Abstract
Finding an effective way to greatly tune spin Hall angle in a low power manner is of fundamental importance for tunable and energyefficient spintronic devices. Recently, topological insulator of Bi_{2}Se_{3}, having a large intrinsic spin Hall angle, show great capability to generate strong currentinduced spinorbit torques. Here we demonstrate that the spin Hall angle in Bi_{2}Se_{3} can be effectively tuned asymmetrically and even enhanced about 600% reversibly by applying a bipolar electric field across the piezoelectric substrate. We reveal that the enhancement of spin Hall angle originates from both the charge doping and piezoelectric strain effet on the spin Berry curvature near Fermi level in Bi_{2}Se_{3}. Our findings provide a platform for achieving low power consumption and tunable spintronic devices.
Introduction
Driving magnetization switching by currentinduced spinorbit torque (SOT) is one of the most promising means to achieve magnetic random access memories (MRAM) due to the merits in ultrafast, nonvolatile, and energyefficient operation^{1}. In a typical SOTdriven device, the inplane charge current is converted into spin current in the heavy metal layer via the spin Hall effect^{2}. The spin current further injects into the adjacent ferromagnetic layer, exerting torque on the magnetic moment and driving magnetization switching. The power consumption of SOTMRAM devices can be further reduced by improving the chargespin conversion efficiency in the nonmagnetic spin Hall layer^{3,4,5} or enhancing the spin current transmission at the nonmagnet/ferromagnet interface^{5,6,7}. Here, the spin Hall angle defined as the ratio of spin current density J_{s} to charge current density J_{c} is crucial in SOT devices. Pursuing materials with a large spin Hall angle is a prerequisite for achieving low power consumption SOT devices. In this context, topological insulators^{8}, 2D materials^{9}, antiferromagnets^{10}, and Weyl semimetals^{11,12,13} with novel quantum states have been actively investigated. Topological insulators such as Bi_{2}Se_{3} and Bi_{2}Te_{3} show an exceptionally large spincharge conversion efficiency than conventional heavy metals due to the helical spinmomentum locking in the surface states^{14,15,16}. Recently, magnetron sputtered Bi_{2}Se_{3} films exhibiting both large spin Hall angle and highly compatible with industrial production, are regarded as optimal materials for the SOT switching^{17,18}. Despite these exciting prospects, topological insulators are problematic because of their relative high resistivities. Exploring interesting approaches to further improve energy efficiency is a challenge and opportunity.
The electric fieldinduced mechanical strain has been demonstrated to effectively mediate the magnetic anisotropy, exchange coupling, spin structure, and SOT magnitude in the ferromagnetic layer^{19,20,21,22}. In addition, the surface charge doping related to the ferroelectric polarization will also contribute to the tuning effect. Due to the dielectric nature of ferroelectric materials, the electric field can be applied without the leak current. Hence the Joule heating is suppressed in electric field controlling, which is suitable for low energy consuming information technology. However, in the spin Hall materials, the electric field control of the chargespin conversion ratio has been rarely studied. Considering that the intrinsic spin Hall conductivities are strongly dependent on the position of Fermi level, which can be tuned by the charge doping and strain. The strain effect usually shows a symmetric tunning effect with respect to the positive and negative electric fields due to the same lattice deformation, while the charge doping effect always shows an asymmetric tunning effect^{23}. Thus building the multifunctional hybrid devices by introducing electric field controlling is particularly attractive to obtaining tunable spin sources and further reducing the power consumption of SOTMRAM devices.
In this work, the electric field dramatic tuning of spin Hall angle in Bi_{2}Se_{3} films sputtered on the piezoelectric substrates was demonstrated. The values of spin Hall angle under different electric fields are measured using an in situ planar Hall system. With applying an electric field, the chargespin conversion efficiency was significantly enhanced in a reversible and reproducible manner. The maximum spin Hall angle was determined to be 13.45 at E = −12 kV/cm which is six times larger than the initial state. It is interesting to find the spin Hall angle changed asymmetrically while a bipolar electric field was applied across the piezoelectric substrate. By conducting DFT calculation and related control experiments, such great tunability as well as the asymmetrical tuning effect are considered to be originating from the combination effect of the mechanical strain and the interfacial charge doping between Bi_{2}Se_{3} and PMNPT. It turns out the mechanical strain enhances the spin Hall angle symmetrically, whereas the charge doping changes the spin Hall angle in an asymmetrical way.
