Detection of Short-Waved Spin Waves in Individual Microscopic Spin

Letter pubs.acs.org/NanoLett

Detection of Short-Waved Spin Waves in Individual Microscopic Spin-Wave Waveguides Using the Inverse Spin Hall Effect T. Brac̈ her,*,†,∥ M. Fabre,† T. Meyer,‡ T. Fischer,‡,§ S. Auffret,† O. Boulle,† U. Ebels,† P. Pirro,‡ and G. Gaudin† †

University Grenoble Alpes, CEA, CNRS, Grenoble INP, INAC, SPINTEC, F-38000 Grenoble, France Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany § Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, D-67663 Kaiserslautern, Germany ‡

S Supporting Information *

ABSTRACT: The miniaturization of complementary metal−oxide−semiconductor (CMOS) devices becomes increasingly difficult due to fundamental limitations and the increase of leakage currents. Large research efforts are devoted to find alternative concepts that allow for a larger data-density and lower power consumption than conventional semiconductor approaches. Spin waves have been identified as a potential technology that can complement and outperform CMOS in complex logic applications, profiting from the fact that these waves enable wave computing on the nanoscale. The practical application of spin waves, however, requires the demonstration of scalable, CMOS compatible spin-wave detection schemes in material systems compatible with standard spintronics as well as semiconductor circuitry. Here, we report on the wave-vector independent detection of shortwaved spin waves with wavelengths down to 150 nm by the inverse spin Hall effect in spin-wave waveguides made from ultrathin Ta/Co8Fe72B20/MgO. These findings open up the path for miniaturized scalable interconnects between spin waves and CMOS and the use of ultrathin films made from standard spintronic materials in magnonics. KEYWORDS: Spintronics, spin waves, spin orbit torques, inverse spin Hall effect, Brillouin light scattering, spin-wave lifetime research field of spin−orbitronics:18,19 The use of spin−orbitcoupling phenomena not only allows for the efficient manipulation of spin-wave dynamics.20,21 Effects like the inverse spin Hall effect (iSHE), which is particularly pronounced in asymmetric layer stacks featuring a ultrathin ferromagnetic metal in contact with a heavy metal,22−26 in combination with spin pumping27−32 have been proposed as a spin-wave detection scheme.30,32−35 However, its application for the detection of propagating spin waves in CMOScompatible all-metallic layer systems on the micro- and nanoscale has not been demonstrated thus far. These material systems are of great importance due to their convenient growth

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agnonics and magnon spintronics1−6 explore the transport of information in the form of spin waves and magnons, their quanta, and its interconnection with conventional electronics. Spin waves are an excellent candidate for a new generation of nanoscaled wave-based logic devices with a low power consumption and a small footprint.1,7−9 Recent advances in magnonics have provided important proofof-concept devices such as a magnon transistor,10 spin-wave multiplexers,11,12 spin-wave couplers,13−16 or beam splitters.17 However, there is still a large gap between the sizes and the material systems used in these lab-scale experiments and the demands for a scalable integration into CMOS circuits. The required decrease of the devices’ feature size comes along with a necessary reduction of the spin-wave wavelength. Hence, suitable schemes to detect spin waves with arbitrary wavelength are needed. An interesting new family of effects for the spinwave manipulation and detection has been provided by the © 2017 American Chemical Society

Received: June 9, 2017 Revised: November 13, 2017 Published: November 17, 2017 7234

