Spintronics Based on Topological Insulators

Yabin Fan* and Kang L. Wang†

Department of Electrical EngineeringUniversity of California, Los Angeles

California 90095, USA*yabin@seas.ucla.edu†wang@ee.ucla.edu

Received 6 September 2016Accepted 14 October 2016Published 31 October 2016

Spintronics using topological insulators (TIs) as strong spin–orbit coupling (SOC) materials haveemerged and shown rapid progress in the past few years. Di®erent from traditional heavy metals,TIs exhibit very strong SOC and nontrivial topological surface states that originate in the bulkband topology order, which can provide very e±cient means to manipulate adjacent magneticmaterials when passing a charge current through them. In this paper, we review the recentprogress in the TI-based magnetic spintronics research ¯eld. In particular, we focus on the spin–orbit torque (SOT)-induced magnetization switching in the magnetic TI structures, spin–torqueferromagnetic resonance (ST-FMR) measurements in the TI/ferromagnet structures, spinpumping and spin injection e®ects in the TI/magnet structures, as well as the electrical detectionof the surface spin-polarized current in TIs. Finally, we discuss the challenges and opportunities inthe TI-based spintronics ¯eld and its potential applications in ultralow power dissipation spin-tronic memory and logic devices.

Keywords: Topological insulators; spin–orbit torques; magnetization switching; topologicalspintronics.

1. Introduction

One goal in the ¯eld of spintronics is to controland manipulate magnetic moment using the leastpossible power though electrical means.1–3 Begin-ning with the discoveries of giant magnetoresis-tance (GMR)4,5 and tunneling magnetoresistance(TMR),6–12 which allowed electrical readout ofthe relative orientation of magnetic moments inspin valves13,14 and magnetic tunnel junctions(MTJs), the spintronics ¯eld has further developedthrough theoretical prediction and experimentalobservation of the spin-transfer torque (STT)

e®ect,15–20 which allows manipulation and switchingof magnetic moment by the electrical current.STT-based two-terminal MTJ structures haveserved as e±cient magnetoresistive random accessmemory (MRAM)21–23 elements, where the `read'and `write' processes use the same current path, andthereby have the intrinsic electrical wear-out prob-lem, that is, the dielectric breakdown of the tunnelbarrier due to the large current in the `write' pro-cess.24 One of the methods to overcome this issue isto use high spin-orbit coupling (SOC) materials,such as heavy metals and topological insulators

†Corresponding author.

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(TIs), where the spin Hall e®ect (SHE) or the to-pological surface states can be employed to generatelarge spin torques by passing a lateral current in thethree-terminal MTJ structures.25,26 In this case, the`read' current path and the `write' current path canbe well separated and the spin torque is generatedwithout charge current traversing the tunnel barri-er. This separation signi¯cantly improves the MTJreliability while also giving better output signal.Since these materials all have strong SOC we call thegenerated torques spin–orbit torques (SOTs).27,28 Inthe following two paragraphs, we brie°y introducethe recent SOT research in the heavy metal and TI-based magnetic structures.

In heavy metals (e.g., Pt and Ta), due to thestrong relativistic SOC, the SHE29–33 is resultedwhich can generate a transverse spin current andconsequently, a steady-state spin polarization/ac-cumulation at the edges or surfaces of the heavymetals when passing a charge current through them.The SHE arises from both the intrinsic34,35 and ex-trinsic mechanisms.36–39 The SHE was ¯rst detectedby optical method in semiconductors with largeSOC (e.g., GaAs and InGaAs)40,41 and later, it wasdiscovered in heavy metals and has been studiedextensively, due to the fact that SHE in heavymetals is very e±cient to produce spin current thatcan apply very strong SOTs on an adjacent mag-netic layer and signi¯cantly in°uence its dynamics,for example, the SHE-induced tuning of magneticdamping42–45 and spin wave attenuation,46,47 exci-tation of spin wave oscillations,48 magnetic preces-sion,43 SHE-induced switching25,49–51 and magneticdomain wall motion,52–54 etc., have been reported inthe past several years. In particular, the SHE-in-duced magnetization switching25,49,50 represents thelandmark achievements in the SHE research ¯eld,which suggest potential applications in heavy metal-based MRAM devices.26 The spin Hall angle,25,29,50

de¯ned as the generated spin current density versusthe incident charge current density, is used toquantify the SHE strength in heavy metals and thenumber is usually smaller than 1. Therefore, mate-rials that can generate SOT more e±ciently thanheavy metals await explorations.

