Direct detection of pure spin-current by x-ray pump-probe measurements. Abstract

Transcription

1 Direct detection of pure spin-current by x-ray pump-probe measurements J. Li, 1 L. R. helford, 2 P. hafer, 3 A. Tan, 1 J. X. Deng, 1 P.. Keatley, 2 C. Hwang, 4 E. Arenholz, 3 G. van der Laan, 5 R. J. Hicken, 2 and Z. Q. Qiu 1 1 Dept. of Physics, Univ. of California at Berkeley, Berkeley, CA 9472, UA 2 Department of Physics and Astronomy, University of Exeter, tocker Road, Exeter, Devon, EX4 4QL, United Kingdom 3 Advanced Light ource, Lawrence Berkeley National Laboratory, Berkeley, CA 9472, UA 4 Korea Research Institute of tandards and cience, Yuseong, Daejeon 35-34, Republic of Korea 5 Magnetic pectroscopy Group, Diamond Light ource, Didcot, Oxfordshire, OX11 DE, United Kingdom Abstract Just like an electric current represents a flow of electron charge, a spin current represents a flow of electron spin (angular momentum). 1,2,3 Following the great success of charge-current based electronic technology, it is believed that spin-current based spintronics will be the next-generation information technology. 4 Despite great progress in spin-current research in the last decade, the observation of spin current has remained indirect, being measured through the effect of the spin current on other physical entities. These indirect measurements have led to many ambiguities and even controversy because of the mixture of spin current with other effects. It has become extremely important to detect spin current directly in order to further develop spintronics research. By synchronizing a microwave waveform with the synchrotron x-ray pulses, we use the ferromagnetic resonance (FMR) of the (Ni 81 Fe 19 ) layer in a /Cu/Cu 75 Mn 25 /Cu/ multilayer to pump a pure spin current into the Cu 75 Mn 25 spacer layer, and then directly probe the spin current in the Cu 75 Mn 25 layer by a time-resolved x-ray magnetic circular dichroism (XMCD). This element-specific pump-probe measurement unambiguously identifies the AC spin current in the Cu 75 Mn 25 layer. In addition, phase resolved x-ray 1

2 measurements reveal a characteristic bipolar phase behavior of the spins that is a fingerprint of spin-current driven spin precession. 2

3 The concept of spin current is of central importance in spintronics research, having grown from the realization that a spin polarized electrical current carries not only electron charge but also electron spin (angular momentum) that can exert a spin transfer torque. 1,2,3 Just as charge current is responsible for the operation of electronic devices, spin current could be utilized to switch local magnetic moments in future spintronic devices. 5 Great progress has been made in the last decade by separating the spin current from the charge current, thus opening the opportunity for spintronics based on pure spin current with low energy dissipation. 6 In comparison to the rapid progress made in generating spin currents by various methods, such as electrical spin injection and accumulation, 7 and the spin Hall effect, 8, 9 the detection of a pure spin current has remained mostly indirect, being achieved through measurement of effects induced by the 1, 11 spin current such as spin-torque driven magnetization precession, spin-current induced second-harmonic optical effects, 12 and the inverse spin Hall effect (IHE), 13,14,15 etc. uch indirect measurements of spin currents may be influenced by induced magnetic order in the nonmagnetic layer at the inteace which could result in ambiguous or even contradictory interpretations. 16,17,18,19,2,21,22,23 An attempt to directly measure a spin current in a nonmagnetic material by monitoring the spin polarization near the Fermi level yielded a negative result within the measurement sensitivity. 24 Instead of focusing on the DC spin current, it was recently proposed that a spin current pumped by the coherent precession of a ferromagnet [e.g., ferromagnetic resonance (FMR)] carries not only a time-averaged DC spin current but also a much larger AC spin current. 25 Although FMR studies have successfully demonstrated the creation of a pure spin current by spin precession in ferromagnetic(fm)/non-magnetic(nm) multilayers 11,26,27, the AC spin current was not observed directly. Recently it was suggested that an AC spin current may generate an AC voltage by means of the IHE. 28,29,3 However, electrical inductance effects made it difficult to unambiguously identify the voltage component induced by the AC spin current. With all the controversy surrounding the measurement of spin current, it has become extremely important to make a direct observation of the pure spin current 3

