Photo-spin-voltaic effect

DOI: 1.138/NPHYS3738 Photo-spin-voltaic effect David Ellsworth 1, Lei Lu 1, Jin Lan,3, Houchen Chang 1, Peng Li 1, Zhe Wang 3, Jun Hu, Bryan Johnson 1, Yuqi Bian 1, Jiang Xiao 3,, Ruqian Wu,3, and Mingzhong Wu 1 1 Department of Physics, Colorado State University, Fort Collins, CO 853, USA. Department of Physics and Astronomy, University of California, Irvine, CA 997, USA. 3 Department of Physics, Fudan University, Shanghai 33, China. Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai, 33, China. 1. Materials and Experimental Methods The substrates for yttrium iron garnet (Y 3Fe 5O 1, YIG) and Ga-doped YIG film samples were single-crystal (111)-oriented gadolinium gallium garnet (Gd 3Ga 5O 1, GGG). The.9-m-thick YIG films, the 1.-mthick YIG films, and the 78-m-thick Ga-doped YIG films were grown by liquid phase epitaxy techniques. 1 The doped YIG films contain.5% (atomic) of gallium. The 1-nm-thick YIG films were grown by RF sputtering.,3 The 1.-m-thick barium hexagonal ferrite (BaFe 1O 19, BaM) films were grown on singlecrystal c-axis in-plane sapphire substrates by pulsed laser deposition techniques. The and Cu layers were grown by DC sputtering at room temperature. The YIG, doped YIG, and BaM films were characterized by field-in-plane ferromagnetic resonance (FMR) measurements. Fitting of the FMR frequency vs. field responses with the Kittel equation yielded an effective saturation magnetization (πm s) of 19 G for the.9-µm-thick YIG films, 95 G for the 78-µm-thick Ga-doped YIG films, 1757 G for the 1- nm-thick YIG films, and 387 G for the 1.-m-thick BaM films. Static magnetic measurements indicated that the BaM films had an effective uniaxial anisotropy field of 1.5 koe and a remnant magnetization of 3 G, both along the in-plane c axis. The optical spectra of different light sources were measured with an Ocean Optics IRRAD visible spectrometer (35-1 nm) and an Ocean Optics NIRQuest51-.5 near-infrared (NIR) spectrometer (95-5 nm). The light was collected using an Ocean Optics QP--VIS-NIR patch cord with a µm fiber optic core and an Ocean Optics P5-1-FLUORIDE patch cord with a 5 μm core for visible and NIR measurements, respectively. The optical transmission properties of the samples and the optical filters were measured with the same spectrometers and patch cords by placing the sample or filter over the end of the patch cord, between the fiber and the light source. Note that the responses of the various shortpass and long-pass filters used in this experiment are not ideal. The short-pass filters in particular function more like band-stop than edge filters. See, for example, the blue curve in Fig. e for the 8 nm shortpass filter. However, we were able to take advantage of the complicated response of these filters and were able to do more extensive comparisons to the theory detailed below. For the phot-spin-voltaic (PSV) measurements the magnetic field was provided by a pair of permanent magnets and was measured by a LakeShore model 5 gaussmeter. The electrical voltages were measured by Cu wires attached to the sample with silver paste and connected to a Keithly 18A nanovoltmeter. The temperatures were measured by National Instruments USB-TC1 thermometers with Omega 5SC-TT-T--3 Type-T thermocouples. For the measurements of the data shown in Figs. and, the sample was mounted horizontally on a stage beneath the light, as shown in Fig. a, and a piece of NATURE PHYSICS www.nature.com/naturephysics 1 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 white grid paper was used to align the sample. The reflection of light from the paper slightly enhanced the signal strength. For the measurements of the data in Figs. and S the sample was mounted in the same way, but instead of a piece of white paper used a piece of black tape to eliminate reflections. For the measurements of the data presented in Fig. 3 the sample was mounted vertically between two lights, as shown by the small diagrams at the top of Fig. 3A, as viewed from above. With this configuration there are no reflections from the sample holder. In order to maximize the signal-to-noise ratio, the experimental setup was placed on an optical table to minimize mechanical vibrations and was covered with an enclosure to minimize air flows. To minimize the temperature gradients across the sample thickness and length, an 8 cm fan was used to circulate air within the sample enclosure. The