Correspondence should be addressed to G.M.C and

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1 Thermal spin-transfer torque driven by the spin-dependent Seebeck effect in metallic spin-valves Gyung-Min Choi 1,2, Chul-Hyun Moon 2,3, Byoung-Chul Min 2, Kyung-Jin Lee 3,4, and David G. Cahill 1 1 Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA 2 Center for Spintronics, Korea Institute of Science and Technology, Seoul , Korea 3 Department of Materials Science and Engineering, Korea University, Seoul , Korea 4 KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul , Korea Correspondence should be addressed to G.M.C (gchoi11@illinois.edu) and D.G.C(d-cahill@illinois.edu) Supplementary Note 1: Demagnetization-driven spin generation Ultrafast demagnetization by an ultrashort laser pulse was reported nearly two decades ago [1]. Recently, theoretical research predicted demagnetization-driven spin current in terms of spindependent transport of hot electrons in a magnetic layer [2]. The findings of several subsequent experiments have been interpreted as supporting this hypothesis [3-5]. However, in our previous work [6] where a ferromagnet is indirectly heated by a thick Pt layer, we showed that ultrafast demagnetization produces volumetric spin generation due to the temperature difference between electrons and magnons of a ferromagnet combined with angular momentum conservation of electron-magnon coupling. Owing to this conservation, the demagnetization-driven spin generation rate is the negative of the demagnetization rate, NATURE PHYSICS 1

2 gg SS = dddd dddd. (S1) We obtain dm/dt from time derivative of measured M(t). We measure demagnetization of [Co/Pt] and [Co/Ni] with both pump and probe beams incident on the Pt side of samples (Fig. S1 (a)). By comparing the transient Kerr rotation ( M) and static Kerr rotation (M), we determine the peak M/M: 0.26±0.04 and 0.23±0.04, respectively, for [Co/Pt]/Cu-10/CoFeB and [Co/Pt]/Cu- 100/CoFeB samples; 0.08±0.01 and 0.07±0.01, respectively, for [Co/Ni]/Cu-10/CoFeB and [Co/Ni]/Cu-100/CoFeB samples. A change in the thickness of the Cu heat sink layer from 10 nm to 100 nm only slightly reduces the demagnetization because the peak demagnetization, which is proportional to the peak magnon temperature, is mostly controlled by the thickness of the heat absorbing layer, Pt, not by the thickness of the heat sink layer, Cu. The difference in M/M between [Co/Pt] and [Co/Ni] originates from the different Curie temperatures (Fig. S1 (b)). When the excursion in the magnon temperature is 100 K above room temperature, M/M is 0.22 and 0.08 for [Co/Pt] and [Co/Ni], respectively (Fig. S1 (b)). The M/M and saturation magnetization of 4.2 and A m -1 for [Co/Pt] and [Co/Ni], respectively, lead to a spin generation term gs that is two times larger using [Co/Pt] as FM1 than using [Co/Ni] (Fig. 3 (b) of the main text). Supplementary Note 2: Initial energy distribution in thermal modeling There are two aspects to the initial deposition of energy from the pump optical pulse. The first aspect is to analyze how much optical energy is absorbed by electrons in the Pt+FM1 layer and how much optical energy is absorbed directly by electrons in the underlying Cu layer. We calculated the light absorption from the optical model for the multilayer structure by a transfer matrix method, using the refractive indexes of 1.76, ii 5.9, ii 5.6, and 1.73 for the 2 NATURE PHYSICS

