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Spin pumping with coherent elastic waves

We show that the resonant coupling of phonons and magnons can be exploited to generate spin currents at room temperature. Surface acoustic wave (SAW) pulses with a frequency of 1.55 GHz and duration of 300 ns provide coherent elastic waves in a ferromagnetic thin film/normal metal (Co/Pt) bilayer. We use the inverse spin Hall voltage in the Pt as a measure for the spin current and record its evolution as a function of time and external magnetic field magnitude and orientation. Our experiments show that a spin current is generated in the exclusive presence of a resonant elastic excitation. This establishes acoustic spin pumping as a resonant analogue to the spin Seebeck effect.

We show that the resonant coupling of phonons and magnons can be exploited to generate spin currents at room temperature. Surface acoustic wave (SAW) pulses with a frequency of 1.55 GHz and duration of 300 ns provide coherent elastic waves in a ferromagnetic thin film/normal metal (Co/Pt) bilayer. We use the inverse spin Hall voltage in the Pt as a measure for the spin current and record its evolution as a function of time and external magnetic field magnitude and orientation. Our experiments show that a spin current is generated in the exclusive presence of a resonant elastic excitation. This establishes acoustic spin pumping as a resonant analogue to the spin Seebeck effect.
The generation and detection of pure spin currents is vigorously investigated for the injection and transportation of spin information [1][2][3][4][5][6] . Spin currents may be generated, e.g., via the spin Seebeck effect 7-10 , or via spin pumping 6,[11][12][13][14][15][16] . In the latter approach, electromagnetic waves in the GHz regime, i.e., microwave photons are used to resonantly excite magnetization dynamics in a ferromagnet (FM) and thus drive a spin current into an adjacent normal metal (N). Here we show that the resonant absorption of elastic waves, i.e., microwave phonons in a FM/N bilayer can be used to acoustically drive a spin current. This establishes the spin current generation by a resonant phonon-magnon coupling and thus an interaction of lattice and spin degrees of freedom. In this sense, acoustic spin pumping can be seen as a resonant analogue of the spin Seebeck effect 17 . This resonant magnon-phonon coupling is a complementary approach to the non-resonant acoustic spin-current generation recently observed by Uchida et al. 18 in a ferromagnetic insulator. In particular, we use a metallic ferromagnet and are able to tune the system in and out of acoustically driven ferromagnetic resonance via the application of an external magnetic field. As shown in the following, we find clear evidence for a resonant spin current generation. However, within the experimental sensitivity limit, we do not observe a spin current in the off-resonant condition. Our findings are thus in accordance with conventional, photon-FMR-driven, spin pumping experiments. The resonant phonon-spin current conversion discussed in this letter opens intriguing perspectives for applications in, e.g., microelectromechanical systems (MEMS), since elastic deformation can now be used for spin current generation. Thus, phonon-driven spin pumping is a pathway for the resonant generation of a spin current in the absence of a real, external electromagnetic driving field. Furthermore, phonon-driven spin pumping can be disentangled from microwave rectification effects induced by free space electromagnetic waves [19][20][21]  (FMR) 24 in ferromagnet/normal metal bilayers. The acoustic FMR is excited by a surface acoustic wave (SAW) propagating in a cobalt/platinum (Co/Pt) thin film bilayer in the presence of an externally applied, static magnetic field. Via inverse magnetostriction 25 , the SAW induces magnetization dynamics in the Co thin film which in turn generate a spin current at the Co/Pt interface. The sample is depicted schematically in Fig. 6(a). It consists of a Co (10 nm)/Pt (7 nm) bilayer deposited on