primary light source was a 1 W 1 VAC halogen light bulb. FMR-driven spin pumping measurements were also carried out on the /YIG(.9 m)/ggg samples. The experimental configuration was similar to that shown in Fig. a in the text. Instead of a light bulb, a 5- µm-wide microstrip line was placed on the top of the sample (on the side and perpendicular to the sample length) and was fed with microwaves. When the magnetic field ( H=9) was fixed and the microwave frequency was swept, one observed a negative ISHE voltage signal at the FMR frequency of the YIG film. The voltage flipped its sign when the magnetic field direction was reversed. As a result, it can be concluded that the ISHE voltage signals for the FMR and PSV spin pumping processes showed opposite signs for the same sample/field/electrode configuration.. Multiplication Rule The multiplication rule states that the degrading factor of the observed PSV signal due to the use of multiple filters is the product of the degrading factors due to each single filter. If one defines the PSV signal with no filter, with only filter A, with only filter B, and with both filters A and B as VV, VV A, VV B, VV AB respectively, the multiplication rule can be expressed as VV AB VV = VV A VV VV B VV The establishment of the multiplication rule observed in the experiment implies that the PSV must be generated by the light in a relatively narrow wavelength (λλ) range, as argued below. From experimental observations, it is reasonable to write down the PSV signal as VV = TT(λλ)II(λλ)CC(λλ) dλλ where TT(λλ) is the general transmission function of the light filter(s), II(λλ) is the general incident total light intensity, and CC(λλ) is the general conversion function between the incident light intensity and the PSV signal. All of these three parameters are functions dependent on λλ. Then the multiplication rule implies that the following relation for two filters, A and B, is satisfied II(λλ)CC(λλ) dλλ TT A (λλ)tt B (λλ)ii(λλ)cc(λλ) dλλ = TT A (λλ)ii(λλ)cc(λλ) dλλ TT B (λλ)ii(λλ)cc(λλ) dλλ Considering the complicated behaviors for II(λλ), TT A (λλ), and TT B (λλ), generally Eq. (S3) is not satisfied since the integration and multiplication operations do not commute. To satisfy Eq. (S3), the special condition CC(λλ) = CC δ(λλ λλ ) must be satisfied, where δ(λλ) is the Dirac delta function. This condition signifies that the main contribution for the PSV signal must come from the light in a narrow wavelength centered at λλ. (S1) (S) (S3) 3. Diffusion Processes NATURE PHYSICS www.nature.com/naturephysics 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 SUPPLEMENTARY INFORMATION With the incident light intensity of II, the total optical spin excitation in the ferromagnetic region can be estimated as ss = AAAAdd (εε εε ), where AA denotes the coefficient between the light intensity II and the light s electric field, dd is the effective thickness of the ferromagnetic region, and εε () is the imaginary part of the dielectric function for up-spin (down-spin). Since the magnetization in the atomic layers away from the /magnetic insulator () interface are unaffected by the film, the optical excitation in these layers is spin un-polarized. A spin current density, JJ e (JJ h ), and a spin density, ss e (ss h ), inside the film then results from the outward diffusion of non-equilibrium spin-polarized hot electrons (holes). One may estimate JJ and ss by solving a diffusion equation, with boundary conditions at the / (zz=) and /vacuum (zz=dd) interfaces described by { DD ss(zz) e/h zz ss(zz) ττ e/h + AAAAdd (εε εε )δ(zz) = ( < zz < dd), ss(zz) zz = (zz =, dd), where DD e/h is the spin diffusion coefficient for the electrons/holes, ττ e/h is the spin relaxation time for the electrons/holes, and II is the light intensity. Since very few atomic layers near the / interface are spin polarized by the film, one can use the delta function δ(zz) along with AAAAdd (εε εε ) to describe the source of spin polarization. Accordingly, the spin current distribution inside the film is given as JJ e/h (zz) = DD e/h ss e/h zz = AAAAdd (εε εε sinh zz dd LL ) e/h, sinh dd LL e/h where LL e/h = DD e/h ττ e/h is the spin mean free path of the electrons/holes, and the sign is for the spin carried by the electrons/holes. Considering that the excited hot electrons carry much higher energy than the holes, a reasonable spin mean free path relation is LL e LL h. Specifically, under