3 SUPPLEMENTARY INFORMATION sapphire, Pt, Cu, and capping oxide and assuming the refractive index of [Co/Pt] or [Co/Ni] is the same as that of Pt. For the sapphire substrate/ Pt (20)/ FM1 ([Co/Pt] or [Co/Ni]) (3.2)/ Cu (100)/ Capping oxide (15) (units in nm) structure, the optical calculation predicts that the Pt+FM1 layer absolves 98.5 % and the Cu layer absorbs 1.5 % of the total absorbed energy (Fig. S2 (a)). In other words, the direct absorption of optical energy in the Cu layer is negligible. For simplicity, in the thermal modeling, we assume the Pt+FM1 layer absolves 100 % of energy. Within the Pt+FM1 layer, the optical calculation predicts an exponential decay of light energy at a length scale of 11 nm (Fig. S2 (a)). The second aspect of the problem is the effect of ballistic motion of electrons before thermalization. For s/p band metals, such as Au, the ballistic motion can distribute energy deeply into the layer, and the length scale for energy distribution can be >100 nm [7]. For d band metals, such as Pt, the electron-phonon coupling is much stronger and therefore the length scale for energy distribution is on the order of 20 nm [7]. When we compare the results of the thermal modeling using an initial energy distribution with a length scale of 11 versus 20 nm in the Pt+FM1 layer, we find the difference is not significant (Fig. S2 (b)). In the thermal modeling of Fig. 2 of the main text, we distribute the initial energy in the electron heat capacity of the Pt+FM1 layer with a decay length of 20 nm. Given the initial energy distribution, the temperature evolution of each layer is determined by parameters of heat capacity, thermal conductivity, and electron-phonon coupling of each layer. These parameters for thermal modeling in Fig. 2 in the main text are summarized in Supplementary Table I. Supplementary Note 3: Analytic estimation of heat current NATURE PHYSICS 3

4 The heat current, JQ, through FM1 in the Pt/FM1/Cu (effect of FM2 can be ignored when its thickness much smaller than others) structure can be estimated by assuming that the initial energy deposited by the pump optical pulse is initially confined to the Pt layer and that JQ decays exponentially in time, JQ = J0 exp(-t/τ): Pt acts as a heat absorbing layer and Cu acts as a heat sink layer. The total energy transfer (time integral of JQ) from Pt to Cu is then determined by the relative thickness of Cu compared to the thickness of Pt, 0 JJ 0 ee tt/ττ dddd = EE abs CC Cu h Cu, CC Pt h Pt +CC Cu h Cu (S2) where τ is the thermal relaxation time, Eabs is the energy fluence absorbed by Pt, CPt is the heat capacity of Pt, CCu is the heat capacity of Cu, hpt is the thickness of Pt, and hcu is the thickness of Cu. Solving equation (S2) leads to equation (1) of the main text. The thermal relaxation time, τ, is determined by the heat capacities, thicknesses, and thermal resistances of the multilayer structure. The dominant mechanism of thermal resistance is different for Pt and Cu because of their large difference in the electron-phonon coupling: the major thermal resistance of Pt is h/λ, where Λ is the electronic thermal conductivity; the major thermal resistance of the Cu layer is 1/(gh), where g is the electron-phonon coupling parameter. Then, τ is approximately given by, ττ ( 1 CC Pt h Pt + 1 CC Cu h Cu ) 1 ( h Pt ΛΛ Pt + h FM1 ΛΛ FM1 + 1 gg Cu h Cu ). (S3) In the Pt (20 nm)/ FM1 (3.2 nm)/ Cu (h nm) structure, Eq. (S3) leads to τ of 30 and 40 ps with hcu of 100 and 10 nm, respectively. Applying these τ to Eq. (1) of the main text, JJ QQ 100 ee tt/(30 ps) GW m -2 with Cu 100 nm and JJ QQ 35 ee tt/(40 ps) GW m -2 with Cu 10 nm. Despite the simplicity, this estimation of JQ agrees well with the numerical simulation using a finite difference method (inset of Fig. 2 (c) in the main text). 4 NATURE PHYSICS

5 SUPPLEMENTARY INFORMATION Supplementary Note 4: Demagnetization signal seen through Cu layer When we measure TR-MOKE on the Cu side of samples, the Kerr rotation due to the demagnetization of [Co/Pt] or [Co/Ni] decreases exponentially with increasing Cu layer thickness by, θθ Demag exp ( 4ππππh ), (S4) λλ where κ is the extinction coefficient and h is the thickness of Cu, and λ is the wavelength of light. From the light transmission measurement, we determine κ = 5.6±0.3 for Cu (Fig. S3 (a)). Given the peak θdemag of 75 and 19 µrad on the Cu side of [Co/Pt]/Cu-10/CoFeB and [Co/Ni]/Cu- 10/CoFeB samples, respectively, the peak θdemag on the Cu side should be 0.02~0.04 µrad for the [Co/Pt]/Cu-100 sample (Fig. S3 (b)). To get θk by spin accumulation, we subtract the residual demagnetization signal from the raw data assuming the peak of θdemag on the Cu side of the [Co/Pt]/Cu-100 sample is 0.03 µrad (Fig. S3 (c)). For the [Co/Ni]/Cu-100 sample, the peak of θdemag is less than 0.01 µrad and can be neglected. The demagnetization signal of [Co/Pt] or [Co/Ni] significantly contributes to TR-MOKE on the CoFeB side of [Co/Pt]/Cu-10/CoFeB and [Co/Ni]/Cu-10/CoFeB because of the small Cu thickness. To get the precession data of CoFeB, we subtract the demagnetization signal assuming a polynomial functional form (Fig. S4). Supplementary Note 5: dm/dt-driven spin accumulation at 10 ps We have included zoomed-in figures in Fig. 3 (b) in the main text to show that dm/dt goes to zero after 3 ps within the uncertainties of our measurement. In principle, a small negative contribution to spin generation from dm/dt exists after 3 ps as the temperature of the metal layers equilibrate. As the magnon temperature of FM1 decreases until > 100 ps (Fig. 2 in the main text), NATURE PHYSICS 5

