Determination of spin Hall angle in heavy metal/CoFeB-based heterostructures with interfacial spin-orbit fields
Witold Skowroński, Łukasz Karwacki, Sławomir Ziętek, Jarosław Kanak, Stanisław Łazarski, Krzysztof Grochot, Tomasz Stobiecki, Piotr Kuświk, Feliks Stobiecki, Józef Barnaś
aa r X i v : . [ phy s i c s . a pp - ph ] O c t Determination of spin Hall angle in heavy metal/CoFeB-based heterostructures withinterfacial spin-orbit fields
Witold Skowroński, ∗ Łukasz Karwacki, † Sławomir Ziętek, Jarosław Kanak, Stanisław Łazarski, Krzysztof Grochot,
1, 3
Tomasz Stobiecki,
1, 3
Piotr Kuświk,
2, 4
Feliks Stobiecki, and Józef Barnaś
2, 5 AGH University of Science and Technology, Department of Electronics, Al. Mickiewicza 30, 30-059 Kraków, Poland Institute of Molecular Physics, Polish Academy of Sciences,ul. Smoluchowskiego 17, 60-179 Poznań, Poland Faculty of Physics and Applied Computer Science,AGH University of Science and Technology, 30-059 Kraków, Poland Center for Advanced Technology, Adam Mickiewicz University, 89C Umultowska Str., 61-614 Poznań, Poland Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
Magnetization dynamics in W/CoFeB, CoFeB/Pt and W/CoFeB/Pt multilayers was investigatedusing spin-orbit-torque ferromagnetic resonance (SOT-FMR) technique. An analytical model basedon magnetization dynamics due to SOT was used to fit heavy metal (HM) thickness dependenceof symmetric and antisymmetric components of the SOT-FMR signal. The analysis resulted in adetermination of the properties of HM layers, such as spin Hall angle and spin diffusion length.The spin Hall angle of -0.36 and 0.09 has been found in the W/CoFeB and CoFeB/Pt bilayers,respectively, which add up in the case of W/CoFeB/Pt trilayer. More importantly, we have de-termined effective interfacial spin-orbit fields at both W/CoFeB and CoFeB/Pt interfaces, whichare shown to cancel Oersted field for particular thicknesses of the heavy metal layers, leading topure spin-current-induced dynamics and indicating the possibility for a more efficient magnetizationswitching.
I. INTRODUCTION
In heavy metal (HM) layers exhibiting significant spin-orbit coupling, the charge current ( j c ) may be convertedinto the spin current ( j s ) due to the spin Hall effect(SHE). The generated spin current, in turn, may ex-ert a torque on the magnetization in an adjacent fer-romagnet (FM) . This phenomenon can be used, forinstance, to control the magnetization state of next gen-eration MRAM cells or to drive the magnetization pre-cession in spin torque oscillators . It has been alreadyestablished, that in HM/FM bilayers the magnetizationdynamics is driven by two components (damping-like andfield-like) of the spin-orbit-torque (SOT) and by theOersted field produced by the charge current. This ef-fect is often used to quantitatively analyze the spin Hallangle θ = j s / j c . However, one can also expect the inter-face charge-spin conversion originating from the Rashba-type spin-orbit interactions to play a significant rolein such systems. A strong interface effect has alreadybeen found in Ta/CoFeB bilayers and recently inTa/CoFeB/Pt trilayers by analyzing the HM and FMthickness dependence of the SOT-FMR signal lineshape.The above mentioned Rashba phenomenon at the in-terface (known also as the Edelstein-Rashba effect) hasbeen modeled, among others, for a magnetized two-dimensional electron gas (2DEG) in both ballistic anddiffusive regimes . Theoretical results show that theSOT due to interfacial non-equilibrium (current-induced)spin polarization has symmetry similar to that inducedby the spin Hall effect in heavy metals, i.e., there can beboth damping-like and field-like components. However,in contrast to the spin Hall-induced torque and earliermechanisms of spin-transfer torque (STT), the interfacial spin-orbit coupling (ISOC) acts as an effective field onthe magnetization and, therefore, is not associated withtransfer of the transverse part of spin current. Moreover,the field-like component is mostly