the limit LL e dd LL h, the total spin current contributed JJ tot e/h = d z= JJ e/h (zz)dzz is given by JJ e tot and JJ h tot = 1 AAAAdd dd(εε εε ). One can see that the optically excited holes dominate the contribution to overall spin current flowing across the thickness, which is ultimately transformed into the final voltage signal via the ISHE. Meanwhile, the optically excited electrons contribute almost no overall spin currents, due to the extensive spin relaxation processes experienced. (S) (S5) (S). DFT Methods and Parameters To mimic the magnetic proximity effect in the atomic layers near the interface with an, density functional theory (DFT) calculations were carried out. A magnetic moment of. B/atom was introduced in the bulk face-centered-cubic with a lattice constant of 3.9 Å. The 5dsp orbitals of the atoms were treated as valence states, while all the other inner orbitals were treated as core states. The projector augmented wave (PAW) method was adopted for the description of the core-valence interaction. 5, The spin-polarized DFT calculations were performed using the Vienna ab initio simulation package (VASP). 7,8 The electronic exchange correlation among the electrons at the level of a generalized-gradient approximation (GGA) was considered by the use of the PBE function proposed by Perdew, Berke, and Ernzerhof. 9 An energy cutoff of ev was used for the plane wave basis expansion of the wave functions. The spin-orbit coupling was invoked in the self-consistent loop, using the non-collinear mode of the VASP. As a result of the magnetization, the band structure of the shows a small spin splitting as presented in Fig. 5b in the text, and the two spin channels respond differently to the light, as required for the PSV effect. NATURE PHYSICS www.nature.com/naturephysics 3 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 Furthermore, the strong intermixing between the valence states near the Fermi level in two spin channels (bands shown in green in Fig. 5b) suggests the easiness of the spin flipping process in the and hence a short spin mean free path for electrons or holes away from the interface region. To determine the optical response of the ferromagnetic, self-consistent electronic structures were first obtained. Then the frequency dependent dielectric function was calculated according to the expression (in atomic units): 1 εε(ee) = 1 + ππ ΩΩ kk mmmm (S7) {ff mm (kk) ff nn (kk) pp mmmm (kk) [EE mmmm (kk)] EE EE mmmm (kk)+iσσ } where EE is the incident photon energy, ΩΩ is the volume of the unit cell, ff mm (kk) is the Fermi occupancy factor of the mm-th eigenstate with a wave vector kk, EE mmmm (kk) is the energy difference between the mm-th and nn-th states, σσ is a broadening width (σσ =.1 ev in the present work), and pp mmmm is the matrix element of the momentum operator. An adapted version of Eq. (S7) is then used to calculate the spin-dependent dielectric function εε /. For the calculations using Eq. (S7), a fine 777 kk-point mesh in the full Brillouin zone and conduction bands were adopted to ensure the numerical convergence. 5. Comparison of Experimental and Theoretical Results In addition to the qualitative agreements between the experimental observations and the theory discussed in the text, there exist also quantitative agreements between the experimental and theoretical results. Figure S1 shows the comparison of measured and calculated voltages when using filters. The solid circles show the experimental voltages normalized to the voltage obtained without using any filters. The empty circles give the voltages calculated by V I d I T d where I is the experimentally measured light intensity of the halogen lamp (see Fig. c), T is the (S8) Voltage (%) 1 8.9-m YIG 1.-m YIG Calculation 55L 59L 95L 8L 85L 9L 95L 1S 95S 9S 8S 7S 1S+85L 1S+59L 1S+9S 59L+85L 59L+9S 9S+85L 1S+59L+85L 1S+59L+9S 59L+9S+85L 1S+59L+9S+85L 9S+85L Figure S1 Comparison of voltages measured and calculated when optical filters were used. The measured voltages are normalized to the voltage obtained without using any filters. The calculations were carried out with Eq. (S8). ###S(L) denotes a ###-nm short-pass (long-pass) filter..9-m YIG denotes the same sample as described in Fig. and Fig. 3a. 1.