6 ΔM in increases, and consequently there is a small negative component of spin generation due to dm/dt even after 3 ps. However the rate of change in M is so slow after 3 ps that dm/dt becomes negligible compared to the SDSE-driven spin generation at t>3 ps. To verify this argument, we obtain dm/dt after 3 ps from the numerical fitting of demagnetization data up to 100 ps. Calculating spin accumulation including the finite dm/dt after 3 ps shows that this contribution does not make a distinguishable difference in the spin accumulation (Fig. S5). One might argue that the long spin relaxation time (τs) of Cu, 17 ps, can produce an offset in spin accumulation at 10 ps even if dm/dt becomes zero after 3 ps. However, in coupled layers, the layer with the smallest τs will determine if there is significant spin accumulation due to the demagnetization-driven spin generation (gs=-dm/dt) at 10 ps. Because τs of FM1 ([Co/Pt] or [Co/Ni]) is less than 1 ps, the gs=-dm/dt cannot produce an offset in spin accumulation at 10 ps. Even if τs of FM1 were not small, the τs of 0.5 ps of Pt suppresses spin accumulation in the Pt/FM1/Cu structure at 10 ps (Fig. S6). Supplementary Note 6: Magnetic field dependence on the CoFeB frequency The frequency of the CoFeB precession depends on the applied magnetic field. When we increase the in-plane magnetic field from 0.05 T to 0.2 T for the [Co/Ni]/Cu-100/CoFeB sample, the CoFeB frequency increases from 7.8 GHz to 16.4 GHz (Fig. S7). The frequency is well described by Kittel s equation, ff = γγ e 2ππ BB x(bb x + μμ 0 MM S ), where γe = rad s -1 T -1 is the electron gyromagnetic ratio, Bx is the in-plane magnetic field, µ0 is the vacuum permeability, and MS is the saturation magnetization of CoFeB of A m -1. Since μμ 0 MM S BB x, ff BB x. In addition, the amplitude of the CoFeB precession decreases by a half with in-plane field of 0.2 T. This is because the magnetization of [Co/Ni] deviates from perpendicular direction at the in-plane 6 NATURE PHYSICS

7 SUPPLEMENTARY INFORMATION field of 0.2 T. The hysteresis curve of [Co/Ni] shows that in-plane field of 0.2 T significantly tilts its magnetization (Fig. S7 (c)). Although the frequency doubles by increasing the Bx from 0.05 to 0.2 T, we do not observe much difference in the phase: for both fittings in Figs. S7 (a) and S7 (b), we use the same ϕ of - 30 o of the damped cosine function of cos(2 ft+ )exp(-t/ ). Our calculation using equation (6) of the main text also predicts that the magnitude of Bx does not change the phase much (Fig. S8): the phase difference, Δϕ, between [Co/Pt] and [Co/Ni] is 130 o and 120 o at Bx of 0.05 T and 0.2 T, respectively. Supplementary Note 7: Dependence of spin accumulation on τs of FM Given the same spin generation rate, either by demagnetization or by SDSE, in FM1, the amount of spin accumulation in Cu (or spin current to FM2) is determined by τs of FM1: a longer τs produces a larger spin accumulation (Fig. S9). For the spin accumulation by demagnetization, if we assume the same τs for [Co/Pt] and [Co/Ni], [Co/Pt] would produce more than two times larger spin accumulation than [Co/Ni] because of larger demagnetization (Fig. S1 (a)). However, the measured spin accumulation is about two times smaller in [Co/Pt]/Cu-100 than [Co/Ni]/Cu- 100 (Fig. 3 (a) of the main text), suggesting that τs of [Co/Pt] is much shorter than [Co/Ni]. The spin accumulation by SDSE is also affected by τs, but the dependence is less significant because SDSE creates interfacial spin generation while demagnetization creates volumetric spin generation. Supplementary Note 8: Calculation of spin accumulation in NM To calculate spin accumulation in Cu, we solve coupled spin diffusion equation (equation (3) of the main text) for the Pt/ [Co/Pt] or [Co/Ni]/ Cu structure with boundary conditions of dμs/dz NATURE PHYSICS 7