Results
The low magnification highangle annular darkfield scanning transmission electron microscopy (HAADFSTEM) image gives an overview of the PMNPT/Bi_{2}Se_{3}(8 nm)/NiFe(8 nm)/TaO_{x}(1 nm) structure, as shown in Fig. 1a. The thickness of the layers is similar to the nominal ones. The interface of each layer is smooth and continuous, which indicating the uniform growth of all layers in the stack (see Supplementary Fig. 6). Figure 1b shows the highresolution HAADFSTEM image of the film. The sharp lattice fringes clearly seen in the image reveal the existence of good crystallinity in the Bi_{2}Se_{3}. The Bi_{2}Se_{3} film exhibits a mixing of polycrystalline and amorphous state as a whole (see Supplementary Fig. 7). This result is consistent with the previous report on the sputtered Bi_{2}Se_{3} films^{17,24}. We conducted the Xray photoelectron spectroscopy (XPS) measurement to determine the chemical composition of PMNPT/Bi_{2}Se_{3} (20 nm) structure. Figure 1c, d shows the Bi 4f corelevel spectra and Se 3d corelevel spectra, respectively. For Bi 4f corelevel spectra, the peaks of Bi 4f_{7/2} and 4f_{5/2} energy levels are observed at binding energies about 156.36 eV and 161.72 eV. The Bi 4f levels show a spinorbit splitting of 5.36 eV, which is consistent with the previous report^{25}. Here two other components with the binding energy of 157.08 eV and 162.47 eV nearby the original Bi 4f peaks are observed. Those peaks corresponding to the BiO bound are due to the little oxidation when measuring the XPS spectra^{26}. Two peaks correspond to the Se 3d_{5/2}, and 3d_{3/2} with binding energies of 51.56 eV and 52.42 eV appear at the Se 3d corelevel spectra. The splitting of Se 3d level is determined to be 0.86 eV, comparable to the previous experimental studies^{18,27,28}. By considering the integrated peak intensity with the sensitivity factor, the surface atomic composition ratio of Se and Bi is estimated to be 1.43 (see Supplementary Fig. 8 and Supplementary Note 7). The composition is close to the target, showing the films are normally stoichiometric. To examine the surface roughness of the samples, we conducted the atomic force microscopy (AFM) measurement on the PMNPT/Bi_{2}Se_{3}(8 nm)/NiFe(8 nm)/TaO_{x}(1 nm) sample, as shown in Fig. 1e. The surface roughness Ra is determined to be 0.489 nm, indicating a smooth surface and high film quality which is sufficient for the further SOT study (see Supplementary Fig. 10).
Here we determine the currentinduced SOT effective fields by angular field characterization of the planar Hall resistance at positive and negative testing current. The dampinglike torque induces the perpendicular effective field H_{OOP}, and the fieldlike torque induces the inplane transverse effective field H_{T}. as shown in Fig. 2a. According to the Slonczewski equation^{29}, the perpendicular effective field H_{OOP} can be expressed as \([\hslash /(2e{M}_{{{{{{\rm{S}}}}}}}t)]{J}_{{{{{{\rm{S}}}}}}}({{{{{\boldsymbol{\sigma }}}}}}\times {{{{{\boldsymbol{m}}}}}})\), where σ is the spin polarization unit vector, m is the magnetization vector, J_{s} represent the magnitude of spin current density, and t is the thickness of the ferromagnetic layer. The Hall resistance is directly modified by the small magnetization deviation induced by the SOT effective fields. The direction of the H_{oop} and H_{T} relies on the sign of current. Hence the component of SOT effective fields in angulardependent planar Hall resistance is an odd function of current, whereas other components are even function with respect to the testing current. We take the differential resistance \({R}_{{{{{{\rm{DH}}}}}}}={R}_{{{{{{\rm{H}}}}}}}(+I){R}_{{{{{{\rm{H}}}}}}}(I)\) to extract the contribution from the SOT effective fields and cancel out other effects such as Joule heating^{30}. The inset illustrates the structure of the Hall device and the measurement configuration. The Hall resistance R_{H}(I,θ) is measured using the bipolar input current and rotating the constant 400 Oe inplane external magnetic field H_{ext}. Here I is the input current along the xdirection, and θ represents the angle between the current and the magnetic field.