4 (e.g., a direct measurement of the spin polarization of a pure spin current in a nonmagnetic medium). In this paper, we report an experimental study of a /Cu/Cu 75 Mn 25 /Cu/ multilayer system. A pure spin current was pumped into the Cu 75 Mn 25 layer by exciting FMR of the ferromagnetic layer at 4 GHz. By locking a microwave waveform (pump) with train of synchrotron x-ray pulses (probe), we realized stroboscopic pump-probe measurements of x-ray magnetic circular dichroism (XMCD) and unambiguously identified the AC spin precession of the spin current in the nonmagnetic Cu 75 Mn 25 spacer layer. In addition, phase-resolved spin precession measurements revealed a characteristic bipolar phase behavior of the spins that is a fingerprint of spin-current driven spin precession. The experiment was carried out at the Advanced Light ource (AL) of the Lawrence Berkeley National Laboratory. The x-rays from the AL consist of x-ray pulses of ~7 ps duration at a repetition frequency of f = 5 MHz (or a bunch spacing of 2 ns). If a spin were precessing at the same frequency of f = 5 MHz, all x-ray pulses would probe exactly the same instantaneous state of the spin. ince FMR usually occurs in the GHz range, we delivered a microwave of f = 8f =4 GHz to our /Cu/Cu 75 Mn 25 /Cu/ sample to excite FMR in the layer. The FMR at 4 GHz corresponds to 8 complete cycles of spin precession between consecutive x-ray pulses. Therefore, by locking the f = 4 GHz pumping frequency with the f = 5 MHz synchrotron radio frequency in an exact 8:1 ratio, we were able to realize a pump-and-probe measurement using the x-ray pulses from the AL (Fig. 1). uch x-ray detected FMR (XFMR) measurements using synchrotron x-rays have been successfully demonstrated and provide a unique timeresolved and element-specific tool for the study of spin dynamics. 31 4

5 Fig. 1: chematic drawing of a pump-probe measurement using x-ray pulses from a synchrotron source. By locking the microwave frequency of f = 4 GHz to the synchrotron frequency of f = 5 MHz in an exact 8:1 ratio, the spin precession pumped by the microwave waveform is probed by the x-ray pulses using the element-specific x-ray magnetic circular dichroism (XMCD) effect. We first peormed x-ray absorption spectroscopy (XA) measurements at the Ni, Mn, and 2p core level absorption edges to identify the magnetic states of the, Cu 75 Mn 25, and layers in a (12nm)/Cu(3nm)/Cu 75 Mn 25 (2nm)/Cu(3nm)/(5nm) sample. The non-zero XMCD signals (the difference of the XA for opposite magnetic field directions) at the Ni and edges clearly identify the ferromagnetic state of the and films. The not detectable XMCD signal at the Mn L 3 edge identifies the nonmagnetic state of the Cu 75 Mn 25 film, showing that the two Cu(3nm) layers completely eliminate any magnetic proximity effect 32 of the and layers on the Cu 75 Mn 25 layer in our sample. Element-specific hysteresis loop measurements show that while the and films exhibit the expected ferromagnetic hysteresis loops, the Cu 75 Mn 25 film exhibits a paramagnetic linear dependence of the XMCD signal on the magnetic field, even though the XA spectrum clearly indicates the presence of a tiny quantity of Mn ions. 33,34 Of particular significance for the detection of the AC spin current, the partially-filled 3d bands of Mn, as opposed to the completely filled 3d bands of Cu, make the Mn XMCD 5