8 = 0 at the end of Pt (next to the substrate) and at the surface of Cu. We calculate the demagnetization-driven and SDSE-driven components of the spin accumulation independently (Fig. S10). First, we calculate the demagnetization-driven spin accumulation by including the volumetric spin generation rate of gs = -dm/dt at [Co/Pt] or [Co/Ni]. The dm/dt of [Co/Pt] is approximately two times larger than that of [Co/Ni], but the τs of [Co/Pt] is much smaller than that of [Co/Ni], resulting in the smaller spin accumulation with [Co/Pt] than [Co/Ni]. Second, we calculate the SDSE-driven spin accumulation by including the interfacial spin generation rate of GS described by Eq. (2) of the main text. The SDSE-driven spin current produces a peak spin accumulation at 0.8 ps and an offset in the spin accumulation at 10 ps. Total spin accumulation is the sum of the demagnetization-driven and SDSE-driven ones. To compare calculated spin accumulation with measured Kerr rotation on Cu, we need to know the relationship between the Kerr rotation and spin accumulation θθ ΔMM Cu. In our previous work [6], we have determined θθ ΔMM Cu rad m A -1 assuming τs=0.05 ps of the [Co (0.4)/ Pt (1)] 5/Co (0.4) layer, which is estimated from the theory of Elliot-Yafet [8, 9]. In this work, we determine τs as a fitting parameter for measured spin accumulation and STT results of different FMs (Supplementary Table II). This fitting procedure leads to θθ ΔMM Cu rad m A -1. Recently, we compared θθ of Cu, Ag, and Au and related them to spin-orbit coupling of conduction band ΔMM [10]. The comparison between calculation and measurement of spin accumulation is shown in Fig. 3 (a) of the main text. Supplementary Note 9: Calculation of spin currents to FM2 8 NATURE PHYSICS

9 SUPPLEMENTARY INFORMATION We calculate spin current that is absorbed by CoFeB by solving the coupled spin diffusion equation (equation (3) of the main text) for the Pt/ [Co/Pt] or [Co/Ni]/ Cu/ CoFeB structure with boundary conditions of dμs/dz = 0 at the end of Pt (next to the substrate) and µs = 0 at CoFeB. The spin current is comprised of demagnetization-driven and SDSE-driven components. We find that the demagnetization-driven spin current does not differ much between [Co/Pt] and [Co/Ni] because the smaller dm/dt of [Co/Ni] is compensated by a larger τs of [Co/Ni]. The major difference in the efficacy of the two ferromagnetic layers results from the SDSE-driven component that persists for ~100 ps and has negative (positive) sign for [Co/Pt] ([Co/Ni]) (Fig. S11). When we solve the coupled-spin-diffusion equation for the Pt/FM1/Cu/FM2 structure with spin generation in FM1 held constant, JS_FM2 decreases by a factor of 2 with increasing the Cu thickness from 10 to 100 nm because it is difficult for spins to diffuse through a thick Cu layer. Therefore, given the similar dm/dt in FM1, the demagnetization-driven JS_FM2 with Cu 100 nm is approximately half of that with Cu 10 nm. By contrast, the SDSE-driven JS_FM2 is comparable with Cu 10 nm and 100 nm. This is because the spin generation rate by SDSE, GS of equation (2) in the main text, is proportional to the heat current through FM1; GS with Cu 100 nm is more than twice larger than that with Cu 10 nm. This larger heat current compensates for the larger spin loss by the thicker Cu layer. The JS_FM2 with Cu 10 nm is shown in Fig. S 11, and JS_FM2 with Cu 100 nm is shown in Figs. 6 (a) and (b) in the main text. Supplementary Note 10: Proposed explanation for different signs of SS of [Co/Pt] and [Co/Ni] In the 3d transition metals, the s electrons are the main carriers of electrical current, and the interband sd scattering controls σ [11-13]. We approximate σσ = nnee 2 ττ ssss /mm, where n is NATURE PHYSICS 9