Figure 2b shows the typical planar Hall resistance R_{H} as a function of θ measured at ±10 mA and the corresponding R_{DH} curve for Bi_{2}Se_{3}(8 nm)/NiFe(8 nm)/TaO_{x}(1 nm) structure on thermally oxidized Si substrate. Here we assume that the top 1 nm Ta capping layer is fully oxidized and has almost no impact on the spin transport properties^{31,32}. The value of H_{OOP} and H_{T} can be obtained by fitting the following equation
where C is the resistance offset, R_{AHE} is the anomalous Hall resistance, and H_{perp} is the magnetic field along the z direction when measuring the anomalous Hall resistance. The Oersted field contribution H_{Oe} is estimated to be 6.66 × 10^{−3} Oe/mA calculated by Ampere’s law with considering the current shutting effect (see Supplementary Note 9). The R_{H} is the magnitude of sin(2θ) component in the corresponding planar Hall resistance curve. Here the value of \(\frac{{{{{{\rm{d}}}}}}{R}_{{{{{{\rm{AHE}}}}}}}}{{{{{{\rm{d}}}}}}{H}_{{{{{{\rm{perp}}}}}}}}\) is determined to be 3.175 × 10^{−5} Ω/Oe by taking the slope of R_{AHE} versus H_{perp} at a small 1 mA testing current (see Supplementary Note 3).
After determining the value of R_{H}, H_{Oe}, and \(\frac{{{{{{\rm{d}}}}}}{R}_{{{{{{\rm{AHE}}}}}}}}{{{{{{\rm{d}}}}}}{H}_{{{{{{\rm{perp}}}}}}}}\) parameters, the effective field H_{OOP} and H_{T} can be obtained by fitting the angulardependent R_{DH} data into Eq. (1). Figure 2c shows the R_{DH} results and the fitting curves at different testing currents. The fitting curves are in good agreement with the experimental data. The amplitude of R_{DH} curve increases with increasing the testing current, indicating the contribution from the currentinduced SOT effective fields. Figure 2d shows the linear fitting result of SOT effective field H_{SO}, including H_{OOP} and H_{T} with respect to the testing current. The effective spin Hall angle can be calculated by
where M_{s} is the saturation magnetization and equal to 663.45 emu/cm^{3} (see Supplementary Fig. 4), t_{FM} is the thickness of the ferromagnetic layer, and J_{NM} is the current density in the nonmagnetic layer. The value of \(\frac{{H}_{{{{{{\rm{OOP}}}}}}}}{{J}_{{{{{{\rm{NM}}}}}}}}\) is obtained by the slope of the linear fitting result. The spin Hall angle of our 8 nm Bi_{2}Se_{3} is determined to be 2.18, comparable with the previous study on sputtered Bi_{2}Se_{3} and the STFMR analysis (see Supplementary Note 1). This ensures that the measurements and analysis of spin Hall angle are performed precisely and reliable.