DOI: 10.1021/acs.nanolett.7b02458 Nano Lett. 2017, 17, 7234−7241

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Nano Letters by sputter-deposition as well as their compatibility with other spintronic concepts such as magnetoresistive random access memories,36,37 envisioning an easy fabrication of hybrid magnon-spintronic devices. In addition, these material systems feature large current induced spin−orbit torques, promising new degrees of freedom in the design of magnonic devices.20,21,24,36,38−41 Here, we present the detection of short-waved spin waves by the iSHE. These waves have been excited in microscopic Ta/ Co8Fe72B20/MgO spin-wave waveguides (SWW) by nanometric coplanar waveguides (CPWs). This material system exhibits large current-induced spin orbit torques and a comparably low magnetic damping39,40 and is widely used in magnetic tunnel junctions. By using different CPWs with welldefined wave-vector spectra, we show that down to spin-wave wavelengths of λ ≈ 150 nm the detection by the iSHE is independent of the spin-wave wavelength. By performing additional measurements using microfocused Brillouin light scattering spectroscopy (BLS),42 we show that the excitation is indeed local and, consequently, the iSHE allows for the detection of localized spin-wave dynamics. Thus, the iSHE can be used to detect information transport by short-waved spin waves. The studied rectangular SWWs have been fabricated from a Ta/CoFeB/MgO trilayer, which has been deposited by sputterdeposition on an oxidized Si substrate. The CoFeB is deposited in a wedge with a thickness gradient. A schematic of the fabricated structures is shown in Figure 1a. Close to the transition thickness of CoFeB from in-plane to out-of-plane magnetization (d = 1.3 nm), the SWWs are patterned as rectangular strips where the CoFeB is still in-plane magnetized. The SWWs are connected to leads at their edges, which allow for the detection of the rectified voltage arising from spin-wave dynamics. On top of the SWWs, CPWs of three different types have been structured: Type A features 120 nm wide wires with a s = 500 nm center-to-center spacing, type B 70 nm wires with s = 300 nm and type C 70 nm wires with s = 150 nm. The CPWs are used to create a dynamic Oersted field which excites propagating spin waves with well-defined finite wave vectors in the SWW.43−46 Because of their different sizes, they feature different Fourier spectra bk (see inset of Figure 1b and the Supporting Information), which allows for the excitation of different wave vectors. The reported electrical measurements have been performed on three 5 μm wide SWWs, each featuring a different CPW of type A, B, and C. The magnetic properties of the SWWs have been characterized by means of spin torque ferromagnetic resonance spectroscopy (ST-FMR).47,48 In this experiment, a dynamic RF current is sent through the SWW, which excites the quasi-ferromagnetic resonance. This excitation gives rise to a rectified voltage measured across the leads (see Methods for more details). Exemplary ST-FMR spectra are shown by the shaded peaks in Figure 1b for an excitation frequency of f = 4.8 GHz. From measurements of this kind, we determined the effective magnetization Meff = Ms − H⊥ in the SWW by an analysis of the dependence of the resonance frequency on the applied magnetic field. Here, Ms denotes the saturation magnetization of the CoFeB and H⊥ the anisotropy field due to the perpendicular magnetic anisotropy present in this layer system. The resonance frequencies are fitted using the Kittel equation in the absence of any in-plane anisotropies, neglecting the small deviation of the wire’s shape anisotropy from the one of an extended thin film. From this analysis (the corresponding

Figure 1. (a) Schematic of the investigated sample. A Ta/CoFeB/ MgO trilayer is patterned into a spin-wave waveguide (SWW) with leads to measure the voltage drop along the SWW. On top of an insulating Al2O3 layer, the nanometric, shorted coplanar waveguides (CPWs) with wire spacing s act as spin-wave excitation source. (b) Exemplary detected spectra at an excitation frequency of 4.8 GHz (solid lines) and analytical calculations of the expected excitation spectra of the CPWs (dashed lines). Black, CPW type A, s = 500 nm; red, CPW type B, s = 300 nm; green, CPW type C, s = 150 nm. The shaded peaks show exemplary ST-FMR spectra of the SWW. The inset shows the Fourier spectra bk of the CPWs. The blue dashed arrow indicates the wave vector at which the excited spin-wave intensity is expected to fall below the experimental noise level. Both the measured voltage and the expected intensity have been normalized to their respective maximum for a given CPW.