6 signal easier to detect within the experimental sensitivity. In addition, the and films show a distinct difference in coercivity (H c ) and saturation field, indicating that the Cu(3nm)/Cu 75 Mn 25 (2nm)/Cu(3nm) spacer layer prevents any static interlayer coupling between the and layers. Fig. 2: DC XMCD measurement of /Cu/Cu 75 Mn 25 /Cu/ at the Ni,, and Mn L 3 edges. (a) chematic drawing of sample. (b) DC XA and XMCD show that the and are ferromagnetic, and that the Cu 75 Mn 25 is paramagnetic. The Cu layers eliminate magnetic polarization of the Cu 75 Mn 25 by the and layers. The spacer layer of Cu/Cu 75 Mn 25 /Cu prevents static interlayer coupling between the and layers. For the dynamical study, we first measured the FMR in a (12nm)/Cu(3nm)/Cu 75 Mn 25 (2nm)/Cu(3nm) sample without a layer, by measuring the XMCD at the Ni L 3 edge. The incident x-ray direction is orthogonal to the applied magnetic field (Fig. 1), so that the XMCD probes only the transverse component of the precessing moment. Then by setting the time delay between the microwave -field (pump) and the x-ray pulse (probe) to measure the absorptive (imaginary) component of 6

7 the dynamic susceptibility, the pump-probe XMCD signal measures the spin precession amplitude 35. Fig. 3(a) shows the dependence of the spin precession amplitude upon the applied magnetic field. The position of the Lorentzian-shaped peak shows that the undergoes FMR at H res = 235 Oe for 4 GHz with a full width half maximum linewidth equal to ΔH 1/2 =95 Oe. By changing the time delay between the microwave waveform and the x-ray pulses, the pump-probe XMCD measurement explores the full spin precession as shown by the sinusoidal shape of the XMCD signal as a function of the time delay [Fig. 3(b)]. The oscillation period of 25 ps corresponds exactly to the f = 4 GHz spin precession frequency. In comparing the three sinusoidal curves at magnetic fields of H=15, 235, and 32 Oe, it is obvious that the spin precession exhibits not only an amplitude resonance but also a phase shift as the magnetic field is swept through the FMR resonance field. Fig. 3: AC XMCD measurement of the spin precession amplitude ( ) in /Cu/Cu 75 Mn 25 /Cu. (a) The spin precession amplitude as a function of magnetic field. A Lorentzian-shaped FMR peak is observed at a resonance field of 7

8 H res =235 Oe with a full width half maximum linewidth of H 1/2 =95 Oe. (b) The sinusoidal time dependence of the XMCD signal reveals precession of the spin. A clear phase shift occurs as the magnetic field crosses the resonance field. It is believed that the spin precession of a FM layer (e.g., the in our sample) pumps a pure spin current into a neighboring metallic layer where I g 4 d dt (1) is a unit vector parallel to the spin and g is the dimensionless spin-mixing conductance 36. Taking the time-average of Eq. (1) leads to a DC spin current direction parallel to DC I with. Almost all previous works have focused on this DC spin current. However, an attempt to directly observe the spins associated with a DC spin current yielded a negative result. 24 It was noticed only recently that in theory a much greater AC component can be generated by spin precession 25. Attempts to AC I detect this AC spin current by indirect measurements (e.g., IHE) have encountered similar effects to those that occur in measurements of DC spin current, while an electromagnetic inductive effect also induces an AC voltage that mixes with and obscures that due to the AC spin current. 29,3 If the FMR in our /Cu/Cu 75 Mn 25 /Cu/ sample indeed generates much larger AC spin current than DC spin current, then a direct measurement of Mn spin precession would signify direct detection of the pure AC spin current in the nonmagnetic Cu 75 Mn 25 spacer layer. Fig. 4(b) shows measurements of the, Cu 75 Mn 25, and spin precession at the FMR resonance field of H res = 235 Oe. To eliminate any possible artifact, we peormed the XMCD measurement using both left-circularly (red dots) and right-circularly (blue dots) polarized x-rays. The reversed XMCD signals observed for opposite x-ray polarizations confirm that the sinusoidal signals in Fig. 4(b) are indeed due to the spin 8