We perform the in situ planar Hall measurements at different electric fields to characterize the electric field control spin Hall angle of Bi_{2}Se_{3}. The Hall device with the same multilayer structure is fabricated on a PMNPT substrate that applies the electric field and generates mechanical strain, as demonstrated in Fig. 3a. The electric field is applied perpendicular to the PMNPT substrate up to ±12 kV/cm. The representative R_{DH} results measuring at ±6 mA testing current under 0 kV/cm, −12 kV/cm, and 0 kV/cm back electric field are shown in Fig. 3b. The constant baseline of the results is substracted to directly compare the amplitude and line shape of the R_{DH} curves under different electric fields. The R_{DH} curves under −12 kV/cm exhibit a larger amplitude than that of 0 kV/cm, indicating the increment of the SOTinduced effective fields. Specifically, the peaks around 115° and 245° nearly disappear under the electric field at −12 kV/cm. Such dramatic change in the line shape is due to an increase of the cos(θ) component to the total line shape, which corresponds to a remarkable enhancement of perpendicular effective field H_{OOP}. Note that there are no obvious changes in the R_{DH} curves between 0 kV/cm and 0 kV/cm back, implying a reversible switching behavior.
The H_{OOP} versus the testing current from 0 kV/cm to −12 kV/cm is presented in Fig. 3c. The determined effective fields are proportional to the testing current, and the linear fitting agrees with the data well. The values of \(\frac{{H}_{{{{{{\rm{OOP}}}}}}}}{{J}_{{{{{{\rm{NM}}}}}}}}\) derived from the linear fitting are 1.227 × 10^{−9} Oe/(A m^{−2}) and 7.976 × 10^{−9} Oe/(A m^{−2}) under 0 kV/cm to −12 kV/cm, respectively. Figure 3d demonstrates the spin Hall angles under different electric fields applied across the PMNPT substrate. Interestingly, it is found that the electric fielddependent spin Hall angle is significantly asymmetric with respect to the zero field. The spin Hall angle of Bi_{2}Se_{3} has been enhanced by using both positive and negative electric fields. Especially, the spin Hall angle of Bi_{2}Se_{3} exhibits a significant increment up to 13.45 under −12 kV/cm, which is about 6 times larger than the initial state.
Generally speaking, two effects from the PMNPT substrate are expected to be responsible for the change of the spin Hall angle in Bi_{2}Se_{3}, i.e., strain effect^{19,33} and charge doping effect^{23,34}. In order to clarify the mechanism of the tunning result, it is necessary to directly distinguish the strain effect and charge doping effect. Inserting a charge dissipation layer such as 5 nm Cu between PMNPT substrate and Bi_{2}Se_{3} layer is an effective way to separate those two effect^{34,35}. The charge doping effect can be excluded in this condition since the charge will be dissipated in the Cu layer. Here we further perform the same study with structure PMNPT/Cu(5 nm)/Bi_{2}Se_{3}(8 nm)/NiFe(8 nm)/TaO_{x}(1 nm). Figure 4 gives a comparison of electric field control spin Hall angle between PMNPT/Bi_{2}Se_{3}/NiFe structure and PMNPT/Cu/Bi_{2}Se_{3}/NiFe structure. After inserting the Cu dissipation layer between Bi_{2}Se_{3} and PMNPT, the electric field control spin Hall angle in Bi_{2}Se_{3} shows a symmetry behavior at positive and negative electric fields. That is due to the almost equivalent lattice deformation induced by the piezoelectric strain^{36}. After separating the strain effect, the higher enhancement of spin Hall angle in PMNPT/Bi_{2}Se_{3}/NiFe structure at the negative electric field can be attributed to the contribution of the charge doping effect.
To theoretically understand the tunning mechanism, we further investigate the external electric field effect on the spin Hall angle of Bi_{2}Se_{3} by firstprinciple calculation. The spin Hall conductivity (SHC) of Bi_{2}Se_{3} which is proportional to the spin Hall angle, as a function of inplane strain and charge doping have been studied respectively.
