Observation of anomalous spin-torque generated by a ferromagnet

Transcription

1 Observation of anoalous spin-torque generated b a ferroagnet A. Bose* 1, D. D. La, S. Bhuktare 1, S. Dutta 1, H. Singh 1, S. Miwa, A. A. Tulapurkar 1 1 Departent of Electrical Engineering, Indian Institute of Technolog Boba, Powai, Mubai , India Graduate School of Engineering Science, Osaka Universit, Toonaka, Osaka , Japan *arnabbose@ee.iitb.ac.in Over the ears central research of spintronics has focused on generating spin-current to anipulate nano-agnets b spin torque. So far electricall 1 9 and therall driven spin-torques 10 1 have been experientall deonstrated. These torques can be attributed to either Slonczewski s spin-transfer torque (STT) 13 or field-like torque (FLT) 3,8,14. STT arises when ferroagnet absorbs spin current generated b an was like spin-hall effect (SHE) 15,16, spin-puping 17, spin-nernst effect 18, spin-(dependent) Seebeck effect 19 1 etc. Field-like torque is generall observed in asetric agnetic tunnel junctions (MTJ) with current perpendicular to the plane (CPP) geoetr 3,14, and ferroagnet/heav etal bilaer where Rashba 8 or Dressulhous 7 spin orbit interaction is present. Control of agnetization dnaics is not onl interesting fro phsics perspective but also useful in technological applications 3,4. We have experientall observed a new for of spin torque which is copletel different fro conventional STT and FLT. This unconventional spin torque is exerted b a fixed agnet on a free agnet in spin valve structure with current in-plane (CIP) geoetr. The observed spin torque originates fro an out of plane effective agnetic field with setr of (M J), where M denotes the agnetization direction of fixed FM and J denotes current densit. This torque could be potentiall useful for switching out-of-plane agnets in high densit MRAM. Spin-orbit torque 4,7,8,5 has evolved in a proising wa to anipulate spins since last few ears. Heav etals like Pt 6, anti-ferroagnets 7,8, two diensional aterials 9,30 and seiconductor sstes 7 have been recentl studied as candidates for generating spin torques. However ferroagnetic etal (FM) itself has its own spin-orbit coupling which is responsible for various effects like: anisotropic agneto resistance (AMR), planar Hall effect (PHE) and anoalous Hall effect (AHE). AHE is analogous to SHE in heav etal which can induce spin current in neighbouring etal and cause spin orbit torque (Fig. 1b). Previous studies show that spin Hall angle of FM 31,3 is quite coparable to Pt. Hence FM can be considered as good candidate for SOT To stud spin orbit torque b FM we need FM(free)/Cu/FM(fixed) heterostructure where fixed laer will be source of spin current which will exert torque on another FM separated b Cu spacer. Based on this principle we carried out spin-torque ferroagnetic resonance (ST- FMR) 3,7,6 easureent of current in-plane giant-agnetoresistive (GMR) stack consisting of Ta(5 n)/ru(5 n)/irmn(7 n)/cofe( n)/cu(5 n)/cofe( n)/cu(5 n). However we surprisingl observe the existence of a new kind of torque which is copletel different fro standard spin-orbit torque b FM (owing to its AHE) which we initiall expected. This unconventional spin-torque depends on the utual orientation of fixed laer agnetization direction (M) and direction of in-plane current flow (J) and anifests itself as an effective agnetic field perpendicular to M and J (H (M J)). This is also arkedl different fro the spin torques observed in current perpendicular to plane (CPP) devices, where the spin torque depends onl on the angle between the directions of free and fixed laer agnetizations (Fig. 1a). We fabricated GMR stack as shown in Fig. 1c. Magnetization of botto ferroagnetic CoFe was pinned b annealing the saple at 300 C for two hours in external in-plane agnetic field of 0.6 T. Top CoFe ( n) is free laer which is separated fro botto fixed agnetic laer b 5 n thick Cu spacer. Top CoFe (free laer) is protected b 5 n of Cu cap. The stack was pattered to rectangular shape (375 µ 5 µ) b optical lithograph and argon ion illing. Radio frequenc (RF) current is passed in plane of the GMR stack and voltage is easured through an inductor of a bias-tee (Fig. 1e). Frequenc is swept in presence of constant external field. For FM/HM structure generall agnetic field is swept to easure ST- FMR 7,6,8 but frequenc sweep 3,5,6,14 is favourable in case of GMR and MTJ structure since fixed laer can also ove at higher field which can lead to erroneous result. Resistance of the saple depends on the utual