Then it comes to TIs.55–57 TIs are such materialsthat the SOC is large enough to invert the bandstructure in the bulk,58 and consequently they areexpected to be the most promising candidates toexploit the SOTs when coupled to magnetic mate-rials.59–61 Compared with the research on SHE in

heavy metals, TI-based spintronics is a relativelynew emerging research ¯eld. However, it has shownrapid progress62 and promising applications on SOTdevices.63–65 Distinct from heavy metals, TIs notonly have very strong SOC, but also possess theunique spin-momentum-locked Dirac fermions onthe surface,55–57 as demonstrated by the spin-resolved ARPES66,67 and circularly-polarized light-induced photocurrent experiments,68–70 which makethem very e±cient for generating spin current/ac-cumulation when passing a charge current throughthem.71 Starting with the electrical detection ofsurface spin-polarized current in TIs,72–77 SOT andspin current-related research has been carried out inTI-based magnetic structures. For example, SOT-induced magnetization switching in magnetic TImaterials,63,64 spin–torque ferromagnetic resonance(ST-FMR) measurements65,78 and spin pumping/spin injection experiments79–83 in TI/ferromagnetmetal structures, and spin-polarized tunnelingspectroscopy study in TI/oxide/ferromagnet struc-tures84 have been carried out recently. The TI-basedmagnetic spintronics research is currently a fastdeveloping ¯eld.

In this paper, we review the recent progresses inthis newly emerged ¯eld of TI-based spintronics.The paper is organized as follows. First, Sec. 2 o®ersan introduction to the giant SOT-induced magne-tization switching in magnetically doped TI struc-tures. The SOT e±ciency in TI is revealed to bealmost three orders of magnitude larger than thosereported in heavy metals. Section 3 discusses theST-FMR measurements in TI/ferromagnet metalstructures which show very large SOT e±ciencyat room temperature. Section 4 reviews the spinpumping and spin injection experiments in variousTI/magnet structures which suggest promising spin-to-charge conversion e®ect. Electrical detection ofsurface spin-polarized current in TIs is discussed inSec. 5, emphasizing the interplay between magneticelectrode and accumulated spins on the topologicalsurface. This is followed by summary and conclu-sions in Sec. 6, discussing the potential and oppor-tunities in the TI-based spintronics ¯eld.

2. SOT-Induced MagnetizationSwitching in Magnetic TI Materials

TIs are a new class of materials which have invertedband structure in the bulk due to the strong SOC58

and nontrivial metallic Dirac fermions on the surface

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which are protected by the bulk topology order.55–57

The surface Dirac fermions are described by theHamiltonian55,56,58,85,86: HDiracðkx; kyÞ ¼ }vDð�xky��ykxÞ, where } is the reduced Planck constant, vD isthe Dirac electron velocity, kx and ky are the Diracelectron momentum, �x and �y are the Pauli ma-trices denoting the electron spin. The eigenstates ofthis Hamiltonian naturally give rise to the spin-momentum locking feature, namely, the Dirac elec-tron's spin is locked perpendicular to its momentumin the kxky-plane and the spin texture is clockwiseabove the Dirac point while anticlockwise below theDirac point, as depicted in Fig. 1(a). In the TI ma-terial when a lateral electric ¯eld is applied, due tothe spin-momentum locking feature of the surfacestates and the shift of the Fermi surface in the k-space, a certain spin polarization is induced withthe surface charge current,71 and the polarization isgoverned by the charge current direction. For in-stance, when the surface charge current is °owingalong the –x direction (i:e., Ix < 0), as shown inFig. 1(b), the Dirac electrons' spin is polarized alongthe –y direction; the reversed current case is dis-played in Fig. 1(c). Because of the strong SOC andthe topology protection nature of the surface states,these spin-polarized surface currents are expected tobe able to apply very e±cient SOTs to adjacentmagnetic materials.59–61