LiNbO 3 between two Al (70 nm) interdigital transducers (IDTs) 26 with a periodicity of 20 µm. For all results shown in this letter, the acoustic delay line shown in Fig. 6(a) is operated at its 9 th harmonic frequency ν = 1.548 GHz at room temperature. A SAW is launched at the input IDT and induces a time varying pure lattice strain ε(t) = ε cos(2πνt) along x with amplitude ε into the ferromagnet 27 . Via magnetoelastic coupling, ε(t) excites magnetization M precession as depicted schematically in Fig. 6(b). The magnetization precession can relax via the emission of a spin current J s into the normal metal (Pt) 12 . We detect J s along z via the inverse spin Hall effect 22 , which results in an electric field E ISH ∝ M × J s . More precisely, we measure V DC ∝ E ISH · y (cf. Fig. 6(b)). The input IDT generates not only a SAW but also an electromagnetic wave (EMW) upon the application of a rf voltage. Thus, the aforementioned microwave rectification effects can contribute significantly to V DC . However, since the velocity of the SAW (the speed of sound) is about five orders of magnitude slower than that of the EMW (the speed of light), a time resolved study of V DC and the transmitted SAW power P IDT allows for a separation of SAW and EMW driven effects. We thus apply SAW pulses as depicted in Fig. 6(c) and study the time dependent evolution of V DC and P IDT using a two channel oscilloscope. For the generation of the SAW pulses we apply +30 dBm rf pulses with ν = 1.548 GHz, a pulse width t w = 310 ns and a pulse period t r = 57.3 µs to the input IDT. By studying P IDT (t) and V DC (t) for various external magnetic field H orientations and magnitudes we can unambiguously identify phonon driven spin-pumping as shown in the following.
We first turn to the separation of contributions to P IDT and V DC due to the SAW and the EMW. In Fig. 2(a) we show the transmitted rf power P IDT as a function of time t for application of H at α = 10 • . As the SAW has a velocity of 3440 m/s and the sample features a center to center IDT spacing of 1.8 mm, the SAW transit time is t t = 0.52 µs. In contrast, the EMW propagates with the speed of light and is thus expected to appear almost instantaneously with the microwave pulse at t ≈ 0. Indeed, in the P IDT (t) trace shown in Fig. 2(a), two signals are observed, the first of which begins at t ≈ 0 and is attributed to the EMW. The rectangular shape and duration mimics the applied microwave pulse. At t SAW = 0.7 µs a Gaussian pulse of smaller magnitude is recorded. This pulse is due to the SAW reaching the output transducer. The separation of EMW and SAW pulses allows us to distinguish between photon and phonon driven contributions to P IDT (t). We now turn to the external magnetic field dependence of P IDT shown in Fig. 2 Here we plot ∆P IDT = P IDT (µ 0 H) − P IDT (µ 0 H ref ). We use µ 0 H ref = 30 mT as reference magnetic field and investigate data obtained at the FMR magnetic field µ 0 H res = ±4 mT (dashed and dotted line, respectively). For both values of H, one observes a pronounced dip in ∆P IDT at t SAW . This SAW attenuation is attributed to acoustically driven FMR, which results in a damping of the SAW as detailed in Ref. 24 . We now turn to the simultaneously recorded voltage V DC (t) in the Co/Pt bilayer. Since the latter is positioned at a distance of d MSP = 1.3 mm from the input IDT, the SAW pulse is expected to reach the bilayer 0.1 µs before it is detected at the output IDT. This yields a maximum SAW amplitude at the bilayer at t MSP = 0.6 µs, while the EMW is again expected at t ≈ 0. For Fig. 2(c), dominated by EMW driven effects as evident from its time dependence and shape. In particular, no signal is observed at t MSP . This is not surprising, since no acoustic FMR and thus no spin current is excited for these parameters. In contrast, the FMR condition is fulfilled at µ 0 H res = ±4 mT. In Fig. 2  a spin current via the inverse spin Hall effect 15 . In contrast, the EMW causes a field-symmetric contribution to ∆V DC , which means that no EMW driven spin-pumping is observed.