10 number density, m * is the effective mass, and τsd is the relaxation time and is primarily determined by the density of states of d electrons at EF, N d (EF), and the sd scattering matrix VV ssss kk,kk, 1 ssss 2 ττ ssss = 2ππ ħ NNd (EE F ) VV kk,kk kk. (S5) Mott s original two current model assumes that the spin of s electrons is conserved during scattering process at temperature well below the Curie temperature where the number of magnons is negligible [11-13]. In our experiment, the relatively short spin relaxation time, especially for [Co/Pt], suggests that the spin-flip scattering occurs with a non-ngligible number of magnons. Here we extend the Mott s sd scattering model including the spin-flip scattering process. Using Matthiessen's rule, the relaxation time of s electron can be expressed in terms of spin-conserving sc and spin-flipping relaxation times, ττ ssss and ττ sf ssss : 1 = 1 sc + 1 ττ ssss ττ ssss ττ sf. ssss (S6) Consequently, the difference in the density of states of majority and minority d electrons gives rise to the spin-dependent relaxation time of majority and minority s electrons: 1, = 2ππ (NN ħ, d (EE F ) Σ sc + NN d, (EE F ) Σ sf ), ττ ssss (S7) where Ʃ sc and Ʃ sf are the summation in Eq. (S5) for the spin-conserving and spin-flipping sd scatterings, respectively. Then spin-dependent σ is then σσ, = nnee2 mm ħ (NN 2ππ, d (EE F ) Σ sc + NN d, (EE F ) Σ sf ) 1. (S8) Thus, the energy derivative of σ, becomes σσ, = nnee2 mm d ħ 2ππ ( NN, d Σ sc + NN, Σ sf ) (NN d, (EE F ) Σ sc + NN d, (EE F ) Σ sf ) 2. EE F EE F (S9) Here, we ignored the energy dependency of Ʃ for simplicity under the assumption that the scattering matrix is approximately constant near EF. 10 NATURE PHYSICS

11 SUPPLEMENTARY INFORMATION These simple derivations indicate that the sign of SS is determined by the signs and magnitudes of NN d,, and the relative magnitude of Ʃ sc and Ʃ sf. The band structure shows EE F d d NN < 0 and NN > 0 for [Co/Pt] and [Co/Ni] [14]. If Ʃ sc >> Ʃ sf, σ / E > 0 and σ / E < 0, EE F EE F which consequently gives SS < 0. This is the case of the [Co/Ni] layer which shows a relatively long spin relaxation time. By contrast, if Ʃ sc Ʃ sf, there could be a sign inversion in the spindependent σ/ E, i.e., σ / E < 0 and σ / E > 0, which consequently result in SS > 0. The very short spin relaxation time of the [Co/Pt] layer suggests Ʃ sc Ʃ sf. Supplementary References 1. Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, (1996). 2. Battiato, M., Carva, K. & Oppeneer, P. M. Superdiffusive spin transport as a mechanism of ultrafast demagnetization. Phys. Rev. Lett. 105, (2010). 3. Malinowski, G. et al. Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin angular momentum. Nature Phys. 4, (2008). 4. Melnikov, A. et al. Ultrafast transport of laser-excited spin-polarized carriers in Au/Fe/MgO(001). Phys. Rev. Lett. 107, (2011). 5. Rudolf, D. et al. Ultrafast magnetization enhancement in metallic multilayers driven by superdiffusive spin current. Nature Comm. 3, 1037 (2012). 6. Choi, G.-M., Min, B.-C., Lee, K.-J., & Cahill, D. G. Spin current generated by thermally driven ultrafast demagnetization. Nature Commun. 5, 4334 (2014). NATURE PHYSICS 11