In light of the above arguments, di®erent TI/magnet structures63–65,78 have been studied to probethe SOT e®ect. In particular, Ref. 63 reported theSOT-induced magnetization switching in the TI/Cr-doped TI bilayer heterostructure. Since magneti-cally doped TIs (e.g., Cr-doped TIs)87–94 show veryrobust ferromagnetism at low temperature, the TI/Cr-doped TI bilayer heterostructure87,95 providesthe ideal platform to study the SOT. In Ref. 63, the(Bi0:5Sb0:5Þ2Te3/(Cr0:08Bi0:54Sb0:38Þ2Te3 bilayer wasprepared, as illustrated in Fig. 2(a), with the topTI being three quintuple layers (QLs) and the bot-tom Cr-doped TI six QLs. In this bilayer hetero-structure, the Cr-doped TI magnetization can besuccessfully switched by scanning the longitudinalcurrent in the presence of a ¯xed in-plane magnetic¯eld, as plotted in Fig. 2(b), suggesting a giantSOT is generated by the current °owing throughthe bilayer. The switching is very e±cient, requir-ing a critical current density below 8:9 � 104 A/cm2. Furthermore, in Ref. 63, the strength of SOTwas calibrated by the second harmonic measure-ment.27,96 Most importantly, the spin–torque ratio#ST, de¯ned as the strength of SOT per unit chargecurrent density, ranges from 140 to 425, whichis almost three orders of magnitude larger thanthose reported in heavy metal/ferromagnet het-erostructures (HMFHs).25,27,29,43,49,50,96 Both theSOT-induced switching results and the harmonicmeasurement data are consistent with the bottomsurface spin-momentum locking in the bilayerheterostructure, indicating that the Cr-doped TIlayer bottom surface Dirac fermions have a verylarge contribution to the giant SOT.

Since the bulk of magnetic TI behaves as asemiconductor,87,89,97 the current-induced SOT inCr-doped TI materials can also be controlled by thegate electric ¯eld.64 In Ref. 64, a top-gated Hall barstructure made of Au(electrode)/Al2O3(20 nm)/Cr0:16(Bi0:50Sb0:42Þ2Te3(7 nm)/GaAs(substrate) wasprepared, as shown in Fig. 3(a). The top gate volt-age can e®ectively tune the carrier density at theAl2O3/Cr-doped TI interface, and consequently thenet SOT in the Cr-doped TI layer can be modulated.As evidenced by the second harmonic measure-ment,27,63,96 the SOT strength can be modulated bya factor of four by gate tuning within the accessiblevoltage range, which is almost two orders of mag-nitude larger than that reported in HMFHs.98 Fur-thermore, in Ref. 64, it is demonstrated that themagnetization can be switched by scanning gate

(a)

(b)

(c)

Fig. 1. Charge current-induced surface spin polarization in TI.(a) Schematic illustration of the spin-momentum locked helicalspin texture of the surface states in TI: clockwise spin textureabove the Dirac point while anticlockwise spin texture belowthe Dirac point. (Reprinted with permission from Ref. 73.Copyright 2014, American Chemical Society.) (b) Schematic ofsurface spin polarization for a charge current °owing along –xdirection (i.e., Ix < 0). (c) Schematic of surface spin polariza-tion for a charge current °owing along x direction (i.e., Ix > 0).

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voltage with constant current and in-plane magnetic¯eld applied in the Cr-doped TI ¯lm, as shown inFig. 3(b). The gate voltage enabled switching pointstowards device applications such as electric-¯eldcontrolled magnetic memories that are compatiblewith modern ¯eld-e®ect semiconductor technologies.The gate control of SOT was compared with the net

spin-polarized surface current conducting throughthe Cr-doped TI ¯lm, and the intrinsic spin–torqueratio #ST from the surface current is determined tobe 116, again demonstrating the interfacial Diracfermion origin of the giant SOT.

Both works63,64 suggest that the current-inducedSOT is very e±cient in magnetic TI materials. The

(a) (b)

Fig. 3. (a) 3D schematic of the Hall bar structure made from the Al2O3(20 nm)/Cr-doped TI(7 nm)/GaAs(substrate) stack with atop gate electrode (light gray). Standard four-point measurement setup is displayed. A gate voltage of Vg can be applied between thetop gate and the source contact. (b), Magnetization switching induced by scanning Vg in the presence of constant By and IDC for X:(IDC ¼ 20�A;By ¼ 0:1TÞ and Y: (IDC ¼ 20�A;By ¼ �0:1TÞ. Insets show the corresponding initial and ¯nal magnetization con-¯gurations. All the measurements are performed at 1.9K (color online). (Reprinted with permission from Ref. 64. Copyright 2016,Macmillian Publishers Ltd: Nature Nanotechnology.)

(a) (b)

Fig. 2. Magnetization switching through giant SOT in the TI/Cr-doped TI bilayer heterostructure. (a) 3D schematic of the TI/Cr-doped TI bilayer heterostructure, the external magnetic ¯eld Bext, the magnetizationM and the out-of-plane anisotropy ¯eldBK. (b)Current-induced magnetization switching in the TI/Cr-doped TI bilayer at 1.9K in the presence of a constant in-plane magnetic ¯eldwith By ¼ þ0:6T (blue squares) and By ¼ �0:6T (red circles), respectively (color online). (Reprinted with permission from Ref. 63.Copyright 2014, Macmillian Publishers Ltd: Nature Materials.)

