like torques were observed in Py/MoS2 bilayers and the strong SOT exhibited purely interfacial nature. [START_REF] Zhang | Research Update: Spin Transfer Torques in Permalloy on Monolayer MoS2[END_REF] A further study has experimentally shown that one can change the allowed symmetries of SOT in spin-source/ferromagnet bilayer devices with low crystalline symmetry.

An out-of-plane anti-damping torque was generated when the current was applied along a lowsymmetry axis of WTe2/Py bilayers which provided a new strategy to control SOT. [START_REF] Macneill | Control of Spin-Orbit Torques Through Crystal Symmetry in WTe2/Ferromagnet Bilayers[END_REF] Electric-field control of magnetization dynamics has been widely studied for realizing highperformance, low-power spintronic memory and logic devices. For example, the electric-field control of ferromagnetism in magnetic semiconductors through modulation of the carrier concentration, [START_REF] Chiba | Electrical Manipulation of Magnetization Reversal in a Ferromagnetic Semiconductor[END_REF] electric-field manipulation of magnetization reversal by using multiferroics, [START_REF] Heron | Deterministic Switching of Ferromagnetism at Room Temperature Using an Electric Field[END_REF] and voltage-controlled magnetic anisotropy in ultrathin ferromagnet/oxide junctions. [START_REF] Amiri | Voltage-Controlled Magnetic Anisotropy in Spintronic Devices[END_REF] The electric-field control of SOT has been reported in a Cr-doped topological insulator thin film using a top-gate field-effect transistor structure, in which the SOT strength can be modulated by a factor of four within the accessible gate voltage range, and it shows strong correlation with the spin-polarized surface current in the film. [START_REF] Fan | Electric-Field Control of Spin-Orbit Torque in A Magnetically Doped Topological Insulator[END_REF] However, the related research of electric-filed control of SOT in 2D materials is still inadequate. Monolayer WS2 is a n-type semiconductor of 2D material which shows excellent electronic and optoelectronic properties with relatively high mobility up to ~100 cm 2 Vs -1 and on/off ratio up to ~10 8 . [START_REF] Gao | Large-Area Synthesis of High-Quality and Uniform Monolayer WS2 on Reusable Au Foils[END_REF][START_REF] Cui | High-Performance Monolayer WS2 Field-Effect Transistors on High-kappa Dielectrics[END_REF] It is possible to change the carrier distribution in monolayer WS2 by applying a back-gate voltage through the dielectric layer. And, the WS2 monolayer has extremely strong SOIs: several hundreds of millivolts in the valence bands and several tens of millivolts in the conduction band. [START_REF] Wang | Strong Interface-Induced Spin-Orbit Interaction in Graphene on WS2[END_REF] Therefore, it is much interesting to investigate the current induced spin transfer torque resonance phenomenon and the electric-filed control of SOT effect in WS2/Permalloy bilayer device.

In this work, high quality WS2 monolayers were grown using CVD method and the WS2/permalloy bilayer device was fabricated by electron beam evaporation and photolithography technique. The effect of SOT in WS2/ NiFe (Py) bilayer was investigated by the spin-torque ferromagnetic resonance (ST-FMR). Current induced field-like torque (τ⊥) and anti-damping-like torque (τ∥) were observed. Furthermore, the ratio of τ⊥/τ∥ in WS2/Py bilayer could be modulated by applying back-gate voltage which can adjust the semiconducting nature of WS2. Our work provided a strategy to electrically control SOT by utilizing the semiconducting TMDs.