12 7. Hohlfeld, J. et al. Electron and lattice dynamics following optical excitation of metals. Chem. Phys. 251, (2000). 8. Elliot, R. J. Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors. Phys. Rev. 96, (1954). 9. Yafet, Y. Solid State Physics Vol. 14 (eds Seitz, F. & Turnbull, D.) (Academic, New York and London, 1963). 10. Choi, G.-M. & Cahill, D. G. Kerr rotation in Cu, Ag, and Au driven by spin accumulation and spin-orbit coupling. Phys. Rev. B 90, (2014). 11. Mott, N. F. The resistance and thermoelectric properties of the transition metals. Proc. R. Soc. Lond. A 156, (1936). 12. Mott, N. F. The electrical conductivity of transition metals. Proc. R. Soc. Lond. A 153, (1936). 13. Mcguire, T. R. & Potter, R. I. Anisotropic magnetoresistance in ferromagnetic 3d alloys. IEEE Trans. Magn. 11, (1975). 14. Uba, S. et al. Optical and magneto-optical properties of Co/Pt multilayers. Phys. Rev. B 53, (1996). 15. Touloukian, Y. S. ed. Thermophysical Properties of High Temperature Solid Materials. vol. 1(Macmillan, New York, 1967). 16. Tari, A. The Specific Heat of Matter at Low Temperatures. (Imperial College Press, London, 2003). 12 NATURE PHYSICS

13 SUPPLEMENTARY INFORMATION Supplementary Table I: Parameters for the thermal modeling: Ctotal is the total heat capacity, γ the electronic heat capacity coefficient, σ is the electrical conductivity, Λ the thermal conductivity, and ge-p the electron-phonon coupling parameter. We set the interfacial thermal conductance, G=100 MW m -2 K -1, at the sapphire/pt interface. sapphire Pt [Co/Pt] [Co/Ni] Cu Ctotal (10 6 J m -3 K -1 ) 3.08 a 2.85 a 3.15 b 3.89 b 3.45 a γ (J m -3 K -2 ) 721 c 699 b 930 b 97 c σ (10 7 Ω -1 m -1 ) 0.66 d 0.23 d 0.3 d 3.9 d Λ (W m -1 K -1 ) 30 f 50 e 20 e 26 e 300 e ge-p (10 16 W m -3 K -1 ) 42 f 42 g 42 g 7 f a Reference 15. b Obtained by the weighted sum of heat capacities of Pt, Co, and Ni. c Reference 16. d Obtained from four-point probe measurement. e Obtained by from electrical conductivity and Wiedemann-Franz law. f Obtained as fitting parameters for thermal transport analysis. g We use the same value of Pt. NATURE PHYSICS 13

14 Supplementary Table II: Comparison of spin accumulation in the Pt/FM/Cu structure with different FM: M/M is the peak demagnetization of FM, θk is the peak Kerr rotation on Cu, and τs is the spin relaxation time of FM. Data of sample 1 and 2 are taken from Ref. [6], data of sample 3 are taken from Ref. [10], and data of sample 4 and 5 are taken from Fig. S1 in Supplementary Note 1 and Fig. 3 (a) of the main text. Samples 1, 4, and 5 are fabricated at Korea Institute of Science and Technology; samples 2 and 3 are at University of Illinois. M/M θk (µrad) τs (ps) Sample 1 a (0.25 * ) 0.02 Sample 2 b Sample 3 c Sample 4 d Sample 5 e a Pt(30)/[Co(0.4)/Pt(1)] 4/Co(0.2)/Ni(0.4)/Co(0.2)/Cu(80) (unit in nm) b Pt(30)/[Co(0.4)/Pt(1)] 4/Co(0.4)/Cu(100) (unit in nm) c Pt(20)/[Co(0.4)/Pt(1)] 4/Co(0.4)/Cu(100) (unit in nm) d Pt(20)/[Co(0.2)/Pt(0.4)] 5/Co(0.2)/Cu(100) (unit in nm) e Pt(20)/[Co(0.2)/Ni(0.4)] 5/Co(0.2)/Cu(100) (unit in nm) *value after subtracting demagnetization signal from raw data 14 NATURE PHYSICS