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corresponding spin–torque ratios are almost threeorders of magnitude larger than those reported inHMFHs. The gate electric-¯eld control64 providesanother approach besides the lateral current to har-ness the giant SOT in magnetic TI materials, whichpromises potential applications in energy-e±cientgate-controlled SOT devices. Since the Curie tem-perature of the Cr-doped TIs is very low (usuallybelow 30K),89,93 to utilize the giant SOT for roomtemperature applications would require search forhigh Curie temperature magnetic TIs or other roomtemperature insulating (or high resistivity) magneticmaterials that can couple e±ciently withTIs. Indeed,high quality TI/magnetic insulator (e.g., yttriumiron garnet, or YIG) structures and high temperaturemagnetic proximity e®ect99,100 in these structureshave been reported recently, and the potential SOTe®ect looks promising.

3. ST-FMR Probing of the SOT inTI/Ferromagnet Metal Structures

Besides the magnetically doped TIs, current-induced SOT was also probed in the TI/ferromagnetstructures by the ST-FMR technique.65,78,101 InRef. 65, a Bi2Se3(8 nm)/permalloy(16 nm) bilayerstructure was patterned into a micron strip, asillustrated in Fig. 4(a), and a microwave-frequencycurrent IRF was applied into the strip. The current-induced surface spin-polarized Dirac electrons in the

Bi2Se3 layer will exert an oscillating SOT on thepermalloy magnetization to make it precess, yieldingresistance oscillations due to the anisotropic magne-toresistance (AMR) of the permalloy. The mixingbetween the applied alternating current and the os-cillating resistance gives rise to a direct voltage Vmix,which reaches amaximal value in the FMRregime. InRef. 65, Vmix was measured as a function of the ex-ternalmagnetic ¯eldBext at a ¯xed angle’ relative toIRF, as shown in Fig. 4(a), and the FMR resonanceline shape was clearly detected. The Vmix resonanceline shape can be decomposed into the symmetric andantisymmetric components, whose amplitudes re°ectthe strength of the antidamping-like SOT ¿ jj (in-plane) and the ¯eld-like SOT ¿? (perpendicular), asdenoted in Fig. 4(a), respectively. In Fig. 4(b), boththe symmetric and antisymmetric Vmix componentsare plotted as functions of the external ¯eld angle ’,which can be ¯tted to equations proportional to sin(’Þ cos2ð’Þ, agreeing with the AMR and SOT de-pendence on the ¯eld angle. In Ref. 65, Bi2Se3/per-malloy devices with di®erent dimensions weremeasured, and the antidamping-like spin–torqueratio �jj was determined to be between 2 and 3.5 atroom temperature, which is much larger than thosereported in HMFHs.25,27,29,43,49,50,96

To verify whether the measured SOT in TI/ferromagnet structures is arising from the topologi-cal surface states or due to other mechanisms,Wang et al. performed a temperature-dependent

(a) (b)

Fig. 4. (a) Schematic diagram of the permalloy/Bi2Se3 structure and the coordinate system. The yellow and red arrows denote spinmoment directions. Py, permalloy. (b) Measured dependence on the magnetic ¯eld angle ’ for the symmetric and antisymmetricresonance components for a sample (8 nm Bi2Se3/16 nm permalloy device of dimensions 80�m� 24�m). Experimental conditions in(b) are as follows: !=2� ¼ 9GHz, power absorbed ¼ 6.9 dBm (color online). (Reprinted with permission from Ref. 65. Copyright2014, Macmillian Publishers Ltd: Nature.)

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ST-FMR measurement in the Bi2Se3/Co40Fe40B20

bilayers.78 By analyzing both the symmetric (VsÞand antisymmetric (VaÞ components of the ST-FMRvoltage signal at di®erent temperatures, theantidamping-like spin–torque ratio �jj and the ¯eld-like spin–torque ratio �? were both obtained, asplotted in Fig. 5. Both �jj and �? show a dramaticincrease as temperature decreases, especially below50K. Since the antidamping-like SOT in HMFHsshows a weak temperature dependence102–105 andthe ¯eld-like SOT normally decreases102,103 as tem-perature is lowered in HMFHs, the observed signi¯-cant increase of �jj and �? in the Bi2Se3/Co40Fe40B20

bilayer when temperature decreases was attributedto contribution from the topological surface statesin Ref. 78. Moreover, Ref. 78 also argued thatthe measured out-of-plane SOT in the Bi2Se3/Co40Fe40B20 bilayer could be due to the warpinge®ect of the topological surface states.71,106,107