dominating, which canbe attributed to a weak short-range spin-independent dis-order .Another related interfacial effect that occurs at ferro-magnet/heavy metal interfaces is the so-called spin Hallmagnetoresistance effect (SMR) . In the bilayer un-der discussion, some of the electrons flowing from theHM into ferromagnet can have spin component parallelto the magnetization of the ferromagnetic layer – dueto external magnetic field, magnetic proximity effect, ormagnetic anisotropy in the ferromagnet. This compo-nent of spin current is reflected from the interface and via the inverse spin Hall effect (ISHE) in HM is con-verted to the charge current flowing parallel to the initialcurrent, which results in a reduced resistance. In con-trast, the perpendicular component of spin current, thatgives rise to spin torque exerted on the magnetization,is almost completely absorbed, and thus does not leadto charge current induced by ISHE. Although this effectoccurs mostly near to the interface, it is strongly depen-dent on the thickness of HM layer. It has been previ-ously assumed that the origin of FMR signal in the caseof HM/FM systems is the anisotropic magnetoresistance(AMR) of FM , which might be the case for somesystems. However, one should also take into account acontribution to the signal from SMR, as it has the sameangular symmetry as AMR .In this work, the SOT-FMR technique is used toinvestigate W/CoFeB and CoFeB/Pt bilayers, shownschematically in Fig. 1(a) and (b), as a function of thick-ness of HM ( t HM ). We have chosen W and Pt as a source of spin current, since they are characterizedby the spin Hall angles of opposite signs . The evo-lution of symmetric and antisymmetric parts of the res-onance signal with t HM is fitted using the developed an-alytical model. As a result, the magnitudes of the ef-fective magnetic fields associated with damping-like andfield-like components of SOT, as well as interface effects,such as SMR and ISOC, are determined. The model alsoenables evaluation of the spin Hall angle and spin diffu-sion length for each bilayer system. Finally, in the case ofW/CoFeB/Pt trilayer, shown schematically in Fig. 1(c),we have used the values obtained from the constituentbilayers in order to identify the contributions from bothheavy metals and their interfaces to the SOT induced inthe trilayer system.The paper is organized as follows: Section II includesdescription of the experiment. Theoretical model, inturn, is presented in Sec. III, where the formulas for mix-ing voltage and spin Hall angle are derived and discussed.Experimental results are presented in Sec. IV, togetherwith theoretical predictions based on the previous sec-tion. Finally, summary and concluding remarks are pre-sented in Sec. V. II. EXPERIMENT
Magnetron sputtering technique was used to de-posit the following multilayer structures on Si/SiO substrates: W( t W )/CoFeB(5)/Ta(1), CoFeB(5)/Pt( t Pt )and W(5)/CoFeB(5)/Pt( t Pt ) (thicknesses in nm). TheCoFeB layers were deposited from an alloy target withthe composition of 20 at % Co, 60 at % Fe, and 20 at % B.In case of W sputtering, a low DC power of 4 W and 6 cmtarget-sample distance was used, which resulted in depo-sition rate of 0.01 nm/s. Such conditions are essential forgrowth of thick W layers in highly resistive β -phase .The remaining materials were deposited with a 15 W DCpower. For multilayers with a top material susceptibleto oxidation, 1-nm thick Ta layer was deposited, whichoxidized completely and formed a non-conducting pro-tection layer. The thickness of wedges ranged from 0 to10 nm in case of t Pt and t W .The bi- and trilayers were subsequently patterned into100- µ m long ( l ) and 20- µ m wide ( w ) strips using electron-beam lithography and lift-off process with Al(10)/Au(50)contact pads. The resistivity of HM and FM was de-termined using the method described in Ref. [41] andthe resistivity of FM, whose thickness was constant, wason average ρ FM ≈ µ Ω cm. The angular dependenceof the resistance, enabling AMR and SMR