2 orientation of agnetization between free and fixed laer (Fig. 1d) which originates fro current in-plane GMR effect 1. Clear GMR hsteresis is observed (Fig. 1d) which doinates over other effects like AMR etc. On application of RF current if spin torque (STT, FLT, new kind of torque, Oersted field-torque) is applied on free laer it undergoes precession which results in oscillation of resistance due to the GMR effect. Hoodne ixture of RF current and oscillator resistance can result in large DC voltage at resonance of free laer 3. Since we have doinant GMR (Fig. 1d) effect we expect axiu signal when angle between free and fixed laer is 90 degree and signal should vanish when free and pinned laers are parallel or antiparallel. Figure 1 (a) Conventional GMR/MTJ stack where current flows perpendicular to plane resulting Slonczewski-like spin-transfer torque (STT) and field-like torque (FLT). (b) Tpical bi-laer structure consisting of heav etal (HM) and ferroagnet (FM). Spin-torque is produced on FM due to bulk charge to spin conversion b SHE (STT) or interfacial Rashba spin-orbit coupling (Rashba-like FLT). (c) Scheatic of a GMR stack where in plane current can produce out-of-plane effective field (H ) driven torque on free laer where H field is deterined b the utual orientation of applied current and agnetization of fixed laer H (M J). (d) Magnetoresistance of GMR stack when agnetic field is applied parallel to pinned laer. (e) Scheatic diagra of ST-FMR experiental set up. (f) ST-FMR signal of CIP-GMR stack while angle between free and fixed laer is 90 degree and applied power 18 db. Inset of (f) shows the Kittel s fit of resonance frequenc as a function of agnetic field applied along X-axis. Figure 1.e-f show the experiental set up and results of dc voltage produced b ST-FMR of current in-plane (CIP) GMR respectivel. Clear dc voltage consisting of setric Lorentzian V S C 1 4 f f0 and anti-setric Lorentzian 4 f f0 VA C 4 f f 0 is observed for different values of external agnetic field (Fig. 1f). Resonance frequenc, f 0 as a function of applied agnetic field was obtained b fitting the data to a cobination of setric Lorentzian and anti-setric Lorentzian. Resonance frequenc can be fitted well to Kittel s forula: f0 HP HExt HP HExt H (inset of Fig. 1f) where H P is in-plane anisotrop field (~50 Oe), H is out of plane anisotrop field ( Oe), H ext is external applied field and is groagnetic ratio ( A/-sec). Anti-setric coponent of dc voltage arises fro Oersted field as ore current flows below the free laer. The setric Lorentzian

3 coponent can arise fro in-plane polarized spin-current absorbed b free laer (Fig. 1a,b) or in-plane current driven out-of-plane agnetic field (Fig. 1c). Studing angular dependence of ST-FMR we can ascribe that observed setric coponent in our experient originates fro in-plane current driven out-ofplane agnetic field (H (M J). We use the co-ordinate sste as shown in Fig. 1e. The saple is in X- Y plane and RF current flows along X axis (Fig. 1e). The equilibriu agnetization direction of free laer () and pinned laer (M) are in X-Y plane and ake angles of θ and θ M with respect to X axis (direction of RF current flow). Figure ST-FMR experient of current in-plane (CIP) GMR saple for different configurations. RF current is passed along X-axis. Angle of free and fixed laer with respect to X axis is θ and θ M respectivel. (a) is for θ M = 90, θ = 0. (b) is for θ M = 90, θ = 180. (c) is for θ M = +90, θ = 0. (d) is for θ M = +90, θ = 180. (e, f) Experiental data of standard ST-FMR experient on Pt/Ni bi-laer. Magnetization of free laer is set to 45 0 (figure e) and (figure f) with respect to applied RF current flow direction. In all these cases, black curve shows easured dc voltage, which is well fitted b (red curve) cobination of setric Lorentzian (blue curve) and anti-setric Lorentzian (green curve). To understand the behaviour of spin-torque generated b fixed agnet, we studied detailed angular dependence as shown in figure and 4. Figure a and b show ST-FMR spectru for external field H=450 Oe along X axis and along X axis respectivel while direction of fixed laer is along Y axis (θ M = 90 ). Background voltage has been subtracted fro the experiental dc voltage data as shown b the black curve in all figures. (DC voltage with both free and pinned laer agnetizations along X-axis is taken as background (See suppleentar inforation)). Fitted red curve is su of setric Lorentzian (blue curve) and anti-setric Lorentzian (green curve). We can see fro Fig a and b that, in both these cases antisetric coponent (V A ) reains the sae which is consistent with ST-FMR easureent with GMR effect detection, but surprisingl setric coponent (V S ) inverts its sign. This cannot be explained if we assue that