In addition, the Fermi level position-dependentST-FMR measurements were performed in Ref. 101in the (Bi1-xSbxÞ2Te3/Cu/permalloy trilayer struc-tures, with di®erent x values controlling the Fermilevel position in the (Bi1-xSbxÞ2Te3 ¯lm. The SOTe±ciency was found dramatically suppressed whenthe Fermi level is near the Dirac point, possiblyowing to the degeneracy of surface spins at thatspeci¯c point. This result suggests the Fermi levelposition is critical for optimizing the SOT e®ect.One drawback of the ferromagnet metal-based ST-FMR measurements is that due to the impedancemismatch between the TI layer and the ferromagnetmetal, it is hard to determine the current distribu-tion in the whole structure, and most of the current

is shunted through the metal layer. To overcomethis problem, it is advisable to apply the ST-FMR technique in the TI/magnetic insulatorstructures (e.g., TI/YIG). For this purpose, themagnetic resonance force microscope (MRFM)108 orthe microwave-frequency magneto-optical Kerre®ect (MOKE)109 measurements may be favored.

4. Spin Pumping and Spin Injectioninto TIs

TIs' spin-momentum locked surface states not onlycan generate giant SOT when passing a chargecurrent through them, but also can provide the idealplatform for spin-to-charge conversion when spincurrent is injected onto the TI surface. By the spinpumping technique in a TI/ferromagnet structure,spins can be e®ectively injected onto the TI surfaceand converted to a transverse charge current. InRef. 79, Shiomi et al. studied the spin pumping andthe spin-to-charge conversion e®ects in the Ni81Fe19(20 nm)/Bi1:5Sb0:5Te1:7Se1:3 (BSTS) samples byusing coplanar waveguide, and the induced trans-verse charge voltage on TI was detected by a nano-voltmeter, as schematically shown in Fig. 6(a). TheBSTS is a bulk-insulating TI material. By sweepingthe external magnetic ¯eld and applying microwave,the ferromagnet Ni81Fe19 will reach the FMR regimeand spins can be e®ectively pumped onto the TIsurface. Due to the spin-momentum locking, theinjected spins will move only along one direction onthe TI's surface, creating a voltage di®erence on thetwo ends of the TI ¯lm, as illustrated in Fig. 6(b).By careful analyses, the antisymmetric part of the

(a) (b)

Fig. 5. Temperature dependence of (a) antidamping-like spin–torque ratio and (b) ¯eld-like spin–torque ratio in Bi2Se3(20 nm)/CoFeB(5 nm) devices measured through the ST-FMR technique (color online). (Reprinted with permission from Ref 78. Copyright2015, American Physical Society.)

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measured voltage was successfully obtained, asplotted in Fig. 6(c), which is a demonstration of thespin-to-charge conversion e®ect. The conversion ef-¯ciency is determined to be 10�4 and the spinpumping e®ect can only be observed at low tem-perature (< 27K), which might be due to the bulkconduction in the very thick BSTS samples (0.1–0.5mm) as explained in Ref. 79.

Using similar technique, Deorani et al. studiedthe spin pumping and spin-to-charge conversione®ects in the Ni81Fe19/Bi2Se3 structure,

80 where theBi2Se3 is more conducting than BSTS, but the bulkconduction is minimized due to thinner Bi2Se3 ¯lmthicknesses (5−35nm). The spin-to-charge conversione±ciency (or the so-called spin Hall angle in Ref. 80)and spin di®usion length in Bi2Se3 were obtainedto be 0.0093� 0.0013 and 6.22� 0.15 nm, respec-tively, at room temperature, and their valueswere observed to increase as the temperaturedecreases. In Ref. 81, Jamali et al.measured the spinpumping and spin-to-charge conversion e®ects in

the CoFeB/Bi2Se3 bilayers. They found the spin-to-charge conversion e±ciency of Bi2Se3 can be as largeas 0.43 at room temperature, which is primarilydue to the bulk inverse SHE and is hard to distin-guish from the inverse Edelstein e®ect (IEE) of thetopological surface states. In Ref. 82, Baker et al.studied the FMR spin pumping e®ect in theCo50Fe50/Bi2Se3/Ni81Fe19 trilayer structure, andthey found the Gibert damping increases approxi-mately linearly with the Bi2Se3 layer thickness,suggesting that Bi2Se3 is a very e±cient spin sink.