Kittel fits are shown by the white lines in Figure 2) and assuming49 Ms = 1250 kA m−1, we find an effective surface anisotropy constant of K⊥ = H⊥Msd/4 ≈ 0.59 mJ m−2 per surface, a value in the expected range for such Ta/CoFeB/MgO layer systems.49,50 The different positions of the resonance peaks are due to the thickness gradient in the CoFeB layer. From type C to type A, the thickness d of the CoFeB reduces and, consequently, the anisotropy field H⊥ slightly increases, because H⊥ ∝ K⊥/d. In all SWWs, we find field-line widths on the order of a few mT, featuring a linear dependence on the quasi-FMR-frequency. From the measured values, we extract an upper limit of the Gilbert-damping parameter of about α ≈ 0.019, assuming the entire damping is Gilbert-type. 7235


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Figure 2. Color-coded measured and expected spin-wave intensities as a function of the applied frequency and applied magnetic field. Both have been normalized to their respective maximum for a given frequency. The upper panel shows the measurement and the lower panel the analytical calculations. (a) CPW type A: wire width 120 nm, wire spacing s = 500 nm. (b) CPW type B: wire width 70 nm, s = 300 nm. (c) CPW type C: wire width 70 nm, s = 150 nm. The white lines represent the Kittel fits obtained from the ST-FMR measurements. In both panels, the dashed lines are guides to the eye indicating the position of the maxima of the spectra expected from the calculations.

maximum, which is on the order of μV for the applied power. Further detail on the absolute values of the measured voltages are discussed in the Supporting Information. As can be seen from Figure 1b, the frequency separation between the FMR (shaded peak) and the peak of the CPW excitation increases and the width of the SWR peaks grows as the CPWs become smaller. This is because the smaller CPWs can excite up to larger wave vectors, which makes the peak wider and centered around a higher wave vector (cf. inset of Figure 1b).44,46 To describe the spin-wave spectrum in the SWWs, we use the analytical formalism presented in ref.45 with the incorporation of the PMA and finite line width discussed in the Supporting Information. Assuming an effective width of the SWW of weff = 5 μm, a separation of z = 54.5 nm between the CPWs and the CoFeB (given by thicknesses of the oxide layers, the Ti buffer and half of the Au thickness), and an exchange constant of Aex = 10 pJ m−1 as well as the other material parameters stated above, we calculate the expected spin-wave intensity spectrum excited by the CPWs which are represented by the dashed lines in Figure 1b. Hereby, we average over the two emission directions along the wire, which are not equal due to the interplay of the in-plane and out-of-plane component of the Oersted field (cf., e.g., ref 45 and the comparison to the spectra obtained by BLS in Figure 3). Furthermore, we only consider the fundamental width mode n = 1 in the calculations since the

In the following, we address the excitation and detection of propagating spin waves with finite wave vectors in spin-wave rectification (SWR) experiments and we show that this technique allows for the wave-vector independent detection of the locally excited spin-wave dynamics in a large wave-vector range. In the SWR-experiment, the CPWs are used to excite propagating spin waves and the (rectified) dc voltage arising from these driven spin-wave dynamics is measured by the leads at the edges of the SWW.51 Hereby, the excitation as a function of the spin-wave wave vector is determined by the spatial extent of the excitation source (see inset of Figure 1b and the Supporting Information). The SWWs are magnetized along their short-axis to maximize the torque from the in-plane Oersted field created by the CPWs. In this geometry, the contribution of the iSHE to the dc voltage is maximum, while the contribution due to the anomalous magnetoresistance is minimum.51,52 The solid lines in Figure 1b show exemplary SWR measurements performed with the three different CPWs, which gives access to different wave-vector ranges. The SWR voltage U due to the iSHE is proportional to the square of the dynamic magnetization m2 and, thus, the spin-wave intensity. The measurements have been performed using a microwave frequency of 4.8 GHz with an applied power of P = 800 μW = −1 dBm. The voltages have been normalized to their individual 7236