We adopt the maximally localized Wannier functions with Wannier90 in combination with the VASP package to calculate the SHC^{37,38,39,40}. Firstly, we calculate the SHC of bulk Bi_{2}Se_{3} with R3m space group and find its SHC is 38.58 (ħ/e)S/cm, which is mainly attributed to the electrons around the Fermi level nearby the Γ point in the Brillouin zone (Fig. 5a). It is known that the electric field induces biaxial strain in Bi_{2}Se_{3} via PMNPT substrate^{41}. Thus, we systematically investigate the relationship between SHC of Bi_{2}Se_{3} and the biaxial strain. As shown in Fig. 5c, both the tensile and compressive strains can induce the increment of SHC. Moreover, the tensile and compressive strains tune the SHC almost symmetric when the strain is small (<0.25%). When the strain becomes larger, i.e., to the maximum value of our experimental data 0.5%, the asymmetric SHC appears. Nevertheless, the asymmetric difference is less than 20%, much smaller than the experimental results where three times asymmetric is observed (Fig. 3d). This result is consistent with the experimental observation where the charge transfer effect is excluded (Fig. 4).
To further explore the charge transfer effect induced by the PMNPT substrate, we additionally calculate the electronic structure of a heterostructure composed of Bi_{2}Se_{3} and PbTiO_{3}(001) (a simplified model to PMNPT). Considering that the optimized lattice constant of Bi_{2}Se_{3} is 4.16 Å and that of PbTiO_{3} is 3.90 Å, the \(1\times \sqrt{7}\) unit cell of Bi_{2}Se_{3} is commensurate to the \(1\times 2\sqrt{2}\) surface unit cell of PbTiO_{3}(001). Figure 5b shows the calculated differential charge density distributions for TiOterminal Bi_{2}Se_{3}/PbTiO_{3}(001) heterostructure. It is seen that obvious electron transfer from PbTiO_{3} to Bi_{2}Se_{3} occurs when PbTiO_{3} is under the negative electric field, whereas there is almost no electron transfer when the electric field is switched to positive. Note that the above results have been confirmed by the DFT calculations based on the HSE06 functional^{42,43}, which is well known to give rise to reliable band gaps in semiconductors (see Supplementary Fig. 11). In addition, we have considered the vacancy defect effect in Bi_{2}Se_{3} on the interface charge transfer and calculated the differential charge density of Se vacancy defect at the interface (see Supplementary Fig. 12). As one can see, the Se vacancy defect does not affect the charge transfer from PbTiO_{3} to Bi_{2}Se_{3}. Moreover, the effect of metallic covering layer (NiFe alloy) on Bi_{2}Se_{3} interface charge transfer has been investigated. Here we simply consider the Fe/Bi_{2}Se_{3} heterostructure, due to the similar effect on the charge transfer between Ni and Fe elements. The charge transfer from PbTiO_{3} to Bi_{2}Se_{3} still occurs when the negative electric field is applied. Whereas, when the electric field is reversed, there is almost no charge transfer between PbTiO_{3} and Bi_{2}Se_{3}. This result is similar to the case without the metallic covering layer. We have further calculated the averaged charge density difference along the outofplane z direction denoted as Δρ(z) by integrating it over the x–y plane (see Supplementary Fig. 13). It is found that the Se atoms at the interface have a nature of obtaining electrons from Fe atoms when no external electric field is applied. It should be noted that the negative external electric field further benefits the electron transfer from the Fe layer to Bi_{2}Se_{3}. These results confirm that the additional electrons transferred from PMNPT to Bi_{2}Se_{3} can be preserved in Bi_{2}Se_{3}.
We have then calculated the SHC of bulk Bi_{2}Se_{3} as a function of the charge doping concentration (e/unitcell) under 0.5% biaxial strain. As shown in Fig. 5d, the SHC significantly increases with the increase of doped charge concentration from −0.1 to −0.7 e/unitcell, but it decreases from 0 to 0.3 e/unitcell. Such a significant increase of SHC with charge doping can be due to the upshift of the Fermi level, which involves the contribution of conduction electrons around the Γ point to the spin Berry curvature. Especially, the SHC becomes about three times as that without electron transfer under 0.5% strain when the charge doping is about −0.7 e/unitcell. These results show that the asymmetry of the spin Hall angle is mainly from the charge transfer effect. In addition, compared to that of the initial state without strain and charge doping, the coordinated effect of strain and charge doping can increase the SHC of Bi_{2}Se_{3} by 4.5 times in our DFT calculations, which is close to the experimental observation (6 times).