-m YIG denotes a 5.8-mm-long, 1.8-mm-wide (. nm)/yig(1. m)/ggg(. mm) sample. The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig. b. NATURE PHYSICS www.nature.com/naturephysics 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 SUPPLEMENTARY INFORMATION experimentally measured filter transmission (see Figs. d, e, and f), and is theoretically calculated using DFT (see Fig. 5c). One can see that the measured voltages match very well with the calculated voltages for the majority of the different filter configurations. What s more, such matching is true for both of the two samples. One important point should be made about the above experiment/theory comparison - if one shifts the peak center of the profile from.7 ev to 1.3 ev, the level of the agreement between the calculated and measured voltages decreases notably, as shown in Fig. S. Specifically, Figure S gives three sets of voltage values calculated using three different profiles: (1) the actual DFT result as presented in Fig. 5c in the text, () a Gaussian profile that best fits the main peak of the DFT result which is centered at.7 ev and has a width of.5 ev, and (3) a Gaussian profile that is the same as () but with its center shifted to 1.3 ev. While the agreement between the experimentally measured voltages and the theoretically calculated voltage values are satisfactory for both cases (1) and (), it is much worse for case (3). This result clearly indicates the importance of having the correct data of the absorption spectra. This result together with that shown in Fig. S1 indicates the strong dependence of the PSV effect on the band structure of the or, more explicitly, the strength of spin-orbit coupling in the. The results from Figs. S1 and S also indicate the critical wavelength range for the PSV effect in the / system which should be around 18 nm (.7 ev). This agrees with the experimental observation presented in Fig., namely, that there exists a narrow wavelength range over 1- nm that is critical for the PSV effect. This agreement, together with the facts that the layer-caused reduction in the transmission of the sample is almost constant over the entire range and the light-on- configuration yields weaker PSV signals than the light-on- configuration, provides an evidence that the PSV effect mainly stems from an optical effect, not a thermal effect, when illuminated by the halogen lamp. In case - 1..8... DFT calculation Assumed a peak at.7 ev Assumed a peak at 1.3 ev. 1 3 Photon energy (ev) a Voltage (%) 1 9 8 7 5 3 1 b 55L 59L 95L 8L 85L 9L 95L 1S 95S 9S 8S 7S 1S+85L 1S+59L 1S+9S 59L+85L 59L+9S 9S+85L 1S+59L+85L 1S+59L+9S 59L+9S+85L 1S+59L+9S+85L DFT calculation Assumed a peak at.7 ev Assumed a peak at 1.3 ev Experimental data Figure S Wavelength characteristics of the PSV effect. a, profiles, which are the difference between the imaginary parts of dielectric functions for the spin-up and spin-down channels. The green profile was obtained by DFT calculations and is the absolute value of the value shown in Fig. 5c in the text. The light-blue profile shows a Gaussian profile that fits the main peak of the green profile centered at.7 ev. The light-red profile shows a Gaussian profile that is the same as the light-blue profile but with the peak center shifted to 1.3 ev. b, Comparison of voltages measured and calculated when optical filters were used. The measured voltages are normalized to the voltage obtained without using any filters. ###S(L) denotes a ###-nm short-pass (long-pass) filter. The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig. b in the text, and the sample was a 5.8-mm-long, 1.8-mm-wide (. nm)/yig(1. m)/ggg(. mm) structure. The calculations were carried out using Eq. (S8) in the text and the three profiles given in a. NATURE PHYSICS www.nature.com/naturephysics 5 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 that light-induced heating plays an important role, one would expect that the layer cause a larger reduction in the optical transmission at a relatively narrow range centered at about 18 nm, and the voltage signals for the light-on- configuration should be stronger than those for the light-on- configuration.. Light-Induced Heating It is known that the efficiency of the light-induced heating somewhat depends on the product of and E (photon energy). This product was calculated from the band structure of, as given in Fig. S3b. One can see a broadband response in the.5-3 ev range (or 1-5 nm in wavelength). The broadband behavior of E is in contrast to the peak behavior of the spectrum shown in Fig. S3a. Two important points should be made about