Besides the spin pumping/spin injection experi-ments on conventional Bi2Se3 or BSTS materials,novel TI material was also used for this purpose. InRef. 83, Rojas-Sanchez et al. utilized a new type TI:�-Sn thin ¯lm in the �-Sn/Ag/Fe/Au structure forthe spin pumping and spin-to-charge conversionmeasurements. The structure and measurementsetup were shown in Fig. 7(a). By applying micro-wave and sweeping external magnetic ¯eld, the Felayer will reach the FMR state and pump spins,

(a) (b)

(c)

Fig. 6. (a) Schematic illustration of FMR-induced spin pumping and spin injection e®ects in the Ni81Fe19/TI structure. (b)Schematic illustration of spin injection and spin-electricity conversion e®ects on the topological surface states. (c) The antisymmetricpart of the measured V divided by the absorption power (�PÞ, denoted ~V

a, for Bi2Se3(BS)/Ni81Fe19 and BSTS/Ni81Fe19 samples at

15K. (Reprinted with permission from Ref. 79. Copyright 2014, American Physical Society.)

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through the Ag layer, onto the �-Sn thin ¯lm. Dueto the surface spin-momentum locking, the injectedspins will be converted to a transverse charge cur-rent through the IEE of the surface states, which canbe consequently measured by a voltmeter. Both theFMR and DC charge voltage signals are plotted inFig. 7(b). Importantly, the IEE length �IEE (de¯nedas the ratio between the 2D transverse charge cur-rent density induced by IEE in the surface of �-Snand the injected vertical 3D spin current density)was found to be 2.1 nm, which is one order of mag-nitude larger than those reported in various Rashbainterfaces.110,111

Spin pumping and spin-to-charge conversionexperiments in TI/ferromagnet metal structureshave an inherent drawback: the induced DC chargecurrent in the TI layer could be partly shunted by theferromagnet metal. To overcome this problem, theTI/magnetic insulator structures (e.g., TI/YIG)could be employed for the spin pumping measure-ments. In addition to the FMR spin pumping tech-nique, other methods were also explored for injectingspins into TI materials. For example, in Ref. 100,Jiang et al. used the thermal spin Seebeck e®ectof YIG to inject spins into (BixSb1�xÞ2Te3 thin¯lm in the (BixSb1�xÞ2Te3/YIG heterostructure,which can induce a pronounced transverse voltagesignal. In Ref. 84, a tunneling structure Bi2Se3 (or(Bi0:5Sb0:5Þ2Te3Þ/MgO/Co20Fe60B20 was utilized toprobe the spin-polarized electron tunneling spec-troscopy. By applying a vertical voltage bias, the

spin-polarized electrons in Co20Fe60B20 can tunnelthrough the MgO barrier and inject onto the TI sur-face, which can be consequently converted to atransverse charge current through the IEE of TIsurface. The measured spin-to-charge conversion ef-¯ciency (or spin Hall angle as in Ref. 84) is 0.8 forBi2Se3 and 20� 5 for (Bi0:5Sb0:5Þ2Te3 (bothmeasuredat 4K), much larger than those reported inHMFHs.25,27,29,43,49,50,96

5. Electrical Detection of the SurfaceSpin-Polarized Current in TIs

As mentioned at the beginning of Sec. 2, when ap-plying a current through TI, due to the spin-mo-mentum locking of the surface states, the surfacecurrent is spin-polarized and a steady-state spinaccumulation will be formed, as illustrated inFigs. 1(b) and 1(c). This surface spin-polarizedcurrent can be detected by electrical means. Spe-ci¯cally, by placing a ferromagnet electrode/oxidestructure on top of TI to form a ferromagnetictunneling contact, the TI surface current spin po-larization can be read out by the magnetoresistance(or voltage) between the ferromagnet electrodeand TI surface: when the TI surface spin-polarizedelectron magnetic moment is parallel with theelectrode magnetization, a low magnetoresistance(voltage) is measured; accordingly, when the TIsurface spin-polarized electron magnetic moment isantiparallel with the electrode magnetization, a high

(a) (b)

Fig. 7. Spin pumping and spin-to-charge conversion e®ects in a new type TI: �-Sn ¯lm. (a) Experimental setup for spin pumpingfrom the Fe layer into �-Sn by FMR. (b) FMR and DC charge current signals from measurements in a cylindrical X-band resonantcavity on InSb j�-SnjAgjFejAu sample. The lower panel shows a DC current signal in agreement with the observation of a Dirac coneat only the �-SnjAg interface. (Reprinted with permission from Ref. 83. Copyright 2016, American Physical Society.)