pinned laer generates spin-current due to its spin-hall effect, which is then absorbed b the free laer. This point can be appreciated b coparing results of standard ST-FMR experient 6 on Ni/Pt saple shown in figure.e and.f. The agnetic field in this case was applied at 45 o (fig.e) and 135 o (fig.f) respectivel. In ST-FMR experient if detection ethod is based on AMR then both V A (which arises fro the Oersted agnetic field of current) and V S (which arises fro spin-current generated via spin-hall effect) should invert the sign siultaneousl on reversal of external field (Fig.e-f) 6 whereas if detection ethod is GMR then there should not be an sign change of V A and V S (see suppleentar inforation). In the

4 experient of in-plane GMR saple we observe V A does not change its sign which is quite expected but V S changes the sign on reversal of external agnetic field. Next we easured ST-FMR signal of the GMR stack for applied field along X axis with pinned laer agnetization along +Y axis (Fig. c and d). When external agnetic field direction is fixed but pinned laer agnetization is inverted we observe that sign of V A is changed which is quite expected (see suppleentar inforation) but V S reains sae (copare Fig. a with Fig. c and Fig. b with Fig. d). This also cannot be explained b conventional STT and FLT ters. In fact, the data shown in Fig. c (or Fig. d) can be obtained fro Fig. a (or Fig. b) b rotating the coordinate sste 180 degree (i.e.: V dc (panel c) = V dc (panel b) and V dc (panel d) = V dc (panel a)). This anoalous result observed in GMR saple can be explained if we assue an out-of-plane effective agnetic field of the for H (M J) is created which exerts torque on the free laer (see suppleentar inforation). An obvious conclusion fro above relation is that if the current flows along the pinned laer agnetization, there should not be an out-of-plane field and hence setric coponent in the dc voltage should vanish. We verified this experientall, and results are shown in Fig. 3a. It can be seen fro figure 3.a that the setric coponent is ver sall in coparison to the anti-setric coponent. We can also have another interesting configuration where the dc voltage contains onl the setric Lorentzian ter but no dispersion. Such a configuration is shown in Fig. 3b, where the pinned laer akes 45 o angle with X-axis and free laer agnetization is along Y-axis. In this case the Oersted agnetic field is parallel to the equilibriu agnetization direction of free laer. Hence it does not excite FMR, whereas the anoalous agnetic field (H ) along Z-axis is non-zero and excites FMR. Fro figure 3b we can see that the anti-setric coponent (V A ) is ver sall in coparison to the setric coponent (V S ). A third special case is where both V A and V S should vanish in principle when fixed laer agnetization is parallel to current flow (X-axis) and free laer agnetization points perpendicular to this (Y-axis). In this case though the GMR detection is active, as both the Oersted field and anoalous field fail to excite FMR, no dc voltage is expected. Such case is shown in figure 3.c where dc voltage signal is fairl sall copared to figure. A sall non zero signal is observed due to slight tilting of fixed laer when external field is perpendicular to it (see suppleentar inforation). These results strongl support the existence of an anoalous in-plane current driven out-of-plane agnetic field in GMR saple. In a control experient where fixed laer and free laer are parallel (θ M = 45, θ = 45 degree) we do not observe an ST-FMR signal (Fig. 3d). This shows that our detection ethod is based on resistance variation of the saple b in-plane GMR effect. We have perfored additional experients to further substantiate the existence of anoalous spin-torque. Figure 4 shows the angular dependence of ST-FMR data where agnetization of pinned laer is along Y direction and external agnetic field of 450 Oe is applied along various values angles (θ H ) with respect to X-axis. As the agnetic field value is uch larger than the coercive field (~50 Oe), the free laer agnetization direction is alost sae as external field direction. It evident that signal is axiu when angle between free and pinned laer is near 90 degree and signal vanishes when it is 0 degree. It is quite consistent with the theor that setric coponent has cosθ dependence (Fig 4c) and anti-setric coponent has cos θ (Fig 4d) dependence if we incorporate such out of plane effective field (H (M J)). However a sall deviation is expected if we consider slight rotation of fixed laer in response to applied external agnetic field (See detailed explanation in the suppleentar inforation).