Discussion
In conclusion, we have demonstrated a giant (more than 600%) and reversible manipulation of spin Hall angle in sputtered Bi_{2}Se_{3} films solely by electric fields across the PMNPT piezoelectric substrate. The spin Hall angle and SOT effective field are evaluated using the angulardependent planar Hall measurement with the in situ electric field. We find that applying an electric field enhances the spin Hall angle from 2.18 to 13.45. Moreover, we conduct the firstprinciples calculation study on the intrinsic spin Hall conductivity in a relevant system to reveal the modulation mechanism. We find this remarkable modulation of spin Hall angle is achieved by the comediating of electricfieldinduced strain and surface charge. Our work experimentally realizes a reversible, wide range, low power consumption manner to controls and even enhances the spin Hall angle in sputtered Bi_{2}Se_{3}. Such controllable manipulation of spin Hall angle with exceptionally large enhancement utilizing electric field points to opportunities to enable energyefficient SOT switching and tunable spintronic devices.
Methods
Film growth
Substrate/Bi_{2}Se_{3}(8 nm)/NiFe(8 nm)/TaO_{x}(1 nm) multilayers were deposited onto thermally oxidized Si and (011)oriented PMNPT substrates by DC magnetron sputtering at room temperature with a base pressure less than 1 × 10^{−7} Torr. The background Ar working pressure was 3 mTorr for depositing all the layers. An in situ quartz crystal microbalance monitored the deposition rates.
Device fabrication
The multilayer stacks were patterned into cross Hall bars and rectangular bars for planar Hall measurement and STFMR measurement respectively using standard maskless ultraviolet photolithography and liftoff procedure. The second step of photolithography was employed to fabricate the Cr(5 nm)/Au(100 nm) contacts.
Characterization
The planar Hall measurements were performed with Keithley 6220 DC current source and Keithley 2812 nanovoltmeter in a homemade probe system. A Lake Shore Model 425 Gaussmeter monitored the magnetic field. The planar Hall resistance was recorded as the magnet was rotated. The in situ electric field across the PMNPT was applied by Keithley 6517B electrometer. A crosssectional TEM sample was prepared by the focused ion beam (FIB, Tescan LYRA 3). The crystal structure of the film was investigated using a probe aberrationcorrected scanning transmission electron microscopy (CsSTEM, Themis Z G2 300 kV, FEI). All of the measurements were performed at room temperature.
DFT calculations
Our calculations are performed using the Vienna ab initio Simulation Package (VASP) based on the DFT^{37,38}. The projector augmented wave method and a planewave basis set are performed. The electron exchangecorrelation functional is described by the generalized gradient approximation of the Perdew–Burke–Ernzerhof functional and the HSE06 hybrid functional^{42,43,44}. The planewave cutoff energy is chosen to be 500 eV. Moreover, at Γcentered k mesh of 24 × 24 × 3 are adopted in the selfconsistent calculations. To better describe the vdW interaction, the optB86bvdW functional is adopted^{45,46}. Then, DFT wave functions are projected to maximally localized Wannier functions using the WANNIER90 package^{39}, and the Kubo formula is performed to calculate the SHC. Dene k points meshes of 100 × 100 × 100 and 150 × 150 × 150 are employed respectively for the cases without charge doping and with charge doping, to perform the Brillouin zone integration for the SHC calculations.
The Kubo formula for SHC is given by
\({\sigma }_{\alpha \beta }^{\gamma }\) is the kresolved term, which is written as^{38,45}
where f_{nk} is the Fermi–Dirac distribution function and \({\varOmega }_{n,\alpha \beta }^{\gamma }(k)\) is the bandprojected spin Berry curvature term written as
where α denotes the spin current direction, β represents the direction of the applied electrical field, and γ shows the spin direction of the spin current. In addition, V is the cell volume and \({N}_{k}^{3}\) is the number of k points in the BZ.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
Code availability
The codes are available from the corresponding author upon reasonable request.
References
Liu, L. Q. et al. Spintorque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).
Manchon, A. et al. Currentinduced spinorbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).