the results shown in Fig. S3b. First, the results indicate that the maximal heating efficiency should occur at the photon energy of about.98 ev (17 nm), but the experimental data clearly indicate that the critical wavelength is not there. Second, the results also indicate that the heating efficiency at. ev ( nm) should be large, but the experimental data show that the measurements using a white LED source ( nm) yielded very weak PSV signals. These two facts provide additional support to the conclusion that heating effect is weaker than the PSV effect in the experiments in this work. -5 a 5 b - - -3 - -1 ( + )E (a.u.) 3 1 1 1 3 Figure S3 Calculated E profiles. a, " profile. b, E profile. and are the imaginary parts of dielectric functions for the spin-up and spin-down channels, respectively, and E is the photon energy. The and data were obtained through density function theory calculations and are the same as those used to Photon energy E (ev) calculate presented in Fig. Sa. -1 1 3 Photon energy E (ev) 7. Photo-Spin-Voltaic Effect vs. Spin Seebeck Effect There had been previous experiments on using light to create a temperature gradient and thereby realize the SSE.,11,1,13 Those experiments also used / structures, the same as in this work. It is possible that the SSE and the PSV effect occur simultaneously in a / structure upon exposure to light. When the temperature difference across the sample thickness (T t) is very small, one can expect that the PSV effect overwhelms the SSE and the measured voltage signals resulted mainly from the PSV effect. This is exactly the case in this work, where the experimental setup was constructed to minimize T t. When T t is relatively large, the SSE is dominant, which is the case studied in Refs. [,11-13]. Note that in the experiments reported in Refs. [11,1,13] the SSE might be the only effect because the wavelength of the NATURE PHYSICS www.nature.com/naturephysics 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 SUPPLEMENTARY INFORMATION Voltage (V) Voltage (V)... a. PSV only b. PSV & SSE c. SSE only -. - - 5 1 15... T t T t Voltage (V) Voltage (V)... - - - -. -. -. - - - 5 1 15 5 1 15 5 1 15 Figure S Comparison between PSV- and SSE-produced voltage signals. a and b present the voltage and temperature Tt signals measured without and with the use of a heat sink, respectively, where Tt is the temperature difference measured across the sample thickness. The sample and measurement configurations were almost identical to those described for the data in Fig. c in the text, and for all the measurements the light was turned on at t=5 s and then off at t=1 s. The situation in a corresponds to a regime where Tt is very small and the PSV effect overwhelms the SSE. The situation in b corresponds to a regime where Tt is relatively large due to the use of a heat sink and the PSV effect and the SSE take place simultaneously and both contribute to the voltage signals. c presents the SSE voltage signals which were obtained by subtracting the PSV voltage signals in a from the voltage signals b. The temperature signals in c are the same as presented in b. laser used for heating is far shorter than the critical wavelength range identified in this work and the PSV effect might be completely absent. In a regime where T t is neither very small nor very large, the two effects coexist. This situation is shown in Fig. S. On can see from the data in Fig. S that, different from the PSV effect, the SSE voltage signal flips its sign when the light illumination direction is reversed, and the SSE voltage varies with time in the same manner as T t. These results evidently confirm that the PSV effect is essentially different from the SSE. Note that it has been studied previously that the SSE voltage vs. time responses should follow the T t vs. time response.,13 It is possible that upon the exposure of a / sample to light, the light absorption raises the temperature of the electrons in the and thereby quickly triggers imbalance among electron, phonon, and magnon systems at the interface, potentially leading to an interface-related SSE. It is believed that such an interface SSE should be weak in the experiments in this work, because it is a thermal effect and should not depend on the wavelength of light, while the observed voltage signals exhibit strong wavelength dependence, as shown in Figs., 5, and S1. The interface SSE is expected to be weak because the exchange of angular momentum between hot electrons (and holes) and quasiparticles (magnons and phonons) is low due to their large energy mismatch. The hot electrons have an energy of a few tenth ev, while the magnons and phonons have an energy of a few mev only. What s more, even though the hot electrons may interact with the magnons, this interaction would have weak spin dependence due to the high energy of the hot electrons. Besides, the current SSE theory is based on the quasi-equilibrium of magnon, phonon, and electron systems; and in the theory both the temperatures and their gradients are well defined. 