RESULTS AND DISCUSSION

High-quality large-area monolayer WS2 was grown on Si(p++)/SiO2 substrate using CVD method. The structure and morphology were characterized by optical microscopy, atomic force microscopy (AFM), Raman and photoluminescence (PL) spectroscopy. As shown in Figure 1a, the distinct contrast of the optical image indicates a triangular shape of as-grown WS2 monolayers with size up to several tens and hundreds of μm. [START_REF] Zhang | Controlled Growth of High-Quality Monolayer WS2 Layers on Sapphire and Imaging Its Grain Boundary[END_REF][START_REF] Tongay | Tuning Interlayer Coupling in Large-Area Heterostructures With CVD-Grown MoS2 and WS2 Monolayers[END_REF] By AFM measurement (see Figure 1b) with a selected triangular WS2 sample, a typical height of WS2 is determined to be ~0.83 nm which is consistent with the theoretically and experimentally reported values of monolayer WS2. [START_REF] Fu | Controllable Synthesis of High Quality Monolayer WS2 on a SiO2/Si Substrate by Chemical Vapor Deposition[END_REF] Figure 1c shows the Raman spectrum of WS2 with characteristic modes of E 1 2g and A1g at 351 cm -1 and 418 cm -1 , respectively. The peak frequency difference of 67 cm -1 indicates a clear signature of monolayer WS2. [START_REF] Zhang | Phonon and Raman Scattering of Two-Dimensional Transition Metal Dichalcogenides From Monolayer, multilayer to bulk material[END_REF] Figure 1d gives a PL spectrum of the as-grown WS2, showing a single characteristic peak at 630 nm (1.97 eV), which also indicates the WS2 is a monolayer. [START_REF] Gutierrez | Extraordinary Room-Temperature Photoluminescence in Triangular WS2 Monolayers[END_REF] For the fabrication of WS2/Py bilayer device, the Py (Ni81Fe19) was deposited directly on the surface of WS2 with ~10 nm thickness to form pure interfacial contact. Photolithography and etching process were used to obtain the WS2/Py bilayer stripe with a size of 45 μm in length and 8 μm in width. The ground-signal-ground (GSG) electrical contacts were patterned by photolithography and Ni (10 nm)/Au (100 nm) metal electrode was deposited using electron beam evaporation. Moreover, pure Py device was fabricated on the same Si(p++)/SiO2 substrate using the same technological process for comparison. This technological process can avoid the contact of WS2 with photoresist and is different from the process used in the work of MoS2/Py bilayer. [START_REF] Zhang | Research Update: Spin Transfer Torques in Permalloy on Monolayer MoS2[END_REF] Figure 2a shows the optical image of one representative WS2/Py bilayer device including contact GSG pads and circuit of the ST-FMR measurement. The ST-FMR technique [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF][START_REF] Fang | Spin-Orbit-Driven Ferromagnetic Resonance[END_REF] was used to measure the SOT produced by WS2/Py bilayers at room temperature. Figure 2b illustrates the schematic device geometry and circuit of electrical-field control of the ST-FMR measurement. A RF current with fixed microwave frequency and in-plane magnetic field were applied through the bilayer at the ferromagnetic resonance condition. The oscillating currentinduced torque causes the Py magnetization to precess, yielding resistance oscillations due to the anisotropic magnetoresistance (AMR) of Py layer. This change in resistance mixes with the alternating current to create a DC voltage, Vdc, across the stripe.

As shown in Figure 2b, two vector components of the current-induced torque, in the m ×(y ×m ) (∥, in-plane) and (y ×m ) (⊥, perpendicular) directions, are respectively obtained from the amplitudes of the symmetric and anti-symmetric components of the resonance lineshape. [START_REF] Mellnik | Spin-Transfer Torque Generated by A Topological Insulator[END_REF][START_REF] Zhang | Research Update: Spin Transfer Torques in Permalloy on Monolayer MoS2[END_REF][START_REF] Macneill | Control of Spin-Orbit Torques Through Crystal Symmetry in WTe2/Ferromagnet Bilayers[END_REF] We interpret the ST-FMR signals within a macrospin approximation for the magnetization direction using the Landau-Lifschitz-Gilbert-Slonczewski (LLGs) equation of motion. [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF] The magnetization equation of motion can be written as follows:

dm dt = -γm ×H + αm × dm dt + γτ ⊥ m ×y + γτ ∥ m ×(y ×m ) ( 1
)
where γ is the gyromagnetic ratio, α is the Gilbert damping parameter and H is the applied magnetic field. [START_REF] Zhang | Research Update: Spin Transfer Torques in Permalloy on Monolayer MoS2[END_REF] The out-of-plane τ⊥ is the magnitude of the field applying field-like torque and the in-plane τ∥ is the magnitude of the field applying anti-damping-like torque. The ST-FMR mixing voltage has the following form:

V dc =V S ∆H 2 (H-H 0 ) 2 +∆H 2 +V A 4∆H(H-H 0 ) (H-H 0 ) 2 +∆H 2 (2)
where Ho is the applied magnetic field at ferromagnetic resonance, and ΔH is the linewidth. [START_REF] Macneill | Control of Spin-Orbit Torques Through Crystal Symmetry in WTe2/Ferromagnet Bilayers[END_REF][START_REF] Kanai | Electric Field-Induced Ferromagnetic Resonance in A CoFeB/MgO Magnetic Tunnel Junction Under DC Bias Voltages[END_REF] The symmetric and anti-symmetric amplitudes, VS and VA, can be obtained by fitting eq 2 to measured DC voltage as a function of applied magnetic field. The symmetric and anti-symmetric amplitudes, VS and VA, are related to the two components of torque as follows: [START_REF] Macneill | Control of Spin-Orbit Torques Through Crystal Symmetry in WTe2/Ferromagnet Bilayers[END_REF] V S = -

I RF 2 dR dφ 1 αγ 2H 0 +μ 0 M eff τ ∥ (3)
V A = -

I RF 2 dR dφ 1+μ 0 M eff /H 0 αγ 2H 0 +μ 0 M eff τ ⊥ (4)
The torque ratio τ⊥/τ∥ can be obtained from eq 3 and eq 4 as follows:

τ ⊥ τ ∥ = V A V S 1 1+μ 0 M eff /H 0 ( 5
)
where μ0 is the permeability in vacuum, Meff is the effective saturation magnetization of Py and can be obtained from the frequency dependent of H0 using the Kittel formula. [START_REF] Chiba | Electrical Manipulation of Magnetization Reversal in a Ferromagnetic Semiconductor[END_REF][START_REF] Fang | Spin-Orbit-Driven Ferromagnetic Resonance[END_REF] f= γ 2π

H 0 H 0 +μ 0 M eff (6)
Figure 3a shows the Vdc conparison for WS2/Py and pure Py device and the fitted symmetric and antisymmetric amplitude components of the line shape. The in-plane magnetic field was oriented at 45° relative to the length direction of the Py stripe and the applied microwave power and frequency is 10 dBm and 5 GHz, respectively. In comparison with the pure Py device, the amplitudes of the symmetric and antisymmetric components of WS2/Py both increase obviously, which is similar to that of MoS2/Py layer. [START_REF] Zhang | Research Update: Spin Transfer Torques in Permalloy on Monolayer MoS2[END_REF] For the pure Py device, normally we should observe no resonance signal at all. However, a very small and symmetric signal was observed in the Py (10 nm) sample. The symmetric signal may arise from the relative phase of microwaves [START_REF] Harder | Analysis of the Lineshape of Electrically Detected Ferromagnetic Resonance[END_REF] or an Oersted field due to nonuniform current flow at the electrode contacts which lead to a self-induced precession of the magnetization. [START_REF] Tsukahara | Self-Induced Inverse Spin Hall Effect in Permalloy at Room Temperature[END_REF] Figure 3b shows the typical ST-FMR spectra for a WS2/Py bilayer excited at different rf frequency from 4 to 10 GHz and fixed power of 15 dBm. The obtained f vs. resonant field curve is well fitted by Kittel formula eq 6 as shown