The contributions to ∆P IDT and ∆V DC due to the SAW and EMW are now investigated as a function of H. We hereby take advantage of the separation of the SAW and EMW in the time domain and attribute ∆P IDT (0.2 µs) and ∆V DC (0.2 µs) to the interaction of the bilayer with the EMW and ∆P IDT (0.7 µs) and ∆V DC (0.6 µs) to the interaction of SAW and bilayer. Figure 3(a) shows ∆P IDT (µ 0 H) for both elastic and electromagnetic interaction. We find a very weak magnetic field dependence of the transmission of the EMW (solid symbols) which shows no indication for FMR driven by the EMW. We however observe a distinct resonant absorption of the SAW (open symbols) which we attribute to acoustically driven FMR 24 . Turning to ∆V DC shown in Fig. 3(b), we in contrast observe a sizeable magnetic field dependence of the EMW transmission at t = 0.2 µs (solid symbols) attributed to microwave rectification effects 20 . The signal shape however is distinctly different from that expected for the spin pumping effect, in particular no reversal of the sign of ∆V DC with reversal of H direction is observed. A detailed investigation of the origin and evolution of ∆V DC due to EMW rectification is beyond the scope of this work. We refer to Refs. 28,29 . At t MSP = 0.6 µs (open symbols) however, only the SAW pulse is present. Here, ∆V DC shows a magnetic field dependence characteristic for spin pumping, in particular featuring a sign reversal with reversal of H direction and extrema at the FMR H field. We furthermore checked whether rf currents induced by the SAW E-Field into the Co/Pt could cause ∆V DC (0.6 µs).
To this end, we deliberately applied such rf currents with ν = 1.548 GHz to the bilayer 30 , which resulted in a dc photovoltage V pv attributed to rectification effects 28,29,31 and spin-torque FMR 32 . As detailed in the supplementary information 30 , the magnetic field dependence of V pv is distinctly different to that of ∆V DC (0.6 µs). We thus attribute ∆V DC (0.6 µs) solely to elastically driven spin pumping.
To show the crucial separation of EMW and SAW driven contributions (∆V DC (EMW) ≫ ∆V DC (SAW)) in a more complete fashion, we plot ∆P IDT and ∆V DC as a function of t and µ 0 H in Fig. 4(a) and (b), respectively (only magnetic field upsweep shown). EMW rectification is observed for t < 0.375 µs yielding a fieldsymmetric contribution to ∆V DC . For the times corresponding to the presence of the SAW pulse, both ∆P IDT and ∆V DC are finite only for a narrow range around the FMR magnetic field µ 0 H res = ±4 mT. One can observe that ∆P IDT is retarded by about 0.1 µs with respect to ∆V DC (indicated by the dashed lines), in accordance to the propagation of the SAW along the delay line. For the investigation of phonon-driven spin pumping with good signal to noise ratio, we average ∆P IDT and ∆V DC for the time range indicated by the dashed lines. This yields the phonon-driven ∆P SAW and ∆V MSP , respectively. ∆P SAW and ∆V MSP are plotted in Fig. 4(c) as a function of H (solid symbols: H upsweep, open symbols: H downsweep). While a field symmetric absorption of rf power is observed for ∆P SAW as expected for acoustically driven FMR 24 , ∆V MSP shows the antisymmetric behavior with respect to H orientation reversal characteristic of spin pumping. Furthermore, the resonance field and linewidth of ∆P SAW and ∆V MSP coincide. Outside of acoustically driven FMR (i.e. µ 0 |H| > 10 mT), the SAW and thus phonons are still present in the ferromagnetic thin film. However, within the resolution of our experiment, ∆V MSP = 0 in this off-resonant condition.