9 precession. To confirm the origin of the much weaker Mn XMCD signal, we also peormed the Mn XMCD measurement at photon energy below that of the Mn L 3 absorption edge (purple dots) to test for any AC signal induced by the microwave -field within the detection circuitry. The absence of any oscillations at energies below the Mn L 3 edge confirms that all possible oscillatory artifacts have been eliminated from our experiment. ince the two Cu layers in /Cu/Cu 75 Mn 25 /Cu/ eliminate magnetic polarization of the Cu 75 Mn 25 layer by the and layers (Fig. 2), we can conclude that observation of Mn spin precession is direct evidence of an AC spin current within the Cu 75 Mn 25 layer. It should be mentioned that all three measurements in Fig. 4(b) were made under the same conditions so that we can compare approximately their relative AC XMCD magnitudes [Fig. 4(c)]. The Mn and AC XMCD signals are ~5% and 1% of the Ni AC XMCD signal, respectively. Note from Eq. (1) that the cone angle of the Mn precession should be, where is the cone angle of the precession [inset of Fig. 4(c)]. Thus the DC component of the Mn precession is equal to the AC component multiplied by a factor of tan while the AC component of Ni precession is equal to the DC component multiplied by a factor of tan Then taking a typical value of 1 o for FMR and the ~8% Ni DC XMCD signal from Fig. 2, we estimate that the Mn spin precession should lead to ~7x1-5 for the AC XMCD signal and ~1.2x1-6 for the DC XMCD signal. This estimate might explain why previous XMCD measurements 24 of the DC spin current have yielded a null result at a sensitivity of 6x1-4, and also shows the advantage of measuring the larger AC spin current. From the pump-probe XMCD measurement, we can also determine the relative phase of the, Cu 75 Mn 25 and spin precession at the FMR resonance field of 235 Oe. Fig. 4(c) shows that the Cu 75 Mn 25 spins have identical phase to the spins. In contrast, the spin precession has an obviously different phase to the spin precession. As shown in Fig. 2, Cu 75 Mn 25 is paramagnetic, so the Cu 75 Mn 25 alone should not exhibit a resonance at the resonance field. The fact that the Cu 75 Mn 25 spins have identical precession phase to the spins shows that the observed Cu 75 Mn 25 spin precession is 9

10 induced by the AC spin current inside the Cu 75 Mn 25 layer. In fact the identical phase of the AC spin current and the FMR spin precession is an important property of the AC spin current in Eq. (1). Microscopically, the s-d exchange coupling in the Cu 75 Mn 25 generates an effective field of the order of Teslas. 37 Therefore an AC spin current carried by the conduction electrons drives a high frequency precession of the localised Mn spins. Given sufficient damping, the local spins will tend to follow the orientation of the conduction electron spins at the frequency of 4 GHz. We also point out that the 2π wavelength of the AC spin current 38 (λ = ) is dominated by the Fermi wave vectors of k k the majority spin k and minority spin k. In materials without ferromagnetic order (such as Cu), the exchange splitting at the Fermi level is negligible (k k ) so that the AC spin current wavelength is much greater than the film thickness. The spin current velocity in Cu was recently estimated to be ~1 nm/ps 39, leading to a propagation distance of ~25 µm during one cycle of 4 GHz oscillation. ince both the wavelength and the propagation distance of the AC spin current are several orders of magnitude greater than the Cu/Cu 75 Mn 25 /Cu spacer thickness (8nm), the variation of the phase of the AC spin current is negligible within the Cu/Cu 75 Mn 25 /Cu layer. That is why we could observe the Mn precession. Otherwise a spatial average over one or more wavelengths would washout the Mn AC signal. Therefore the phase of the spin current must be essentially constant between the /Cu inteace and the Cu/ inteace. Then the interesting question is why there is a phase difference between the spin current and the spin precession? 1