15 SUPPLEMENTARY INFORMATION (a) 0.0 [Co/Ni] (b) 1.0 M/M [Co/Pt] Normalized M 0.5 [Co/Ni] [Co/Pt] Temperature (K) Figure S1: (a) Demagnetization data measured on the Pt side of the [Co/Pt]/Cu-10/CoFeB (black filled circles), [Co/Pt]/Cu-100 (black open circles), [Co/Ni]/Cu-10/CoFeB (red filled triangles), and [Co/Ni]/Cu-100 (red open triangles) samples. (b) The magnetization of the [Co/Pt] (black circles) and [Co/Ni] (red triangles) layers at different temperature. At the temperature excursion of ΔT=100 K, indicated by vertical dotted line, ΔM/M are 0.22 (black arrow) and 0.08 (red arrow) for [Co/Pt] and [Co/Ni], respectively. NATURE PHYSICS 15

16 Light absorption Pt+FM1 Cu (a) T (K) Cu 10 nm T ph of Pt T m of [Co/Ni] T ph of Cu (b) Cu 100 nm T ph of Pt T m of [Co/Ni] T ph of Cu (c) Depth (nm) Figure S2: (a) The optical calculation of the light absorption as a function of depth in the [Co/Pt] or [Co/Ni]/Cu-100 samples. Integration of the plot leads to 98.5 % energy absorption in the Pt+FM1 layer and 1.5 % in the Cu layer. The numerical calculation of time evolutions of temperatures of Pt phonon (black lines), Cu phonon (red lines), and FM1 electron (blue lines) for the (b) [Co/Ni]/Cu-10/CoFeB and (c) [Co/Ni]/Cu-100 samples. Solid and dotted lines in (b) and (c) are obtained with the decay length of 11 and 20 nm, respectively, for the initial energy distribution in the Pt+FM1 layer. 16 NATURE PHYSICS

17 SUPPLEMENTARY INFORMATION (a) (b) (c) Transmission Cu thickness (nm) peak ( rad) [Co/Ni] [Co/Pt] Cu thickness (nm) ( rad) Raw data Demag. (scaled) Figure S3: (a) Light transmission with different Cu thickness. The data (black circles) are normalized by the transmission value of the Cu 20 nm, and the solid line is a fitting with a Cu extinction coefficient of 5.6. (b) The peak Kerr rotation by demagnetization measured on the Cu side of the [Co/Pt]/Cu-10/CoFeB (black circle) and [Co/Ni]/Cu-10/CoFeB (red triangle) samples. Blue squares are data of the Pt (20)/ [Co (0.4)/ Pt (1)] 4/ Co (0.4)/ Cu (20, 40, 60) (units in nm) samples. Solid lines are fittings with a Cu extinction coefficient of 5.6. (c) The raw data (black circles) of the Kerr rotation on the Cu side of the [Co/Pt]/Cu-100 sample and the residual demagnetization data (red triangles), which is scaled to θpeak=0.03 µrad. The Kerr rotation by spin accumulation of the [Co/Pt]/Cu-100 sample (Fig. 3 (a) of the main text) is obtained by subtracting the residual demagnetization data from the raw data. NATURE PHYSICS 17

18 K ( rad) (a) [Co/Pt]/Cu-10 0 (b) [Co/Ni]/Cu-10-2 K ( rad) Figure S4: The Kerr rotation measured on the CoFeB side of the (a) [Co/Pt]/Cu-10/CoFeB and (b) [Co/Ni]/Cu-10/CoFeB samples. The signal from the precession of CoFeB appears on top of demagnetization (solid lines) of [Co/Pt] and [Co/Ni]. 18 NATURE PHYSICS

19 SUPPLEMENTARY INFORMATION M/M (a) M (A m -1 ) (b) Figure S5: (a) Demagnetization data measured on the Pt side of the [Co/Pt]/Cu-100 sample (black circles). The solid line is the fitting with a polynomial function. The dm/dt after 3 ps is obtained by numerical differentiation of the polynomial fitting. (b) The calculated spin accumulation at the surface of the Cu layer of the [Co/Pt]/Cu-100 sample by demagnetization with τs of [Co/Pt] of 0.02 ps: assuming dm/dt is zero after 3 ps (black solid line); including a finite dm/dt after 3 ps from the analysis shown in panel (a) (red dotted line). NATURE PHYSICS 19