determina-tion, was measured at fixed magnetic field H = 500 Oe(which is sufficient to saturate the magnetization) ap-plied at varying angle ϕ with respect to the microstripaxis, using a custom-build rotating probe station. Duringthe SOT-FMR measurements, an amplitude modulatedradio-frequency (RF) current of the corresponding powerof P = 16 dBm and the frequency changing between 4 (c) FIG. 1. Schematic representation of the structures exam-ined in the paper: (a) W/CoFeB, (b) CoFeB/Pt, and (c)W/CoFeB/Pt. Spin currents, j s , and charge currents, j c , areindicated for all studied configurations. Angle ϕ is the anglebetween magnetization m and direction of charge current, j c .Moreover, direction of spin accumulation at the interfaces isindicated. and 10 GHz was injected into the microstripe. The mix-ing voltage ( V mix ) was measured using lock-in amplifiersynchronized to the RF signal. An in-plane magneticfield ( H ) applied at ϕ = 30 ◦ with respect to the mi-crostrip axis was swept from 0 up to 1250 Oe. III. ORIGIN OF THE SIGNAL
Mixing voltage generated in SOT-FMR experimentcan be written down as time-averaged product of RFcurrent with amplitude I RF , I ( t ) = Re { I RF e iωt } , andtime-dependent resistance, R ( t ) , of the system, V mix ≡ h V mix ( t ) i t = h I ( t ) R ( t ) i t . (1)We assume that resistance changes due to a combinationof the AMR and SMR effects , R ( t ) = R + ∆ R cos ϕ ( t ) , (2)where ϕ ( t ) is the time-dependent tilt-angle of the mag-netization from its equilibrium orientation, ∆ R ≡ ∆ R (∆ R AMR , ∆ R SMR ) , and R is the time-independentcomponent of the resistance, which contains terms fromboth AMR and SMR. Here ∆ R AMR is the increment ofanisotropic magnetoresistance of CoFeB assumed to beweakly dependent on the heavy metal thickness. In turn,the SMR contribution , ∆ R SMR ≈ R HM θ HM λ HM t HM tanh t HM λ HM g R HM g R HM tanh t HM λ HM , (3)is strongly dependent on the thickness t HM of HM layer.Furthermore, θ HM in Eq. (3) is the spin Hall angle ofthe HM, λ HM is the spin diffusion length in this mate-rial, and g R HM = 2 e / ¯ hλ HM ρ HM G R HM coth ( t HM /λ HM ) isthe dimensionless real part of the spin-mixing conduc-tance. In Eq. (3) we omitted the imaginary part of thespin-mixing conductance, as vanishingly small. The realpart of spin-mixing conductance can be deduced fromexperiment according to the formula G R HM = 4 πM s t FM γ ¯ h | ∆ α | , (4)where ∆ α is the difference between Gilbert damping co-efficients α of pure CoFeB and CoFeB with W or Pt lay-ers attached, M s denotes saturation magnetization of theHM/FM bilayer, and γ is the gyromagnetic ratio. Therelevant parameters have been collected in Table I. As G R HM is derived experimentally, we treat it as an effectivespin-mixing conductance, which also takes into accountpossible effects due to spin memory losses .The mixing voltage can be written down as follows: V mix = − M s I RF ∆ R sin (2 ϕ ) Re { m y } , (5)where ϕ is the equilibrium angle of magnetization (de-termined by applied magnetic field H ) with respect to thedirection of current, and Re { m y } is the y component ofmagnetization vector found by solving Landau-Lifshitz-Gilbert (LLG) equation in the macrospin approximation, ∂ m ∂t − α m × ∂ m ∂t = Γ . (6)Here, m is a unit vector along the magnetization, and Γ = − γµ m × H eff − γµ m × H ind (7)determines the torques exerted on the magnetization dueto effective magnetic field H eff consisting of the demag-netization field, anisotropy field, and external magneticfield, and due to the current-induced field H ind .The current-induced field H ind consists of in-plane, H k , and out-of-plane, H ⊥ , terms. In systems consist-ing of FM and HM layers, the only contribution to H ⊥ comes from damping-like field, H DL , due to spin currentsinduced by the spin Hall effect in heavy metal layers.The in-plane field, on the other hand, contains compo-nents due to Oersted field, H Oe , and interfacial spin-orbitfield, H so .The damping-like contributions to the effective fieldfrom W and Pt have the same sign due to opposite signsof the corresponding spin Hall angles, H HMDL = ± H HMDL m × (ˆ x × ˆ j HM c ) , (8)where +( − ) corresponds to the spin current flowing fromW (Pt) layer. The amplitude of damping-like field canbe written in the following form: H HMDL = − ¯ hj HM c eµ M HM s t FM ξ HMDL , (9)where ξ HMDL ≈ θ HM (cid:18) − sech t HM λ HM (cid:19) g R HM g R HM (10) is the so-called damping-like spin Hall efficiency.We also introduce the Oersted field, H HMOe = ± j HM c t HM ˆ x × ˆ j HM c , (11)and the spin-orbit field, H HMso = Γ