11 Fig. 4: AC XMCD signals due to, Cu 75 Mn 25, and spin precession in /Cu/Cu 75 Mn 25 /Cu/ at the FMR resonance field of 235 Oe. (a) chematic drawing of the spin precession in each layer due to the pure spin current pumped by the FMR. Note the inverted cone of precession for the Mn spin as described by Eq. (1). (b) pin precession within the, Cu 75 Mn 25, and layers revealed by AC XMCD measurements using left-circular polarized (LCP) and right-circular polarized (RCP) x-rays at the Ni, Mn, and edges respectively. The absence of any oscillations below the Mn L 3 edge energy (purple solid dots) confirms the absence of any artifact in the measurement. (c) The relative magnitude and phase of the, Cu 75 Mn 25, and spin precession. The Cu 75 Mn 25 spin precession is a direct indicator of the AC spin current. 11

12 To understand how the spin current drives the spin precession, we systematically measured the and spin precession at different magnetic fields [Fig. 5(a)] from which the and amplitude [Fig. 5(b)] and phase [Fig. 5(c)] were extracted by sinusoidal fitting of the XMCD signal [the amplitudes are normalized in Fig. 5(a) for clarity]. We first discuss the and precession amplitudes. The extracted amplitude exhibits a Lorentzian-shaped FMR peak at the same resonance field of H res =235 Oe as in /Cu/Cu 75 Mn 25 /Cu [Fig. 3(a)]. However, the line width of H 1/2 =183 Oe in /Cu/Cu 75 Mn 25 /Cu/ is larger than that of H 1/2 =95 Oe in /Cu/Cu 75 Mn 25 /Cu [Fig. 3(a)]. ince the field dependence of the spin current generated by precessional pumping corresponds to the broadened FMR line width, the enhancement of the line width from 95 to 183 Oe suggests that a spin current has been pumped into the layer. Indeed we observe a peak in the spin precession amplitude right at the FMR field [Fig. 5(b)]. ince an isolated single layer has a smaller FMR resonance field, and since the spacer layer in our sample is thick enough to prevent any static - interlayer coupling (see the DC XMCD result and the supplementary section), the peak at the FMR field must be associated with the spin current pumped by the FMR. pin precession within a FM layer driven by a spin-polarized electrical current has previously been demonstrated in spin torque nano-oscillators (TNOs). 1, 4 Applying this idea to the FM 1 /NM/FM 2 sandwich, it is tempting to think that a DC spin current generated by FMR in FM 1 could cause the spin polarization within FM 2 to be deflected away from its equilibrium direction, thus leading to spin precession in FM 2. However this scenario cannot explain our data because under these conditions the spins of FM 2 should precess at the FM 2 FMR resonance field rather than at the FM 1 FMR resonance field. The fact that the peak in Fig. 5(b) appears at the FMR field suggests that the peak is driven by the AC spin current rather than by the DC spin current (see supplementary material for a quantitative analysis). This scenario will then lead to a characteristic bipolar behavior 41 of the precession phase as discussed below. 12

13 Fig. 5: Amplitude and phase relation of the and spin precession. (a) and spin precession at different magnetic fields (Dots are experimental data, lines are sinusoidal fits). The amplitude is normalized for clarity. (b) The amplitude exhibits an FMR peak at H res = 235 Oe. The larger line width of H 1/2 =183 Oe compared to 93 Oe in Fig. 3(a) indicates spin pumping into the layer. Indeed the amplitude shows a peak at the same field. (c) The precession shows the -phase change typical of FMR. The phase of the Cu 75 Mn 25 is identical to that of as indicated by Eq. (1). The phase exhibits a characteristic bipolar behavior that is a fingerprint of AC spin-current driven precession. The solid lines in (b) and (c) are calculated (see supplementary material). (d) From the schematic diagram of the AC spin current, -field torque tot, and the total torque, in the spin precession plane, it is easy to understand the bipolar phase variation, whereby for H>H res and for H<H res (see main text). 13