5 Figure 3 Special case studies. (a) dc voltage when pinned laer is along -X-axis i.e. parallel to current direction, and free laer is along 45. (θ M = 180, θ = 45 ). (b) dc voltage when pinned laer is aligned 45 with respect to X-axis and free laer is along Y-axis (θ M = 45, θ = 90 ). (c) dc voltage when pinned laer is along X-axis and free laer is along Y-axis (θ M = 0, θ = 90 ). (d) dc voltage when pinned laer and free laer along 45 degree with respect to current flow (X-axis) (θ M = θ = 45 ). In all these figures black curve, blue curve and green curve represent experiental data, setric Lorentzian, anti-setric Lorentzian coponents respectivel. Red curve denotes the suation of blue and green curve to fit the experiental data. Applied agnetic field is 400 Oe in all these experients. Figure 4 Angular dependence of ST-FMR data in CIP GMR stack. The pinned laer is along Y axis and in-plane external agnetic field of 450 Oe is applied at various angles. (a,b) show soe of the dc voltage spectra obtained at different angles. (c) and (d) show aplitudes of setric and anti-setric coponents of dc voltage as a function of angle θ H. Experiental data in figure (c) and (d) are well represented b cosθ and cos θ dependence (red curves). Recentl it is proposed that in GMR kind of structure, fixed laer can produce torque on free laer owing to anoalous Hall effect and AMR of FM 33, 34. (The AMR effect is not expected to produce spin torque with in-plane fixed laer.) However in GMR kind of structure, fixed laer and free laer are not decoupled fro each other, as far as in-plane current flow is concerned. Interfacial scattering and reflection of spins take place at the interface through the Cu spacer due to zigzag otion of carriers which causes the in-plane GMR effect. So we cannot think a siple picture of GMR stack where current flows in parallel channels through the fixed laer, free laer and Cu spacer unlike HM/FM bi-laers. If the fixed FM behaves siilar to other heav etal (Pt, Ta, W etc.) we would expect injection of spin-current fro fixed FM to free FM through the spin-transport via Cu spacer. In that situation we would not see sign reversal of setric coponent while reversing the external field as observed here. It is possible that current in-plane GMR effect (interfacial spin scattering and zigzag otion of electrons between fixed and free laer through the Cu spacer) in cobination with spin-orbit coupling could produce such current induced out-of-plane effective field which acts on free laer as spin-torque. We have estiated that approxiatel 15 Oe effective out-of-

6 plane agnetic field is created when average 10 1 A/ current densit flows in FM (top = n)/cu (5 n)/fm (botto = n) heterostructure (details in the Suppleentar Inforation). A detailed icroscopic theor of this torque is lacking here which reains an open question. In suar we have reported unprecedented observation of current induced out-of-plane field generated spin-torque in current-in-plane (CIP) GMR structure. This kind of spin torque can be controlled b anipulating the fixed laer agnetization direction. Such a torque can be highl useful to anipulate perpendicular agnetic bits. References 1. Mers, E. B. Current-Induced Switching of Doains in Magnetic Multilaer Devices. Science 85, (1999).. Kiselev, S. I. et al. Microwave oscillations of a nanoagnet driven b a spin-polarized current. Nature 45, (003). 3. Tulapurkar, A. A. et al. Spin-torque diode effect in agnetic tunnel junctions. Nature 438, (005). 4. Liu, L. et al. Spin-Torque Switching with the Giant Spin Hall Effect of Tantalu. Science 336, (01). 5. Miwa, S. et al. Highl sensitive nanoscale spin-torque diode. Nat. Mater. 13, (014). 6. Nozaki, T. et al. Electric-field-induced ferroagnetic resonance excitation in an ultrathin ferroagnetic etal laer. Nat. Phs. 8, (01). 7. Fang, D. et al. Spin orbit-driven ferroagnetic resonance. Nat. Nanotechnol. 6, (011). 