Using the scaling law derived in Ref. 15 , we can calculate the resonant M precession cone angle Θ res as: with the elementary charge e, the ellipticity P = 0.11 calculated according to Ref. 21 , the resistance R = 37 Ω 33 and width w = 375 µm of the Co/Pt bilayer, the constant C = 4.37 × 10 −11 m 15 and the spin mixing conductance of Co/Pt g ↑↓ = 6 × 10 19 /m 215 . With ν = 1.548 GHz and ∆V MSP = 0.8 µV from Fig. 4(c), Eq. (1) yields Θ res = 1.6 • , comparing well to values found for photon driven FMR in Co 15 . Out of resonance ∆V MSP < 0.1 µV and hence the M precession cone angle is θ < 0.6 • assuming identical P . Using Θ res = 1.6 • , the strain caused by the SAW corresponds to a rf virtual driving field of µ 0 h ME = 1 2 µ 0 ∆HΘ res = 73 µT with µ 0 ∆H = 5.25 mT extracted from Fig. 4(c) as the FWHM of ∆V MSP at resonance. Note that this linewidth is just an estimate since the lineshape of acoustic FMR can deviate from a simple Lorentzian due to the particular properties of the magnetoelastic driving field 24,30 . For acoustically driven FMR, h ME is determined by the magnetic free energy density of the ferromagnetic Co film by 24 where B 1 = 18 MJ/m 334 is the magnetoelastic coupling constant of Co, M s = 1.17 × 10 6 A/m 35 the saturation magnetization and ϕ 0 = 30 • the equilibrium orientation of M for H applied at α = 10 • calculated using the free energy approach detailed in Ref. 24 . Equation (2) yields a strain ε ≈ 5.7 × 10 −6 in the ferromagnet due to the SAW pulse. In an independent experiment, we determined the SAW acoustic power P acoustic = 1 mW by vector network analysis on the input IDT, resulting in a pure strain ε = 9.8 × 10 −6 along x 30 . Thus, according to this order of magnitude estimation, the calculated SAW strain is large enough to account for ∆V MSP by elastic spin pumping.
The characteristic fingerprint of acoustically driven FMR is its dependence on the orientation α of the externally applied magnetic field 24 . Therefore, we recorded ∆P IDT (t) and ∆V DC (t) for −35 • ≤ α ≤ +35 • (Fig. 5). Fig. 5(a) shows the butterfly angular dependency of ∆P SAW characteristic for acoustically driven FMR. In Fig. 5(b), we observe a finite ∆V MSP only for values of α and H where the acoustically driven FMR condition is met, providing further evidence for phonon-driven spinpumping.
In conclusion, we have shown that a spin current can be generated by microwave phonons via rf magnetoelastic interaction in a Co/Pt thin film bilayer. By recording both, the generated inverse spin Hall voltage proportional to the spin current, and the SAW transmission as a function of time for various configurations of the externally applied magnetic field, we are able to discern between effects caused by photonic and phononic excitations. We find that a spin current is generated in the exclusive presence of an acoustic excitation of the Co thin film. This should enable the implementation of, e.g., microelectromechanical systems (MEMS) with the possibility to elastically generate spin current for future spintronic data processing applications. From a fundamental physics point of view our results are an important step towards the study of the interconversion of phononic and spin degrees of freedom.
Financial support from the DFG via GO 944/4-1, SPP 1538 and the German Excellence Initiative via the Nanosystems Initiative Munich (NIM) is gratefully acknowledged. Vt shows a dependence on ϕ0 which is distinctly different than that of VMSP.
Appendix A: DC voltage due to spin rectification and spin-torque effects Surface acoustic waves (SAWs) travelling in piezoelectric substrates such as LiNbO 3 are accompanied by an electric potential 36 in addition to the mechanical displacement. The surface electrical potential of a SAW can be electrically shorted by a conductive thin film which results in a radio frequency (rf) current in the film. In our elastic spin pumping experiments (see main text), such SAW-induced rf currents in the conductive Co/Pt bilayer may give rise to dc voltages due to various mechanisms that result in resonant as well as non-resonant downmixing of the rf current 28,29,31,32 . These rectification voltages may superimpose with the inverse spin Hall effect voltage V MSP used to probe the acoustically driven spin current.