14 The phases of the and spin precession are shown in Fig. 5(c) together with that of Mn at the FMR field of H res = 235 Oe (the small Mn XMCD signal makes it impossible to obtain over the full field range). As the magnetic field is swept through the resonance field of H res = 235 Oe, the phase undergoes a -phase shift typical of FMR. The phase, on the other hand, exhibits an obvious bipolar behavior with the phase value being smaller at H>H res and larger at H<H res than for a single isolated layer (horizontal dotted line). To understand the phase behavior, recall that the phase in FMR is traditionally defined as the angle of the (right-circular) -field vector relative to the component of the spin vector that rotates through 36 in the plane of precession. The physical meaning of the phase will become more transparent by considering the angle between this rotating spin vector and the torque due to the -field (the phase of the -field torque lies behind that of the -field). At H = H res, the Larmor frequency of the is exactly equal to the microwave frequency of 4 GHz and the -field torque acts fully to open the FMR cone angle ( = or ). At H>H res, the Larmor frequency is greater than 4 GHz. Therefore the -field torque must have a component anti-parallel to the direction of precession of the spins ( > or ) so as to slow the precession to 4 GHz [Fig. 5(d)]. imilarly at H<H res, the -field torque must have a component parallel to the direction of precession ( < or ) so as to increase the precession frequency to 4 GHz [Fig. 5(d)]. This explains why there is a -phase shift as the magnetic field is swept through the resonance. For the layer, the spin precession driven by the -field alone should lead to an almost field-independent phase in the vicinity of the FMR. Here is the angle / 2 described by the component of the spin vector in the plane of precession relative to the -field torque direction. In the presence of the AC spin current as described by Eq. (1), the spin precession should be driven by the total torque ( tot ) due to the -field torque plus the AC spin current. Now / 2 is the angle between the component of 14

15 the spin vector in the plane of precession and the total torque direction. Therefore the phase must take a new value so that compensates for the change from the -field torque direction to the total torque direction, i.e., the angle between the total torque direction and the -field torque direction should be ( [Fig. 5(d)]. Recall that the AC spin current has the / 2 ) ( / 2 ) same phase as the precessing spin. Then for H>H res, the fact that the AC spin current vector rotates in advance of the -field torque vector ( >) leads to a total torque that rotates in advance of the -field torque, leading to or [Fig. 5(d)]. imilarly for H<H res, the fact that the AC spin current vector lags the -field torque vector ( <) leads to the total torque vector lagging behind the -field torque direction, leading to or [Fig. 5(d)]. This is exactly the bipolar behavior observed in our experiment. A detailed analysis (see supplementary section) explains this bipolar behavior quantitatively [red solid line in Fig. 5(c)]. Therefore the bipolar behavior of the phase is a fingerprint of the AC spin-current driven d / precession. To be more specific, it is the dt term in Eq. (1) that causes the AC spin current to be in phase with the precession, which then leads to the bipolar variation of the precession phase. In contrast, a static - interlayer coupling torque ~ causes the precessing spin to behave as an effective -field rather than as an -field torque, leading to only a unipolar variation of the precession phase. 42 In summary, we have investigated the spin pumping effect in /Cu/Cu 75 Mn 25 /Cu/ in which the FMR pumps a pure spin current into the Cu/Cu 75 Mn 25 /Cu spacer layer and subsequently generates precession of the spin. We peormed pump-probe XMCD measurements to observe element-specific, Cu 75 Mn 25, and spin precession. Cu 75 Mn 25 spin precession. We directly observed the AC spin current by detecting the The AC spin current has the same phase as the spin 15