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source and no systematic discrepancy with increasing wave vector is observed. Thus, the detection efficiency via the iSHE is independent of the spin-wave wave vector in the experimentally accessible wave-vector range. To demonstrate the feasibility of the iSHE detection in a wide range of frequencies and magnetic fields, Figure 2 compares the measured excitation spectra of the three different CPW types to the corresponding expected excitation spectra in the field-range we can cover with our experiment. The measured voltage and the expected spin-wave intensity are displayed color-coded as a function of the applied field and frequency. The white lines correspond to the Kittel fits obtained from the ST-FMR measurements. The spectra have been normalized individually to their maximum at each frequency to account for the changes of the input impedance. All color maps use an identical, logarithmic scale. As can be seen from Figure 2, the measured spectra are in good qualitative and also quantitative agreement in the probed field- and frequency-range. In the entire range, the noise-limited maximum detectable wave-vector is about 40 rad μm−1 and is determined by the Fourier spectrum of the excitation source. The visible small peak at fields larger than the FMR, which corresponds to a spin-wave mode below the spin-wave band, is associated with an edge mode,53 which is weakly excited by the CPW. To prove that the rectification indeed arises from a local excitation of propagating spin waves, we study the excitation of a CPW of type B by means of microfocused BLS.42 This technique gives access to the spin-wave dynamics with a spatial resolution42 of about 250 nm and can detect spin waves with a wave vector up to kmax ≈ 19 rad μm−1, that is, with λ ≳ 300 nm (see Methods for more details on this technique). The BLS measurements are performed on a 2 μm wide SWW, which is magnetized along the short axis by a fixed external magnetic field. The microwave frequency is swept at an applied power of 1.26 mW = +1 dBm. Figure 3a shows the BLS spectra measured at a distance of about 200 nm to the right edge of the CPW for μ0|Hext| = ±55 mT. The measured spectrum in the vicinity of the CPW is compared to the analytically expected spin-wave excitation spectrum (dashed lines) and the spin-wave dispersion relation of the fundamental mode (dotted green line). Both, measurement and calculations have been normalized to the maximum intensity in the efficient emission direction (in this case for positive magnetic fields). As can be seen from Figure 3, the two field polarities exhibit a strong asymmetry in terms of the overall intensity. The strong asymmetry is mediated by the PMA together with the excitation characteristics of a CPW. The PMA decreases the ellipticity of precession and this way increases the relative spinwave excitation efficiency of the dynamic out-of-plane fields created by the CPWs.54,55 Consequently, the interplay of the dynamic out-of-plane and the dynamic in-plane field components becomes more pronounced, which is responsible for the asymmetric emission of antennae in this geometry (see Supporting Information for more information). Thus, the use of CPWs or similar excitation sources for the spin-wave excitation in ultrathin films with large PMA results intrinsically in a pronounced unidirectional emission. Hereby, this excitation nonreciprocity is, however, a feature of the CPW excitation and not directly connected to the intrinsic nonreciprocity of the classical Damon-Eshbach waves.56 The calculation and experiments agree up to the first minimum of the CPW excitation. This is expected because this

Figure 3. (a) Measured (solid line) and calculated (dashed line) spinwave spectra detected at a distance of about 200 nm to the right edge of the CPW for ±μ0Hext = 55 mT. The dotted green line shows the analytically calculated dispersion relation of the fundamental mode (right y-axis). The magenta line marks the BLS detection limit at k ≈ 19 rad μm−1. (b) Spin-wave intensity as a function of the position along the SWW for different excitation frequencies. Solid lines are exponential fits.

influence of higher modes is negligible (see discussion in the Supporting Information). The analytical calculations assuming a wave-vector independent detection efficiency by the iSHE are in good agreement with the experimentally obtained spectra. The small visible deviations are likely caused by a too simple description of the material’s damping, which is assumed to be entirely Gilbert-type, and by an idealization of the CPWs which neglects their edge roughness or the roughness of the oxide layer they are grown on. The envelope of the expected intensity drops below the noise level of the used experimental setup for wave vectors beyond the third minimum of the CPWs of type A, beyond the second minimum for type B and beyond the first minimum for type C (cf. blue dashed arrow in Figure 1b). This point corresponds to about 40 rad μm−1 for all three types of CPWs and is equivalent to a wavelength of λ = 166 nm for type A and of λ = 150 nm for type B and C, because the minima are situated at integer multiples of 2π·s−1. The experimentally accessible wave-vector range and the envelopes of the measured spectra are predominantly determined by the features of the excitation 7237