HMso ˆ x × ˆ j HM c , (12)with Γ HMso being the amplitude of the effective spin-orbitfield. In the following considerations we include the effec-tive field corresponding to the field-like torque inducedby the spin Hall effect into the spin-orbit field. Thus,the Γ HMso amplitude contains both the interfacial Rashba-Edelstein and spin Hall field-like contributions.By linearizing the LLG equation (6) and inserting theobtained expression for m y into Eq. (5), one obtains thefollowing formula for the mixing voltage, V mix = V S ∆ H ( H − H ) + ∆ H + V A ( H − H )∆ H ( H − H ) + ∆ H , (13)where V S is the amplitude of the symmetric part of thesignal, V S = − I RF ∆ R sin (2 ϕ )2 πf (2 H + M eff ) γµ H ⊥ ∆ H (14)and V A is the amplitude of the antisymmetric componentof mixing voltage, V A = − I RF ∆ R sin (2 ϕ )2 πf (2 H + M eff ) γµ r M eff H H k ∆ H . (15)To obtain the effective spin Hall angle of the structureone could use the ratio of symmetric and antisymmetriccontributions to the mixing voltage, which yields eµ M s t FM ¯ h V S V A r M eff H = 2 eµ M s t FM ¯ h H ⊥ H k . (16)This formula, however, does not give the proper effectivespin Hall angle (defined as θ eff = j s /j c ), as it takes intoaccount all the out-of-plane contributions. This formulacan be rewritten as eµ M s t FM ¯ h H DL H Oe + H so , (17)or equivalently eµ M s t FM ¯ h H DL H Oe
11 + H SO H Oe . (18)Only assuming that H so ≪ H Oe , which is fulfilled forthick HM layers, one obtains the proper effective spinHall angle, consistent with previous works (e.g. Ref. [3]), eµ M s t FM ¯ h t HM H DL H Oe = j s j c ≡ θ eff . (19) (c) (d)(b) V S [ V ] t W [nm] Experiment Fit(a) W/CoFeB V A [ V ] t W [nm] Experiment Fit -- Total Theory -- Oersted Fit -- Spin-orbit H so H Oe H DL E ff e c t i v e f i e l d s [ O e ] t W [nm] e ff t W [nm] W -0.368.54.32.3 (e) V m i x [ V ] H [Oe]t W [nm]:1.5 FIG. 2. DC mixing voltage, V mix , measured in W/CoFeB microstripe as a function of magnetic field, H , is shown in (a). The V mix curves for different t W are artificially offset for clarity. Respective amplitudes of the symmetric and antisymmetric partsvs. t W , together with the fitted curves, are presented in (b) and (c). Solid lines show fitting result to the theoretical model.Calculated components of the effective field as a function of t W are shown in (d). Experimental and theoretical values of theeffective spin Hall angle, θ eff , are presented in (e). The dashed lines (red, green, and orange) represent interpolation of themodel.TABLE I. Parameters for W( t W )/CoFeB(5) andCoFeB(5)/Pt( t Pt ) (layer thicknesses in nm). The last 3rows include parameters obtained from fitting the developedmodel to the experimental data.W/CoFeB CoFeB/Pt Units ρ HM
116 112 µ Ω cm α × α CoFeB(5) × | ∆ α | × µ M s t FM G R × − ( e / ¯ h ) Ω − cm − j c × − / m θ -0.36 0.09 λ Γ so -0.27 0.54 Oe IV. RESULTS AND DISCUSSION