20 M (A m -1 ) [Co/Ni] ( S = 0.1 ps) [Co/Pt] ( S = 0.02 ps) M (A m -1 ) [Co/Pt] ( S = 10 ps) [Co/Ni] ( S = 10 ps) Figure S6: The calculated spin accumulation at the surface of the Cu layer of the [Co/Pt]/Cu-100 (black line) and [Co/Ni]/Cu-100 (red lines) by demagnetization. (a) The τs is set to 0.02 and 0.1 ps for [Co/Pt] and [Co/Ni], respectively. (b) The τs is artificially set to 10 ps for both [Co/Pt] and [Co/Ni] to show τs = 0.5 ps of Pt still prevents the spin accumulation at 10 ps. 20 NATURE PHYSICS

21 SUPPLEMENTARY INFORMATION M z /M (%) In-plane field of 0.05 T (a) In-plane field of 0.2 T (b) Normalized M (c) Perpendicular In-plane B-field (T) Figure S7: The magnetization dynamics of CoFeB of the [Co/Ni]/Cu-100/CoFeB sample (black circles) with in-plane magnetic field of (a) 0.05 T and (b) 0.2 T. Solid lines are damped cosine functions of cos(2 ft+ )exp(-t/ ) with frequency (f) of (a) 7.8 and (b) 16.4 GHz and with phase (ϕ) of -30 o for both (a) and (b). (c) The hysteresis curves of [Co/Ni] with perpendicular (black circles) and in-plane (red triangles) magnetic field. NATURE PHYSICS 21

22 1.0 B x of 0.05 T (a) B x of 0.2 T (b) M z /M (%) [Co/Pt] [Co/Ni] [Co/Pt] [Co/Ni] Figure S8: The calculated CoFeB precession using equation (6) of the main text with in-plane magnetic field (a) 0.05 T and (b) 0.2 T: black solid lines are for [Co/Pt]/Cu-100/CoFeB; red solid lines are for [Co/Ni]/Cu-100/CoFeB. For both (a) and (b), we use the same input spin current, JS, which is shown in Fig. S10 (d) for [Co/Pt/Cu-100/CoFeB and in Fig. S10 (e) for [Co/Ni]/Cu- 100/CoFeB. The phase difference, Δϕ, between [Co/Pt] and [Co/Ni] is 130 o and 120 o at Bx of 0.05 T and 0.2 T, respectively. 22 NATURE PHYSICS

23 SUPPLEMENTARY INFORMATION M peak (A m -1 ) Demag. of [Co/Pt] SDSE M offset (A m -1 ) Demag. of [Co/Ni] S of FM (ps) Figure S9: The calculated peak spin accumulation at the surface of the Cu layer by demagnetization as a function of τs of [Co/Pt] or [Co/Ni]: the black solid line is for the [Co/Pt]/Cu-100 and the red solid line is for the [Co/Ni]/Cu-100 samples. The calculated offset spin accumulation, at 10 ps, by SDSE as a function of τs of [Co/Ni] for the [Co/Ni]/Cu-100 sample (blue solid line) (the SS is assumed to be -10 µv K -1 ) is plotted versus the right-hand axis. NATURE PHYSICS 23

24 300 (a) [Co/Pt]/Cu-100 (b) [Co/Ni]/Cu-100 M (A m -1 ) Demag. SDSE Demag. SDSE Figure S10: The calculated spin accumulation at the surface of the Cu layer by demagnetization (black solid line) and by SDSE (red solid line) of the (a) [Co/Pt]/Cu-100 and (b) [Co/Ni]/Cu-100 samples: we set τs of 0.02 and 0.1 ps, and SS of 6 and -12 µv for [Co/Pt] and [Co/Ni], respectively. 24 NATURE PHYSICS

25 SUPPLEMENTARY INFORMATION 60 [Co/Pt] 0.4 [Co/Ni] 0.4 J S ( A ps -1 ) 30 0 Demag Demag SDSE (S S 6 V/K) SDSE (S S -12 V/K) Figure S11: The calculated spin current that is absorbed by the CoFeB layer in the (a) [Co/Pt]/Cu- 10/CoFeB and (b) [Co/Ni]/Cu-10/CoFeB samples: the black and red solid lines are driven by demagnetization and SDSE, respectively. Insets of (a) and (b) are the SDSE-driven spin currents at time scale of 10~300 ps. All plots are done by setting τs of 0.02 and 0.1 ps, and SS of 6 and -12 µv for [Co/Pt] and [Co/Ni], respectively. NATURE PHYSICS 25