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magnetoresistance (voltage) is produced, similar tothe GMR e®ect observed in spin valve structures.4,5

In Ref. 72, Li et al. fabricated a Fe/Al2O3 fer-romagnet tunneling contact on top of Bi2Se3 thin¯lm, as depicted in Fig. 8(a), to detect the TI surfacespin-polarized current. By sweeping the in-planetransverse magnetic ¯eld to reverse the Fe magne-tization direction, the hysteretic switching betweenhigh and low magnetoresistance (voltage) states was

clearly measured for constant bias current of þ2mAand �2mA °owing through the Bi2Se3 ¯lm, asshown in Figs. 8(b) and 8(c), respectively, demon-strating the current-induced spin polarization on theBi2Se3 surface. Through detailed measurements andanalyses, they found the hysteretic behavior ofmagnetoresistance can persist up to 150K and thespin polarization ratio of Bi2Se3 surface current isabout 20%, close to theoretical expectation values.71

(a) (b)

(c)

Fig. 8. Electrical detection of the surface spin-polarized current in the Bi2Se3/Al2O3/Fe structure. (a) Schematic illustration of thetransport experiment. Voltage measured at the ferromagnetic detector is proportional to the projection of the current-induced TIsurface spin polarization onto the contact magnetization. (b) and (c), Field dependence of the voltage measured using contact Fe asthe detector with the magnetization collinear with the current-induced TI spin polarization for bias currents of þ2mA and �2mA,respectively, at 8K. (Reprinted with permission from Ref. 72. Copyright 2014, Macmillian Publishers Ltd: Nature Nanotechnology.)

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Similarly, in Ref. 73, Tang et al. made a Co/Al2O3 ferromagnetic tunneling contact on top of the(Bi0:53Sb0:47Þ2Te3 thin ¯lm, which is more insulat-ing, to detect the surface spin-polarized current, asillustrated in Fig. 9(a). The hysteretic switchingbehavior between high and low magnetoresistance(voltage) states was measured when the Co mag-netization was reversed by sweeping the in-planetransverse magnetic ¯eld, as plotted in Fig. 9(b), inthe presence of constant current of þ2�A °owingthrough the TI ¯lm. The spin polarization ratio ofthe TI surface current was yielded to be 1.02% at1.9K and the polarization direction was con¯rmed

to be consistent with the TI surface spin-momentumlocking texture (see Fig. 1(a)). Several otherreports74–77 also use similar structures to electricallydetect the TI surface spin-polarized current: inRef. 74, Ando et al. placed a permalloy electrode ontop of BSTS to measure the surface current spinpolarization, and the polarization ratio was found tobe 0.5% at 4.2K; in Ref. 77, Dankert et al. detectedthe spin polarization of TI surface current at roomtemperature by using a Co/TiO2 ferromagnetictunneling contact on top of Bi2Se3; in Refs. 75and 76, Tian et al. studied the surface current spinpolarizations in Bi2Se3 and Bi2Te2Se samples by

(a) (b)

(c) (d)

Fig. 9. (a) Electrical detection of the spin-polarized surface states conduction in (Bi0:53Sb0:47Þ2Te3. Schematic illustration of thedevice structure with one ferromagnetic tunneling contact Co/Al2O3 for spin detection. Measurement setup with a four-probecon¯guration and a lock-in technique is also illustrated. (b) Measured voltage (resistance) at T ¼ 1:9K as the in-plane magnetic ¯eldis swept back and forth under DC bias of IDC ¼ þ2�A. (Reprinted with permission from Ref. 73. Copyright 2014, AmericanChemical Society.) (c) Schematic of the spin-polarized tunnel junction device. The junction area varies from 2� 2 to 10� 5�m2; thewidth of TI channels is ¯xed at 8�m. (d) Field-dependent transverse di®erential resistance dV24=dI13 of Bi2Se3 in the tunnelingcon¯guration. The junction area is 10� 3�m2. (Reprinted with permission from Ref. 84. Copyright 2015, American PhysicalSociety.)

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using the Ni magnetic electrode spin valve structureand the permalloy/Al2O3 ferromagnetic tunnelingcontact, respectively, and found the surface currentspin polarizations in Bi2Se3 and Bi2Te2Se are dif-ferent. The one revealed in the Bi2Te2Se sample isconsistent with the TI surface spin-momentumlocking texture.