The resistivity of each material was determined fromthe measured sheet conductance G = l/ ( wR ) of each mi- crostripe as a function of t HM , according to the proceduredescribed in Ref. [41]. The resistivity of W was constantfor the thicknesses above 2 nm: ρ W = 116 µ Ω cm, whichindicates the existence of the highly-resistive β -phase. InCoFeB/Pt bilayer the resistivity ρ Pt = 112 µ Ω cm wasdetermined. However, we found that the resisistivity ofmagnetron sputtering deposited Pt depends on whetherPt is deposited on crystalline underlayer (Co) or amor-phous CoFeB alloy. In the first case, depending on thethickness of the bottom layer, the resistance was fromabout 20 to 100 µ Ω cm , while in the second casefrom 100 to 200 µ Ω cm . Now, we focus on the mag-netization dynamics investigated by the SOT-FMR tech-nique. Mixing voltage, V mix , as a function of magneticfield, H , measured in W/CoFeB microstripes for selectedthicknesses, t W , is presented in Fig. 2(a). For each t W ,the signal is decomposed into symmetric ( V S ) and anti-symmetric ( V A ) Lorentz functions . The dependence ofthe amplitudes V S and V A on t W is shown in Fig. 2(b)and (c), together with the corresponding fitting basedon the theoretical model presented in the previous sec-tion. Such an approach enables quantitative separation (c) (d)(b) V S [ V ] t Pt [nm] Experiment Fit(a) CoFeB/Pt V A [ V ] t Pt [nm] Experiment Fit -- Total Theory -- Oersted Fit -- Spin-orbit H DL H Oe H so E ff e c t i v e f i e l d s [ O e ] t Pt [nm] e ff t Pt [nm] Pt V m i x [ V ] H [Oe]t Pt [nm]:2.2 FIG. 3. DC mixing voltage, V mix , measured in CoFeB/Pt microstripe as a function of magnetic field, H , is shown in (a).The V mix curves for different t Pt are artificially offset for clarity. Note that symmetry of the signal changes for t Pt = 3 nm.Respective amplitudes of the symmetric and antisymmetric parts vs. t Pt , together with the fitted curves, are presented in (b)and (c). Calculated components of the effective field as a function of t Pt are shown in (d). Experimental and theoretical valuesof the effective spin Hall angle, θ eff , are presented in (e). of the contributions from the Oersted field and interfacialspin-orbit torque to the antisymmetric part of the signal.In addition, it was found that in the case of W/CoFeBbilayer with 5-nm thick FM, the measured magnetoresis-tance is weakly dependent on the thickness of W, indi-cating AMR-like effect and negligible SMR (in contrastto thin FM case, where SMR is dominating ). As aconsequence, the resulting SOT-FMR signal is not de-scribed well with the magnetoresistance change modelledwith Eq. (3). Thus, the experimental results were takeninstead and the model was interpolated for small thick-nesses of W layer. Based on Eqs. (9), (11), and (12),the evolution of the effective fields as a function of t W has been determined and is presented in Fig. 2(d). Inthe case of W, the interface spin-orbit field is relativelyweak: Γ Wso = -0.27 Oe. The experimentally determinedvalues of θ eff , based on Eq. (19), approach the fittedvalue of θ W = -0.36 for thick W layers. Similar exper-imental procedure as well as quantitative analysis wererepeated for the CoFeB(5)/Pt( t Pt ) stripes. The corre-sponding results are presented in Fig. 3. Unlike the Wcase, the DC mixing voltage of Pt stripes unequivocallychanges sign with increasing t Pt , as shown in Fig. 3(a). Thickness dependence of the corresponding symmetricand antisymmetric components are shown in Fig. 3(b)and (c), respectively. Behavior of the symmetric compo-nent is well explained by a combination of the spin Hallinduced damping-like field and SMR effect, in contrastto the above described W/CoFeB bilayer. Fitting of themodel to the experimental data allowed to obtain thespin Hall angle θ Pt = 0 . , opposite in sign to the spinHall angle obtained for W/CoFeB, and the spin diffusionlength λ Pt = 2 . nm. Both values agree with the datapresented in the relevant literature .The sign change of the antisymmetric part of the sig-nal occurs due to a stronger, compared to W/CoFeB bi-layer, interfacial spin-orbit field, Γ Ptso = 0.54 Oe, whichdominates V A for t Pt < nm. Similar field-like torquecontribution in Pt/Co/MgO multilayers was measuredfor the same Pt thickness using harmonic Hall voltagemeasurements .Finally, the spin-orbit-torque-induced dynamics inW/CoFeB/Pt trilayers was investigated and the corre-sponding results are shown in Fig. 4. Similar to theCoFeB/Pt bilayer, symmetry of the SOT-FMR signalchanges for t Pt = 3 nm, as shown in Fig. 