1 This is not applicable to the PSV effect, for which the electrons in the are far from their Sink -. - - 5 1 15... Sink T t T t Voltage (V) Voltage (V)... Sink -. - - 5 1 15... Sink T t T t NATURE PHYSICS www.nature.com/naturephysics 7 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 equilibrium state and the temperature of electrons is not defined. Of course, the spin-selective reflection of hot electrons from the / interface may also contribute to spin currents in the. There are three additional notes that should be made. First, the wavelength characteristics of the PSV effect results from the energy dependence of the light-induced hot electron excitation. The spin-orbit coupling in the that converts spin currents to charge currents is energy independent, just as in the SSE. Second, for the SSE voltage signal presented in Fig. S, the physical process involves lattice-heated electrons, not the hot electrons directly excited by light. Those heated electrons have lower energy than the hot electrons. Finally, there might exist a charge current across the thickness of the layer at the onset of illumination, due to the different diffusion properties of the excited hot electrons and holes. However, this current, if present, should be transient because there is no complete circuit for it to flow in. For this reason, the PSV-produced spin current is not a spin-polarized electron current, but a pure spin flow, and there is neither the ordinary Hall effect nor the anomalous Hall effect in the structure. References 1 R. C. Linares, Epitaxial growth of narrow linewidth yttrium iron garnet films, J. Cryst. Growth 3, 3- (198). T. Liu, H. Chang, V. Vlaminck, Y. Sun, M. Kabatek, A. Hoffmann, L. Deng, and M. Wu, Ferromagnetic resonance of sputtered yttrium iron garnet nanometer films, J. Appl. Phys. 115, 17A51 (1). 3 H. Chang, P. Li, W. Zhang, T. Liu, A. Hoffmann, L. Deng, and M. Wu, Nanometer-Thick Yttrium Iron Garnet Films With Extremely Low Damping, IEEE Magn. Lett. 5, 71 (1). P. Li, D. Ellsworth, H. Chang, P. Janantha, D. Richardson, F. Shah, P. Phillips, T. Vijayasarathy, and M. Wu, Generation of pure spin currents via spin Seebeck effect in self-biased hexagonal ferrite thin films, Appl. Phys. Lett. 15, 1 (1). 5 P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 5, 17953-17979 (199). G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758-1775 (1999). 7 G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci., 15-5 (199). 8 G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 5, 1119-1118 (199). 9 J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 385-388 (199). 1 J. L. P. Hughes and J. E. Sipe, Calculation of second-order optical response in semiconductors Phys. Rev. B 53, 1751-173 (199). 11 M. Weiler, M. Althammer, F. D. Czeschka, H. Huebl, M. S. Wagner, M. Opel, I.-M. Imort, G. Reiss, A. Thomas, R. Gross, S. T. B. Goennenwein, Local Charge and Spin Currents in Magnetothermal Landscapes, Phys. Rev. Lett. 18, 1 (1). 1 M. Agrawal, V. I. Vasyuchka, A. A. Serga, A. Kirihara, P. Pirro, T. Langner, M. B. Jungfleisch, A. V. Chumak, E. Th. Papaioannou, B. Hillebrands, Role of bulk-magnon transport in the temporal evolution of the longitudinal spin-seebeck effect, Phys. Rev. B 89, 1 (1). 8 NATURE PHYSICS www.nature.com/naturephysics 1 Macmillan Publishers Limited. All rights reserved.

DOI: 1.138/NPHYS3738 SUPPLEMENTARY INFORMATION 13 N. Roschewsky, M. Schreier, A. Kamra, F. Schade, K. Ganzhorn, S. Meyer, H. Huebl, S. Geprägs, R. Gross, S. Goennenwein, Time resolved spin Seebeck effect experiments, Appl. Phys. Lett. 1, 1 (1). 1 J. Xiao, G. E. W. Bauer, K. Uchida, E. Saitoh, and S. Maekawa, Theory of magnon-driven spin Seebeck effect, Phys. Rev. B 81, 118 (1). NATURE PHYSICS www.nature.com/naturephysics 9 1 Macmillan Publishers Limited. All rights reserved.