8. Miron, I. M. et al. Perpendicular switching of a single ferroagnetic laer induced b in-plane current injection. Nature 476, (011). 9. Brataas, A., Kent, A. D. & Ohno, H. Current-induced torques in agnetic aterials. Nat. Mater. 11, (01). 10. Choi, G., Moon, C., Min, B., Lee, K. & Cahill, D. G. Theral spin-transfer torque driven b the spindependent Seebeck effect in etallic spin-valves. Nat. Phs.11, (015). 11. Pushp, A. et al. Giant theral spin-torque assisted agnetic tunnel junction switching. Proc. Natl. Acad. Sci. 11, (015). 1. Bose, A. et al. Observation of therall driven field-like spin torque in agnetic tunnel junctions Observation of therall driven field-like spin torque in agnetic tunnel junctions. Appl. Phs. Lett. 109, 03406, (016). 13. Slonczewski, J. C. Current-driven excitation of agnetic ultilaers. J. Magn. Magn. Mater. 159, L1 L7 (1996). 14. Kubota, H. et al. Quantitative easureent of voltage dependence of spin-transfer torque in MgObased agnetic tunnel junctions. Nat. Phs. 4, (007). 15. Hirsch, J. E. Spin Hall Effect. Phs. Rev. Lett. 83, (1999). 16. Valenzuela, S. O. & Tinkha, M. Direct electronic easureent of the spin Hall effect. Nature 44, (006). 17. Brataas, A., Tserkovnak, Y., Bauer, G. E. W. & Halperin, B. I. Spin batter operated b ferroagnetic resonance. Phs. Rev. B 66, (00).

7 18. Bose, A., Bhuktare, S., Singh, H., Achanta, V. G. & Tulapurkar, A. A. Observation of spin Nernst effect in Platinu. arxiv (017). 19. Uchida, K. et al. Observation of the spin Seebeck effect. Nature 455, (008). 0. Walter, M. et al. Seebeck effect in agnetic tunnel junctions. Nat. Mater. 10, (011). 1. Jain, S. et al. Magneto-Seebeck effect in spin-valve with in-plane theral gradient. AIP Adv. 4, (014).. Y. Suzuki et.al., in Nanoagnetis and Spintronics, nd ed., edited b T. Shinjo ( Elsevier B. V., 014), Chap. 3, pp Shara, S., Muralidharan, B. & Tulapurkar, A. Proposal for a Doain Wall Nano- Oscillator driven b Non-unifor Spin Currents. Sci. Rep. 5, (015). 4. Bhuktare, S., Bana, H., Bose, A. & Tulapurkar, A. A. Spintronic oscillator based on spin current feedback using the spin hall effect. Phs. Rev. Appl. 7, 0140 (017). 5. Souanaraanan, A., Reren, N., Fert, A. & Panagopoulos, C. Eergent Phenoena Induced b Spin-Orbit Coupling at Surfaces and Interfaces. Nature 539, (016). 6. Liu, L., Moriaa, T., Ralph, D. C. & Buhran, R. a. Spin-torque ferroagnetic resonance induced b the spin Hall effect. Phs. Rev. Lett. 106, (011). 7. Fukai, S., Zhang, C., Duttagupta, S., Kurenkov, A. & Ohno, H. Magnetization switching b spin orbit torque in an antiferroagnet ferroagnet bilaer sste. Nat Materials 15, (016). 8. Hanuan Singh, Swapnil Bhuktare, Sutapa Dutta and Ashwin A. Tulapurkar. Sign reversal of field like spin-orbit torque in ultrathin Chroiu/Nickel bilaer. (Subitted) 9. MacNeill, D. et al. Control of spin orbit torques through crstal setr in WTe/ferroagnet bilaers. Nat. Phs. 13, (016). 30. Mellnik, A. R. et al. Spin-transfer torque generated b a topological insulator. Nature 511, (014). 31. Miao, B. F., Huang, S. Y., Qu, D. & Chien, C. L. Inverse spin hall effect in a ferroagnetic etal. Phs. Rev. Lett. 111, 1 5 (013). 3. Wang, H., Du, C., Hael, C., P. & Yang, F. Spin current and inverse spin Hall effect in ferroagnetic etals probed b Y3Fe5O1-based spin puping. Appl. Phs. Lett. 104, 0405 (014). 33. Taniguchi, T. Grollier, J. & Stiles, M. D. Spin-transfer torque in ferroagnetic bilaers generated b anoalous Hall effect and anisotropic agnetoresistance. Proc. of SPIE Vol. 9931, 99310W (016). 34. Taniguchi, T., Grollier, J. & Stiles, M. D. Spin-transfer torques generated b the anoalous Hall effect and anisotropic agnetoresistance. Phs. Rev. Appl. 3, (015). Author Contributions GMR fil was deposited b DL with supervision fro YS and SM. The lithographic device fabrication and easureents were carried out b AB with help fro SB, SD and HS. AB analsed the data and wrote the anuscript with help fro AT. AT supervised the project. All authors contributed to this work and coented on this paper.