To check wether such effects need to be considered in the interpretation of our V MSP data, we intentionally exposed the Co/Pt bilayer to rf electrical currents and recorded the resulting dc voltages. To this end, the sample introduced in the main text was used. The Co/Pt bilayer was connected to a bias tee as schematically shown in Fig. 6(a) to enable the detection of dc voltages caused by the rf current applied along the y axis by means of a microwave source (Rohde & Schwarz SMB100A) which was operated in continuous wave mode. A Keithely K2182 Nanovoltmeter was used to record the dc photovoltage V pv .
Following the basic idea detailed in Ref. 32 , a rf current I rf (t) = I rf,0 cos(ωt) ·ê along directionê in the Pt causes an Oersted field h 1 (t) ⊥ I rf (t) in the Co thin film. The Oersted field induces magnetization M precession if the condition for ferromagnetic resonance is met. This causes an oscillation of the bilayer resistance due to the anisotropic magnetoresistance (AMR) 37,38 . Mixing of this resistance with the rf current yields a dc voltage. The voltage may be caused by an oscillation of the longitudinal or the transversal (planar Hall) resistance. As we only measure the voltage drop along y we need to consider the longitudinal resistance for I rf y and the transversal resistance for I rf x.
For I rf y, a voltage drop along y will be due to the longitudinal resistance where ϕ(t) is the angle enclosed between M and x, ∆R = R − R ⊥ and ∆R/R ≈ 2% in Co 37 . We define ϕ(t) = ϕ 0 + Θ(t) with the equilibrium M orientation ϕ 0 and the dynamic small angle M precession Θ(t) around ϕ 0 . To first order in Θ we get We approximate Θ(t) = cos(ωt + η) sin(ϕ 0 )Θ res for the magnetization precession, where the factor sin(ϕ 0 ) accounts for the fact that only the component of h 1 perpendicular to M can drive the precession and η is the phase between driving field and M precession. We thus find the time averaged longitudinal voltage V l = R l (t)I rf (t) = V pv = ∆RΘ res cos ηI rf,0 sin 2 ϕ 0 cos ϕ 0 , in accordance with the angular dependence of the mixing voltage defined in Eq. (2) in Ref. 32 . The normalized magnitude of V l is plotted in the polar plot in Fig. 6(b) for η = 0 • . Thereby, the sign of V l is indicated by the shading. V l bears a similar symmetry as observed in V MSP (see Fig. 5(b) in the main text). Thus, dc effects due to a rf current along y need to be taken into account for the analysis of our elastic spin pumping data. This point will be addressed in more detail in Section C.
We now turn to a voltage drop along y induced by I rf x. This transversal voltage is caused by the transversal resistance Following the same line of argument as for R l (t), but with Θ(t) = cos(ωt + η) cos(ϕ 0 )Θ res we find V t = 1 2 ∆RΘ res cos ηI rf,0 cos(2ϕ 0 ) cos ϕ 0 , which is depicted in the polar plot in Fig. 6(c) for η = 0 • . The magnitude of this dc voltage is maximal for ϕ 0 = 0 • and its symmetry is more complex than that observed in V MSP (see Fig. 5(b) in the main text). Thus, we can exclude rectification voltages due to rf currents along x as a contribution to V MSP due to their dependence on the orientation of the external magnetic field H which is significantly different to that observed in V MSP (see main text). This leaves rectification voltages due to I rf y. In the following, we experimentally demonstrate that latter bear a distinctly difference dependence on the magnitude of H which results in different lineshapes of V MSP and V pv .