16 precession and excites precession of the spin at the same frequency but with a different phase. The fact that the AC spin current has the same phase as the spin precession leads to the characteristic bipolar phase behavior of the spin precession. Our experiment not only directly identifies the AC spin current in the non-magnetic spacer layer, but also shows how the AC spin current transfers its angular momentum so as to generate the spin precession. Method The samples were fabricated in an ultrahigh vacuum (UHV) chamber with a base pressure of 2x1-1 Torr. A 1 mm thick MgO(1) substrate was annealed at 6 for 1 hours before being covered by a shadow mask in the shape of a coplanar waveguide (CPW). A 1 nm thick Cu layer was then evaporated onto the MgO substrate to form a CPW of 5 Ω impedance. The central 25 m wide signal line is isolated from the surrounding ground plane by a 1 m wide gap but is shorted at one end so that microwaves can be delivered from the open end. (12.nm)/Cu(3.nm)/Cu 75 Mn 25 (2.nm)/Cu(3.nm)/(2.5nm) films were deposited sequentially on top of the Cu coplanar waveguide using e-beam evaporators. The sample was covered by a 2 nm Cu protective layer before being taken out of the UHV chamber. We chose as the spin pumping layer because its FMR can be realized at 4 GHz, Cu 75 Mn 25 as the spacer layer because it is paramagnetic above 11 K 43 and because Mn has a much larger XMCD effect than Cu, and a thickness of 2.5 nm for the layer because this is just thicker than the spin coherence length (~2 nm), 44 so that the layer is thick enough to effectively absorb the spin current while being thin enough to permit an XMCD measurement of the Cu 75 Mn 25 and layers below the. In addition, the two Cu layers prevent magnetic polarization of the Cu 75 Mn 25 layer by the and layers. 16

17 Fig. 1: chematic drawing of the pump-probe measurement using x-ray pulses from the synchrotron. A coplanar waveguide (yellow) delivers a microwave waveform to generate the spin precession in the sample (green). The 4 GHz microwave waveform is locked to the x-ray pulse repetition frequency of f = 5 MHz in an exact 8:1 ratio to enable pump-and-probe measurements of the spin precession. The pump-and-probe XMCD measurement was carried out at beamline 4..2 of the Advanced Light ource (AL) of the Lawrence Berkeley National Laboratory. Fig. 1 shows a schematic drawing of the AC XMCD measurement. The CPW and the sample suace lie in the yz-plane with the sample suace normal to the x-axis and with the inplane magnetic field applied parallel to the signal line (z-axis). The x-ray pulses (FWHM 7 ps) are incident in the xy-plane at a grazing angle of 2 so that the XMCD measures mainly the y-component of the spin. A 4 GHz microwave waveform was delivered to the CPW from the open end to generate the magnetic field (h ) in the y- axis direction. 17

18 In an FM 1 /NM/FM 2 structure, where the FM 1 serves as the spin pumping layer, the dynamics of the two magnetic layers are described by di dt ( H eff h ) i i i di dt J int j i sp di i i dt j d dt j. (1) Here i, j=1 or 2 denotes the FM 1 and FM 2 layers, i is a unit vector parallel to the spin, 2 =2.88 GHz/kOe is the gyromagnetic ratio, H eff is the effective magnetic field acting upon the spin that includes both the external field and the anisotropy field, α i is the damping parameter of the single FM i layer, α i sp is the extra damping parameter due to the spin pumping, layers, and h J i int is the static interlayer coupling torque between the FM 1 and FM 2 j is the -field generated by the microwave waveform. For small amplitude precession, the effect of this static interlayer coupling is equivalent to the application of a magnetic field J int j J J to the precessing spin i. While the J int j int AC j AC int j part behaves as an -field, the J int part behaves as a DC field that shifts the FMR j resonance field of the FM i layer. We observed this shift by measuring the resonance field as a function of Cu thickness in a /Cu/ sample (Fig. 2). As the Cu thickness is increased to reduce the /Cu/ interlayer coupling, the FMR field increases and approaches a constant value above ~4 nm Cu. Therefore we conclude that the /Cu/ interlayer coupling vanishes for Cu layers thicker than nm, i.e., we can ignore the interlayer coupling in the /Cu(3.nm)/Cu 75 Mn 25 (2.nm)/Cu(3.nm)/ sample. 18