8 Acknowledgeent: We are thankful to the Centre of Excellence in Nanoelectronics (CEN) at the IIT-Boba Nanofabrication facilit (IITBNF) and Departent of Electronics and Inforation Technolog (DeitY), Governent of India for its support. We also thank to JSPS KAKENHI (JP610300). Copeting Interests: The authors declare that the have no copeting interests. Suppleentar inforation: S1. Derivation of the expression for dc voltage: The reference frae used is shown below. Figure S1 Estiation of ST-FMR voltage The green rectangle denotes the GMR stack cut into rectangular shape. The rf current flows along X-axis. The equilibriu free laer and pinned laer agnetization directions ( ˆ and ˆ pin ) are assued to be in X-Y plane. X -axis is taken to be along ˆ. When current is passed along x direction, it creates Oersted agnetic field along -axis, is given b, h of new ( ˆ pin J ) J pin, h h. The anoalous agnetic field Oe ˆ zˆ, where is a constant and pin,y denotes Y coponent ˆ pin. Assuing sall oscillation of ˆ, we get the following equations: ' and h 11 x ' h 1 sin cos z h ' ' 11 Oe cos J ( sin cos (cos h 11 Oe 11 cos pin, h Oe 1 sin pin, (1) 1 pin, 1 J) (3) J ) () Where denotes the podar susceptibilit tensor. The saple resistance depends on the relative orientation of ˆ and if ˆ oscillates, as follows: R R P R (1 ˆ. ˆ pin R ) R ( pin, xx pin, ) (4) ˆ pin, and undergoes oscillation

9 The hoodne ixture of oscillating current and resistance produces dc voltage given b: V dc 1 I rf 1 Re( R) I 4 rf R[ pin, x Re( x ) pin, Re( )] (5) Fro above equations we see that, Oersted field ter is ultiplied b Re( 11 ) which has a dispersion shape whereas the anoalous agnetic field ter is ultiplied b Re( 1 ) which shows a peak at resonance. Let s now see how dc voltage changes when we reverse ˆ and/or ˆ pin. If we reverse ˆ keeping ˆ pin sae, (i.e. θ θ +π), the Oersted field ter reains the sae as involves factors of sinθ cosθ and cos θ, whereas the anoalous field driven ter inverts as it involves factors of sinθ and cosθ. If we reverse keeping ˆ sae, we see fro equation 5 that V dc gets a inus sign. ˆ pin However, the anoalous field ter itself changes sign if we invert ˆ pin. Thus the Oersted field ter changes sign, whereas the anoalous field ter reain the sae in this case. Cobining above two scenarios, if we reverse both ˆ and ˆ pin, both the ters change sign i.e. dc voltage inverts. These conclusions are in agreeent with the experiental data shown in fig a-d. If the free and pinned laer are parallel (i.e. pin,x =cosθ and pin,y = sinθ ), the dc voltage is 0 as can be seen fro equations,3 and 5. We now take a particular case where the pinned laer is along -axis. Fro equations 3 and 5, the dc voltage is given b: V dc 1 I 4 rf R Re( 1 ) I 4 rf R[cos Re( ) h 11 Oe cos Re( ) J)] (6) The above equation shows that the anti-setric Lorentzian (dispersion) ter has cos θ dependence whereas the setric Lorentzian ter has cosθ dependence in agreeent with the experiental data in figure 4.c-d. S. Estiation of agnetization angle between free and fixed laer and its ipact on ST-FMR data In ST-FMR experient we have swept frequenc for a particular dc agnetic field which is in the range of 400 Oe to 500 Oe. The coercivit of free laer is around 40 Oe. Hence free laer alost aligns to external agnetic field. For exaple at 450 Oe, the estiated axiu difference in between free laer and external field directions is less than.5 degree. The agnetization direction of the fixed laer can change a bit when external agnetic field is applied which can be estiated fro the pinning strength. The agnetization of the stack easured b Kerr rotation (fig S.a) indicates that the pinning field strength is about 1.6 koe. The angular dependence of the setric and anti-setric coponents of the dc voltage shown in fig 4 (and fig S b,c) would show soe deviation fro cosθ and cos θ dependence if fixed laer oves. We have nuericall evaluated the angular dependence taking account the rotation of fixed laer which is shown b the blue curve in fig S. b-c. (The red curve shows cosθ and cos θ dependence.) The experiental results (black data points) are well described b the blue curve. 1