The ferromagnetic tunneling contact structurecan also be employed to study the spin-polarizedtunneling spectroscopy in the ferromagnet/oxide/TIstructure. As already brie°y discussed in Sec. 4, inRef. 84, Liu et al. designed the delicate `T '-shapetunnel junction structure made of TI/MgO/CoFeB,as illustrated in Fig. 9(c). When applying currentbetween terminal 2 and 4 and measuring voltagebetween terminal 1 and 3, it becomes electrical de-tection of the TI surface spin-polarized current;when applying current between terminal 1 and 3and measuring voltage between terminal 2 and 4, itbecomes spin-polarized tunneling study and spin-to-charge conversion measurement through the TIsurface states. Indeed, as shown in Fig. 9(d), thehysteretic switching in the di®erential resistancedV24=dI13 when sweeping the in-plane transversemagnetic ¯eld to reverse the CoFeB magnetization84

clearly demonstrates the spin tunneling from CoFeBto TI and the spin-to-charge conversion on the TIsurface. Besides the above electrical detectionmethods by putting the ferromagnetic electrode orferromagnetic tunneling contact directly on TI, re-cently, people also used graphene as a spin conduc-tor to connect the TI ¯lm and the detector: thesurface spin-polarized current in TI can di®use intographene and be measured non-locally by a ferro-magnetic electrode on graphene.112

6. Summary and Conclusions

We have reviewed the recent progress in the TI-based spintronics ¯eld. In summary, TIs can gener-ate giant SOT with e±ciency orders of magnitudelarger than those reported in HMFHs. The SOT inTIs can also be e®ectively controlled by the gatevoltage. This may suggest applications in gate-con-trolled nonvolatile spintronic memory and logicdevices with signi¯cantly enhanced energy e±cien-cy. TIs are also found very e®ective for spin-to-charge conversion, indicating TIs' potential to serveas spin detectors or e±cient spin-to-charge con-vertors. The spin–torque ratios and spin-to-chargeconversion e±ciencies of TIs reported by di®erent

groups are summarized in Fig. 10. TIs are alsodemonstrated able to generate robust surface spin-polarized current (or steady surface spin accumula-tion), and thus may serve as nice spin currentsources for studying various spin dynamics whencoupled with magnetic materials. These uniqueproperties of TIs are believed to be resulted from theintrinsic spin-momentum locking feature of the to-pological surface states, which stems in its bulk to-pological order (strong SOC), distinct from heavymetals. Since e±cient in generating SOT, TIs mayalso serve as good materials for energy-e±cient SOToscillator applications when coupled with magneticmoment. When combined with CMOS logic cir-cuitry, TI-based SOT devices may also o®er e±cientnonvolatile spin logic circuits.

To utilize these properties of TIs (such as giantSOT and high spin-to-charge conversion e±ciency)would require search for both the right materialsthat can couple e±ciently with TIs and the good TImaterials that can reach bulk-insulating states.Since magnetic TIs have very low Curie temperatureand ferromagnetic metals su®er from shuntingproblem, room temperature magnetic insulators(e.g., YIG) or high resistivity magnetic semi-conductors are expected to be the good candidatesto couple with TIs. Indeed, high quality TI/mag-netic insulator structures (e.g., TI/YIG) and hightemperature magnetic proximity e®ect in thesestructures99,100,113–115 have been reported recently.

Fig. 10. Summary of the spin–torque ratio and the spin-to-charge conversion e±ciency of various TI materials reported bydi®erent groups. � stands for the spin–torque ratio or the spin-to-charge conversion e±ciency of TI, depending on the speci¯cterminology used in the references. The abscissa denotes thecorresponding reference and the measurement temperature foreach �. RT stands for room temperature.

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Both theoretical and experimental works are re-quired to address the interface quality and spintransport/coupling mechanisms at the interfaces(e.g., spin mixing conductance or spin transparency)for their potential applications. We note that veryrecently room-temperature spin pumping e®ect hasbeen realized in the TI/YIG structure.116 In addi-tion, high quality bulk-insulating TIs can be realizedby optimizing the material growth technique.117,118

Since TIs are van der Waals materials, they are easyto grow by molecular beam epitaxy on a large rangeof di®erent substrates, including magnetic insulatorsor even antiferromagnetic materials. The latter mayo®er high frequency energy-e±cient applications.Therefore, the feasibility of combining TIs withvarious magnetic materials and their rich applica-tions will spur further research in this vigorous to-pological spintronics ¯eld based on TIs.

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