4(c). However, (c) (d)(b) V S [ V ] t Pt [nm] Experiment Theory(a) W/CoFeB/Pt V A [ V ] t Pt [nm] Experiment Total Oersted Spin-orbit H DL H Oe H so E ff e c t i v e f i e l d s [ O e ] t Pt [nm] W | e ff / | W | t Pt [nm] Pt V m i x [ V ] H [Oe]t Pt [nm]:1.7 FIG. 4. DC mixing voltage, V mix , measured in W/CoFeB/Pt microstripe as a function of magnetic field, H , is shown in (a).The V mix curves for different t Pt are artificially offset for clarity. Experimentally determined amplitudes: V S and V A are shownin (b) and (c). Solid lines represent theoretical values based on the fitting parameters obtained for bilayer systems. Componentsof the effective field are presented in (d). The effective spin Hall angle of the trilayer, θ eff , relative to | θ W | , is depicted in (e).Note, that the sign of the effective spin Hall angle of the trilayer is positive. in the case of a trilayer, the spin currents from both HMlayers are absorbed in FM, which results in an increasein V S . Note, that for t Pt = 2.5 nm, the Oersted field andinterfacial spin-orbit contributions from both W and Ptare minimized and therefore a pure spin current induceddynamics is observed. Solid lines in Fig. 4(b) and (c)are drawn based on the fitting parameters obtained forW/CoFeB and CoFeB/Pt bilayers showing good agree-ment between the experimental values and theoreticalpredictions.The effective spin Hall angle of the trilayer system,shown in Fig. 4(e), is 1.5 times larger than that forW/CoFeB bilayer alone for t Pt ≈ nm, while for thickerplatinum it decreases to a value closer to the one obtainedfor the CoFeB/Pt bilayer. This drop can be explained bylarger spin-mixing conductance at the CoFeB/Pt inter-face and thus larger spin current flowing through thisinterface. V. SUMMARY
In summary, the spin-orbit-torque-induced dynamicsin W/CoFeB and CoFeB/Pt bilayers and W/CoFeB/Pttrilayer was investigated experimentally by the spin-orbit-torque ferromagnetic resonance technique. Bothsymmetric and antisymmetric parts were resolved in theSOT-FMR signals from the microstripes investigated.Variation of the magnitudes of the corresponding signalswith increasing heavy metal thickness was fitted to thedeveloped theoretical model. From the application pointof view, it is important to note that when combiningferromagnets with materials, which exhibit strong spin-orbit coupling, such as W and Pt, interfaces betweenthose materials play very important role in determina-tion of the torques exerted on magnetization and otherproperties of the constituent materials. We have deter-mined the magnitude of interfacial spin-orbit fields fromW/CoFeB and CoFeB/Pt interfaces and shown how theyinfluence the spin Hall angle and spin diffusion length inthese bilayers as well as in W/CoFeB/Pt trilayer. Inparticular, we have shown that for specific thicknessesof the Pt and W layers, the Oersted field is cancelledby the interfacial spin-orbit field, which leads to a purespin-current induced dynamics.
ACKNOWLEDGMENTS
The authors would like to thank J. Chęciński for helpin calculations and M. Schmidt and J. Aleksiejew for technical support. This work was supported by theNational Science Centre, Poland, grant No. UMO-2015/17/D/ST3/00500. Ł. K., S. Ł., K. G., andT. S. acknowledge support from National Science Cen-tre research project 2016/23/B/ST3/01430 (SPINOR-BITRONICS). Microfabrication was performed at Aca-demic Center for Materials and Nanotechnology of AGHUniversity. ∗ [email protected]; These authors contributed equally tothis work † [email protected]; These authors contributedequally to this work J. E. Hirsch, Phys. Rev. Lett. , 1834–1837 (1999). J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth,and A. H. MacDonald, Phys. Rev. Lett. , 126603 (2004). L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, andR. A. Buhrman, Science , 555 (2012). I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V.Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl,and P. 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