10 Figure S (a) Magneto-optic kerr easureent of the GMR stack (b), (c) Angular dependence of setric (V S ) and anti-setric (V A ) coponent of ST-FMR experient respectivel. Red curve in figure (b) and (c) indicates cosθ and cos θ dependence respectivel. Blue curve in figure (b) and (c) is obtained nuericall taking into account rotation of fixed laer due to finite exchange bias (~1.6 koe). S.3 Nuerical evaluation of the dc voltage signal: We can nuericall evaluate the dc voltage fro equation in section S1. The Oersted agnetic field depends on the current distribution in the saple, which can be obtained fro the electrical conductivities of the various laers in the stack. The anoalous agnetic field is given b, h ( ˆ J ) where J is taken as average current densit flowing in the free laer/cu pin spacer/pinned laer stack and is taken as a paraeter to be evaluated. Following paraeters are used for nuerical calculation. Metal Thickness (n) Resistivit (oh-) Cu (cap) 3 8E-8 CoFe (free laer).7e-7 Cu (spacer) 5 8E-8 CoFeB (pinned).7e-7 Buffer laer (IrMn(7)+R(5)+Ta(5)) 17.5E-7 (equivalent) Length (L x ) of GMR saple is 375 μ and width is 5 μ. Applied field is 450 Oe. Our GMR saple shows high out of plane anisotropic field (~1.35E4 Oe) and higher daping (α=0.09). Chosen resistivit closel atches the experiental and siulated resistance of GMR stack and agneto resistance. Experientall obtained resistance of in-plane GMR stack is around 88 oh whereas siulated result of GMR resistance is 85.5 oh. The rotation of the fixed laer on application of agnetic field is also taken into account in the nuerical calculation. It is found that β gives a reasonable atch to the experiental data as shown in Figure S3.a-b for two different configurations. (Sae experiental data as in fig a,b) This value can be written as β 15 Oe/10 1 (A/ ) i.e. an average current densit of 10 1 A/ passing through

11 CoFe(n)/Cu(5n)/CoFe(n) laers, produces a agnetic field of 15 Oe along Z-direction on the free laer if the pinned laer and current are perpendicular to each other. Figure S3.c shows the configuration when fixed laer is along X-axis and free laer is along Y-axis (sae as fig 4c in the ain paper). The expected dc voltage is zero if we assue that the pinned laer does not rotate i.e. reains along X-axis, when agnetic field along Y-axis is applied. Experientall, we do observe a sall dc voltage (copare Fig S3.a and Fig S3.c) in this configuration which can be explained b the rotation of fixed laer as argued in S. section. Nuerical calculation (red curve in Fig S3.c) including 1.6 koe exchange bias can reproduce the experiental data of figure S3.c. Figure S3.d shows the experiental data when both free and pinned laer are along x-axis (parallel to current) for two different values of external agnetic field (300Oe and 500 Oe). In both these cases we see no signal fro ST-FMR since our detection ethod is based on in-plane GMR. However at low frequenc range (around 1 to GHz) sall peak (aplitude less than 1.5 μv) appears (in all cases) which are agnetic field independent (copare figure S3.a,b and Fig S3.d). This background voltage along with a constant dc background is subtracted fro experiental data shown in ain article. Tpicall resonance frequencies in our experient are the range of 5-6 GHz which allows us to detect ST-FMR signal with inial error. Figure S3 Black squares in all the figures represent data points corresponding to the experient shown in the inset of individual figures. Red curves in (a), (b) and (c) represent nuericall estiated voltage. (d) Background data when free and fixed laers are parallel for 300Oe (red) and 500 Oe (black) applied field.