in Figure 3c. From the fitting, we obtained Meff = 949.4±18.2 KAm -1 and 4πMeff =1.19 T, which is comparable to commonly used Py (~1T). [START_REF] Ganguly | Thickness Dependence of Spin Torque Ferromagnetic Resonance in Co75Fe25/Pt Bilayer Films[END_REF] The microwave frequency dependence of the torque ratio τ⊥/τ∥ was calculated using eq 5 as shown in Figure 3e. The values of torque ratio τ⊥ /τ∥ vary obviously from ~0.1 to ~0.5 with increasing frequency because the ratio τ⊥/τ∥ is directly proportional to the resonant field H0. The strong spin-orbit coupling and broken vertical symmetry together with the intrinsic inversion symmetry breaking in the monolayer WS2 could give rise to a large Rashba-type spin splitting in our WS2/Py bilayer. [START_REF] Xu | Spin and Pseudospins in Layered Transition Metal Dichalcogenides[END_REF][START_REF] Manchon | New Perspectives for Rashba Spin-Orbit Coupling[END_REF] Such type of spinsplitting can give rise to a field-like torque base on the theoretical calculation [START_REF] Haney | Current Induced Torques and Interfacial Spin-Orbit Coupling: Semiclassical Modeling[END_REF]51 . In the measurement, large anti-symmetric voltages VA indicate the existence of significant filed-like torques. And the potent SOT is obtained which supports the interfacial nature of the torque in WS2/Py bilayer device. The ST-FMR measurements under different microwave power were also performed with a fixed frequency at 5 GHz. The amplitude of Vdc increase with applied microwave power, but the resonant fields have little change. The values of torque ratio τ⊥/τ∥ are around 0.19 with tiny fluctuation, seen in Figure S1.

Then, we performed comprehensive full angular (φ) dependence of the ST-FMR signal Vdc.

The ST-FMR measurement was conducted at a series of angle φ from 0° to 360° at fixed frequency of 5 GHz and fixed power of 15 dBm. By fitting the ST-FMR spectra using eq 2, the symmetric ST-FMR resonance components VS and antisymmetric components VA as a function of in-plane magnetic-field angle φ are obtained, shown in Figure 4a and b, respectively.

Accordingly, in the heavy-metal/ferromagnet bilayer, the current induced torque amplitudes follow a cosφ behavior due to the spin Hall effect, the Rashba-Edelstein effect, or the Oersted field. [START_REF] Liu | Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect[END_REF][START_REF] Mellnik | Spin-Transfer Torque Generated by A Topological Insulator[END_REF] The anisotropic magnetoresistance (AMR) in Permalloy follows an cos2φ angular dependence, which enters Vdc as dR/dφ~sin2φ. Two contributions yield a same angular dependence for the symmetric and anti-symmetric ST-FMR components. Therefore, VS and VA can be well fitted by the cosφsin2φ behavior. The cosφsin2φ angular dependence behavior confirms the FMR rectification is due to the interaction of the AMR mixed on the resonance with microwave.

Figure 5a Figure 5d). The torque ratio τ⊥/τ∥ was also calculated using eq 5. Figure 5c intuitively shows that the torque ratio τ⊥/τ∥ increases with back-gate voltage from -80 V to 40 V and keep nearly unchanged from 40 V to 80 V. The variation of torque ratio implies that the SOT in WS2/Py bilayer heterostructure can be effectively regulated and controlled by the electrical field.