19 Fig. 2: FMR in a /Cu/ sample. (a) The FMR at different Cu spacer thicknesses. (b) The FMR resonance field as a function of the Cu thickness. The constant value of the FMR field shows that the - interlayer coupling vanishes above 4nm Cu thickness. To make the physical picture clearer, we ignore the spin current pumped back by the precession. This is justified in the vicinity of the FMR where the precession amplitude is much greater than the precession amplitude. Then the equations of motion for and are d dt d dt d H eff, (2) H dt d dt sp d dt eff, (3) where z is the -field torque, and h ˆ is the (or ) sp,,, damping without the presence of the (or ) layer. Then from Eq. (2), assuming 2 2 H 4M, it is easy to derive that the FMR occurs at H( H 4M ) tan 4 1 field-dependent phase of 2 2 with a M, where 4 M 8 Oe is the saturation magnetization. The field-dependent phase is in excellent agreement with our 19

20 experimental data [solid line in Fig. 5(c)]. For the layer, Eq. (3) shows that the spin precession is driven by the total torque where I (4) I tot d sp is the spin current as described by Eq. (1). I has maximum dt amplitude at the FMR, at which point there should be a peak in the magnitude of tot I, leading to a peak in the amplitude as shown in Fig. 5(b). The change in orientation of the torque from that of precession to change by, where to tot should cause the phase of the and are the phases without and with the presence of the spin current. From the the relationship between in Fig. 5, it is easy to derive that and tot shown tot 1 I / 2( I / )sin (5) 2 2 tan( I / cos ) ( I / )sin (6) 1 Eq. (5) describes the peak in the precession amplitude. Eq. (6) describes the bipolar variation of at H>H res ( / 2 ) and at H<H res ( / 2 ). Noting that the magnitude of the spin-current I sp d dt sp sin, Eqn. (5) and (6) can then be rewritten as tot sin 2 sin 2 (7) sin cos tan( ) 2 sin 1 (8) 2

21 Here sp is a dimensionless number that characterizes the ratio of the spin pumping into the layer relative to the total damping of the layer. Recalling that is proportional to the FMR line width and that the FMR line width is H 1/2 =95 Oe in /Cu/Cu 75 Mn 25 /Cu and H 1/2 =183 Oe in /Cu/Cu 75 Mn 25 /Cu/, we determined the value to be 48. Then both the precession amplitude and phase can be calculated using Eqs. (7) and (8) without any fitting parameters (assuming a constant precession amplitude and phase due to the -field only). The calculated result agrees very well with the experimental data [red solid lines in Fig. 5(b) and (c)]. Finally, we discuss other possible origins of the Mn precession. Firstly, could the field from the CPW generate the Mn spin precession? This seems unlikely because electron spin resonance at 4 GHz occurs at a static field greater than 1 Oe. In addition, the phase of precession at fields lower than the resonance field should be instead of /2 as shown in Fig. 4(c). econdly, could the stray field from the precessing layer within the signal line excite precession within the Mn layer? As shown in Fig. 1, the precession should generate an AC stray field due to poles at the edges of the CPW. However, since our CPW has a width of w=25 m, which is much greater than the thickness (d =12 nm), the stray field should be ~4M sin()d /w 7x1-3 Oe, which is too weak to generate an observable Mn precession. Lastly, could a dipolar field due to the film roughness generate the Mn precession? The hysteresis loops of Figure 2(b) show that the and layers possess very different coercivities, suggesting that any static dipolar field is small on the ~1 Oe scale of the coercivity. Any dynamic dipolar field would be expected to be much smaller than the static dipolar field and hence far smaller than the effective field due to the s-d interaction of the injected spin current with the local Mn moments. In addition, such a dipolar field should also affect the precession, leading to a unipolar rather than a dipolar variation of the phase. Of course a rigorous 21

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