Appendix B: Experimental determination of dc photovoltage
We performed an rf impedance measurement by vector network analysis on the bilayer from which we obtained the rf current density i rf = 1.6 × 10 9 A/m 2 in the Co/Pt bilayer at a power level P = +17 dBm and ν = 1.548 GHz. To demonstrate the rectification of rf currents, we determined V pv as a function of the external magnetic field magnitude µ 0 H applied at α = 10 • for 1.548 GHz ≤ ν ≤ 5.948 GHz. The measured dc photovoltage V pv is displayed in Fig. 7 for selected rf frequencies. At the highest rf frequency ν = 5.948 GHz, two dominantly antisymmetric Lorentzian lines are observed at ±37 mT. These lines shift to smaller magnitudes of the external magnetic field with decreasing rf frequency. Following Ref. 32 , we attribute these lines to the mixing signal caused by the torques due to the Oersted field of the rf current in the Pt layer and the spin transfer torque due to the spin current caused by the spin Hall effect. Furthermore, as particularly evident at lower frequencies, a hysteretic contribution to V pv is observed around zero external magnetic field. This contribution is dominant at ν = 1.548 GHz and is attributed to nonresonant spin rectification 31 . The dc voltage V pv along the bilayer was proportional to the square of the rf current density in accordance to expectations 28,32 . main text). Fig. 8(a) shows ∆V MSP (left scale, squares) and −V pv (right scale, circles), both determined with an rf frequency ν = 1.548 GHz and the external magnetic field applied at α = 10 • . The extrema in V pv and ∆V MSP are located at different values of µ 0 H. Furthermore, the lineshapes are different, which in particular results in a finite V pv at |µ 0 H| ≥ 10 mT, where ∆V MSP vanishes. V pv shows a dominant hysteretic feature around zero external magnetic field while hysteresis in ∆V MSP is minimal. This clearly shows that ∆V MSP and V pv have different physical origins. We moreover note that the extrema in the acoustic FMR signal ∆P SAW (cf. Fig. 4(c) in the main text) do not necessarily coincide with the conventional ferromagnetic resonance field since the magnetoelastic driving field characteristically depends on M orientation 24 . As experimentally observed (cf. Fig. 4(c) in the main text), the extrema of ∆V MSP and ∆P SAW coincide -as expected for acoustic spin pumping. However, the extrema in ∆V MSP are not necessarily located at the conventional FMR magnetic field observed in V pv . This is particularly evident from Fig. 8(b), where we show ∆V MSP and V pv recorded with α = 2.5 • (only magnetic field upsweep shown). The FMR field expected from the Kittel mode coincides with the inflection points in V pv at approximately µ 0 H res ≈ ±7 mT (marked by the arrows). The extrema in ∆V MSP are however located at µ 0 H ≈ ±3 mT (marked by the vertical lines). This is expected for acoustically driven FMR, since in this case the absorbed power and thus the spin pumping signal is given by V MSP ∝ P ∝ h 2 ME χ 24 , where χ is the susceptibility and h ME the magnetoelastic driving field. Depending on the anisotropy of the ferromagnet, the magnitude of h ME depends on H, in particular for low external magnetic fields. Therefore, the product h 2 ME χ is not necessarily maximized at the extrema of χ. This is the reason for the apparent discrepancy between FMR field and ∆V MSP extrema visible in Fig. 8(b). This furthermore proves that V MSP is not caused by any rectification ef-fects in the bilayer, as these would occur exactly at the conventional ferromagnetic resonance field.
In conclusion, the experiments with deliberately applied rf currents I rf show that V MSP is not caused by microwave rectification of I rf induced by the surface acoustic wave. For I rf x, rectification effects can not be the origin of V MSP due to their different dependency on the orientation of H. For I rf y, we experimentally demonstrated that the resulting rectification voltage V pv has a distinctly different lineshape than V MSP . Again, rectification effects due to I rf y thus can not account for V MSP observed.
Reversing this argument, we have experimentally shown that rf currents in the bilayer indeed give rise to rectification voltages at the conventional FMR field. The absence of a corresponding signal in V MSP indicates that SAW-induced currents in the Co/Pt bilayer can safely be neglected in the interpretation of V MSP .