Interestingly, the variation of torque ratio with the back-gate voltage demonstrates similar tendency with the field-effect transistor transfer curves of the monolayer(ML) WS2, as shown in

CONCLUSION

In conclusion, we experimentally investigated SOT in WS2/ Py bilayers. Field-like and antidamping-like torques were observed in WS2/Py bilayer due to spin accumulation of WS2 arising from the interfacial Rashaba-Edelstein effect. More importantly, we demonstrated the effective electric-field control of SOT ratio τ⊥/τ∥ in WS2/Py bilayer taking advantage of the semiconductor property of WS2. The electric-field control of torque ratio effect demonstrated similar tendency with the field-effect transistor transfer curves of the monolayer WS2. We ascribed this phenomenon to the regulation of the carrier density in WS2 and the interfacial characteristics between WS2 and Py. Our results provided a strategy for manipulating spin-orbit torque compatible with field-effect semiconductor devices based on two-dimensional materials TMDs and could be beneficial for the improvement of energy efficiency for spintronic devices in the future.

METHODS

Growth of WS2 Monolayer. High quality WS2 monolayers were grown on a Si/SiO2 (300 nm) substrate (Silicon Quest International Inc., USA) using a CVD method in a quartz tube. During the process of growth, sulfur powder (1 g, 99.99% purity, Alfa Aesar) was put on the upstream of quartz tube, WO3 powder (500 mg,99.8% purity, Alfa Aesar) was put on the downstream with an argon flow at 100 sccm at ~900℃ for 50 min. The WS2 monolayers in a triangular shape and size up to hundreds of μm were finally obtained.

Fabrication of WS2/Py bilayer device. The permalloy (Py) was deposited directly on the surface of WS2 at a thickness of ~10 nm using electron beam evaporation (EBE-09, China) with deposition rate of 1.5 Å/s. The Py stripe at a size of 45 μm in length and 8 μm in width was patterned using photolithography (MA6) and the outer part of the stripe was etched away (IBE-A-150). The ground-signal-ground (GSG) electrical contacts was patterned using photolithography and Ni (10 nm)/Au (100 nm) metal electrode was deposited using electron beam evaporation.

Measurements. The monolayer WS2 was characterized by Raman and PL spectroscopy and AFM. Both Raman and PL spectroscopy were carried out using a Horiba Jobin Yvon LabRAM HR-Evolution Raman microscope with a laser radiation of 532 nm and power of 10 μW. The surface morphology images of sample were obtained with AFM (MultiMode8, Veeco Instruments Inc., USA). We determine the strength of current-induced torque by using a spin torque ferromagnetic resonance (ST-FMR) technique. Microwave signal produced by a generator was applied to the devices through a bias tee using an rf probe. The oscillating current-induced torques cause the Py magnetization to precess, yielding resistance oscillations. The rf current and oscillated resistance generated direct voltage Vdc was recorded by a nano-voltmeter. A voltage source meter (Keithley 2400) from -80 V to 80 V was applied on the gate to provide an electric field.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI:

. ST-FMR measurement results at a series of power, the power dependence of torque ratio τ⊥/τ∥, The back-gate dependence of ST-FMR signals Vdc for Py.

  Figure 5a shows the ST-FMR resonances signals Vdc at a series of back-gate voltage from -

Figure 5d .

 5d Figure5d. This phenomenon can be explained by the regulation of the carrier density in WS2 and

Figure 1 .

 1 Figure 1. Characterization of WS2 sample. (a) Optical image of CVD-grown WS2 samples. The

Figure 2 .

 2 Figure 2. WS2/Py device geometry and ST-FMR measurement circuit. (a) Optical images of

Figure 3 .

 3 Figure 3. ST-FMR measurement results of Py and WS2/Py bilayers. (a) Comparison of ST-FMR

Figure 4 .

 4 Figure 4. Angular dependence of ST-FMR measurement for WS2/Py bilayer at a series of angle φ

Figure 5 .

 5 Figure 5. Electrical-field control of ST-FMR measurement for WS2/Py bilayer. (a) The back-gate

ACKNOWLEDGMENT

The work was supported by the National Natural Science Foundation of China(Grant No. 请曾 老师补充)

AUTHOR INFORMATION

Corresponding Author * zmzeng2012@sinano.ac.cn. * lzy0319@ysu.edu.cn.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.