Ryu, J., Lee, S., Lee, K. J. & Park, B. G. Currentinduced spinorbit torques for spintronic applications. Adv. Mater. 32, 1907148 (2020).
Demasius, K. U. et al. Enhanced spinorbit torques by oxygen incorporation in tungsten films. Nat. Commun. 7, 10644 (2016).
Baek, S. C. et al. Spin currents and spinorbit torques in ferromagnetic trilayers. Nat. Mater. 17, 509–513 (2018).
Lu, Q. et al. Enhancement of the spinmixing conductance in CoFeB/W bilayers by interface engineering. Phys. Rev. Appl. 12, 064035 (2019).
Koo, H. C. et al. Rashba effect in functional spintronic devices. Adv. Mater. 32, 2002117 (2020).
Khang, N. H. D., Ueda, Y. & Hai, P. N. A conductive topological insulator with large spin Hall effect for ultralow power spinorbit torque switching. Nat. Mater. 17, 808–813 (2018).
Husain, S. et al. Large dampinglike spinorbit torque in a 2D conductive 1TTaS_{2} monolayer. Nano Lett. 20, 6372–6380 (2020).
Zhang, W. et al. Spin Hall effects in metallic antiferromagnets. Phys. Rev. Lett. 113, 196602 (2014).
Ding, J. et al. Switching of a magnet by spinorbit torque from a topological Dirac semimetal. Adv. Mater. 33, 2005909 (2021).
Zhao, B. et al. Unconventional chargespin conversion in Weylsemimetal WTe_{2}. Adv. Mater. 32, 2000818 (2020).
Xu, H. et al. High spin Hall conductivity in largearea typeII Dirac semimetal PtTe_{2}. Adv. Mater. 32, 2000513 (2020).
Mellnik, A. R. et al. Spintransfer torque generated by a topological insulator. Nature 511, 449–451 (2014).
Li, C. H. et al. Electrical detection of chargecurrentinduced spin polarization due to spinmomentum locking in Bi_{2}Se_{3}. Nat. Nanotechnol. 9, 218–224 (2014).
Wang, Y. et al. Room temperature magnetization switching in topological insulatorferromagnet heterostructures by spinorbit torques. Nat. Commun. 8, 1364–1370 (2017).
Dc, M. et al. Roomtemperature high spinorbit torque due to quantum confinement in sputtered Bi_{x}Se_{(1x)} films. Nat. Mater. 17, 800–807 (2018).
Dc, M. et al. Observation of high spintocharge conversion by sputtered bismuth selenide thin films at room temperature. Nano Lett. 19, 4836–4844 (2019).
Filianina, M. et al. Electricfield control of spinorbit torques in perpendicularly magnetized W/CoFeB/MgO Films. Phys. Rev. Lett. 124, 217701 (2020).
Shibata, K. et al. Large anisotropic deformation of skyrmions in strained crystal. Nat. Nanotechnol. 10, 589–592 (2015).
Wang, X. et al. Efield control of the RKKY interaction in FeCoB/Ru/FeCoB/PMNPT (011) multiferroic heterostructures. Adv. Mater. 30, 1803612 (2018).
Nan, T. et al. A strainmediated magnetoelectricspintorque hybrid structure. Adv. Funct. Mater. 29, 1806371 (2018).
Sahin, C. & Flatte, M. E. Tunable giant spin Hall conductivities in a strong spinorbit semimetal: Bi_{(1x)}Sb_{(x)}. Phys. Rev. Lett. 114, 107201 (2015).
Dc, M. et al. Roomtemperature spintocharge conversion in sputtered bismuth selenide thin films via spin pumping from yttrium iron garnet. Appl. Phys. Lett. 114, 102401 (2019).
Nascimento, V. B. et al. XPS and EELS study of the bismuth selenide. J. Electron Spectrosc. Relat. Phenom. 104, 99–107 (1999).
Oprea, B., Radu, T. & Simon, S. XPS investigation of atomic environment changes on surface of B_{2}O_{3}Bi_{2}O_{3} glasses. J. NonCrystalline Solids 379, 35–39 (2013).
Ramaswamy, R. et al. Spin orbit torque driven magnetization switching with sputtered Bi_{2}Se_{3} spin current source. J. Phys. D: Appl. Phys. 52, 224001 (2019).
Zhang, G. et al. Quintuplelayer epitaxy of thin films of topological insulator Bi_{2}Se_{3}. Appl. Phys. Lett. 95, 053114 (2009).
Slonczewski, J. C. Currentdriven excitation of magnetic multilayers. J. Magn. Magn. Mater. 159, L1–L7 (1996).
Kawaguchi, M. et al. Currentinduced effective fields detected by magnetotrasport measurements. Appl. Phys. Express 6, 113002 (2013).
Chi, Z. D. et al. The spin Hall effect of BiSb alloys driven by thermally excited Diraclike electrons. Sci. Adv. 6, eaay2324 (2020).
Montoya, E. et al. Spin transport in tantalum studied using magnetic single and double layers. Phys. Rev. B 94, 054416 (2016).
Chen, X. Z. et al. Observation of the antiferromagnetic spin Hall effect. Nat. Mater. 20, 800–804 (2021).
Nan, T. et al. Quantification of strain and charge comediated magnetoelectric coupling on ultrathin Permalloy/PMNPT interface. Sci. Rep. 4, 3688–3696 (2014).
Chen, A. et al. Giant nonvolatile manipulation of magnetoresistance in magnetic tunnel junctions by electric fields via magnetoelectric coupling. Nat. Commun. 10, 243 (2019).
Liu, M. et al. Voltageimpulseinduced nonvolatile ferroelastic switching of ferromagnetic resonance for reconfigurable magnetoelectric microwave devices. Adv. Mater. 25, 4886–4892 (2013).
Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys.—Condens. Matter 32, 165902 (2020).
Guo, G. Y., Yao, Y. & Niu, Q. Ab initio calculation of the intrinsic spin Hall effect in semiconductors. Phys. Rev. Lett. 94, 226601 (2005).
Liu, M. et al. Electrical tuning of magnetism in Fe_{3}O_{4}/PZNPT multiferroic heterostructures derived by reactive magnetron sputtering. J. Appl. Phys. 107, 073916 (2010).
Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).
Heyd, J. & Scuseria, G. E. Efficient hybrid density functional calculations in solids: Assessment of the HeydScuseriaErnzerhof screened Coulomb hybrid functional. J. Chem. Phys. 121, 1187–1192 (2004).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Klimes, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).
Dion, M., Rydberg, H., Schroder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004).
Acknowledgements
The work was supported by the National Key R&D Program of China (Grant No. 2018YFB0407601[M.L.], 2019YFA0307900[Z.Z.], 2021YFB3201802[M.L.], the Natural Science Foundation of China (Grant Nos. 62131017[M.L.], 91964109[M.L.], 12074301[Z.G.], 12004295[P.L.], 51902248[B.P.]), the Innovation Capability Support Program of Shaanxi (Grant No. 2021TD12[M.L.]) and the National 111 Project of China (Grant No. B14040).
Author information
Authors and Affiliations
Contributions
M.L., Z.Z., and Q.L. conceived and designed the experiments. P.L., Z.G., and T.M. carried out the firstprinciple calculations. Q.L. fabricated the sample and performed the experiments with help of X.Z. G.D. characterized the film structure with TEM. Q.L. conducted the STFMR measurements under the guidance of B.P. Q.L., and P.L. wrote the manuscript with modification from M.L. and Z.G. All authors contributed to the discussion of the results.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks the other anonymous reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Lu, Q., Li, P., Guo, Z. et al. Giant tunable spin Hall angle in sputtered Bi_{2}Se_{3} controlled by an electric field. Nat Commun 13, 1650 (2022). https://doi.org/10.1038/s4146702229281w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s4146702229281w
This article is cited by

Intrinsic anomalous spin Hall effect
Science China Physics, Mechanics & Astronomy (2023)

Spintronics intelligent devices
Science China Physics, Mechanics & Astronomy (2023)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.