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around k = 19 rad μm−1), which does not suffice to study the short-waved spin waves interesting for future magnonic applications. In addition, the limitations by optical diffraction also limit the usefulness of BLS for nanoscopic structures. The necessary optical setup evidently also make it a pure tool for laboratory work and it cannot be used in magnonic devices on a chip. The standard inductive techniques used in many laboratories can be integrated on a chip. However, they can only give information about the spin-wave phase by themselves if costly microwave equipment like Vector Network Analyzers or ultrafast oscilloscopes are used. In addition, inductive antennae exhibit a strong wave-vector selectivity given by their Fourier spectrum. Furthermore, the weak inductive coupling between the antenna and the dynamic magnetization limits the applicability of inductive detection for nanoscopic structures as well. Because it scales with the magnetic volume, inductive detection cannot be used for miniaturized structures made from ultrathin films hosting large spin orbit torques or films with low magnetization. In contrast, the iSHE detection excels in such layer systems: iSHE detectors can be easily integrated on a chip. If only thin metallic layers are involved, the iSHE voltage is not shunted and straightforward to detect. Since the iSHE voltage primarily scales with the length of the area over which the voltage is dropping, given either by the local spin-wave dynamics or the position of the leads, it provides a better scaling than inductive detection. In contrast, if thick ferromagnetic layers are used, the iSHE voltage drops due to shunting effects and other effects, like thermal effects arising from an inhomogeneous heating of the magnetic layer, can dominate the electric signal. As we have demonstrated here, the iSHE is not sensitive to the spin-wave wave vector in a large window of spin-wave wave vectors. However, the iSHE detection can, by itself, always only provide amplitude and no phase information. Thus, the latter has to be recovered within the spin-wave system, for instance, by translating it into an amplitude information.34 To conclude, we have demonstrated the wave-vector independent detection of spin waves with wavelengths down to λ = 150 nm in microscopic SWWs made from a Ta/CoFeB/ MgO layer by the iSHE. Up to a spin-wave wave vector of at least 40 rad μm−1, the detected voltage is determined by the excitation spectra from the nanometric CPWs and the finite line width of the spin waves in the ultrathin CoFeB. By employing microfocused BLS, we have demonstrated that the spin-wave excitation is indeed resulting in a local spin-wave intensity around the CPWs. This local excitation is sufficient to allow for an efficient spin-wave detection by the iSHE. This opens up the route for a CMOS-compatible detection of magnonic transport in micro- and nanostructures. In addition, we have demonstrated that despite the presence of interfacial damping, the spin-wave lifetime in the ultrathin Ta/CoFeB/ MgO is comparable to the one in thicker films of commonly used magnonic materials such as Ni81Fe19. This is attributed to the large PMA, which also results in a strongly preferred emission direction by the CPW. The additional large reported current-induced spin orbit torques in this material system24,36,39−41 render it a highly promising system for magnonic applications. Methods. Sample Fabrication. The Ta/CoFeB/MgO trilayer is deposited by sputter-deposition on an oxidized Si substrate. The CoFeB has been deposited in a wedge ranging from a thickness of 0.8 nm up to a thickness of 1.6 nm over the range of a 4 in. wafer. The trilayer is capped with an additional

minimum incidentally corresponds to the maximum wave vector which can be detected by the microfocused BLS setup. In contrast, the detection via the iSHE can efficiently detect spin waves with larger wave vectors. Please note that the position of the first minimum and the cutoff appear at the same frequency for both emission directions, confirming the absence of a sizable Dzyaloshinskii−Moriya interaction in Ta/CoFeB/ MgO.57 Figure 3b shows the spin-wave intensity as a function of the position along the SWW for some exemplary frequencies within the detection range of BLS. Solid lines indicate exponential fits to the data following I(x) = I0 + A·exp(− (x − x0)/(2δ)), where I0 accounts for the offset given by the experimental noise level, δ is the exponential spin-wave amplitude decay length, and A denotes the spin-wave intensity at the point x0. x is the coordinate along the waveguide long axis. These fits have only been performed for distances x > x0 which are sufficiently far from the CPW to ensure that the laser spot is not partially on the CPW. Closer to the CPW, the laser is partially on top of one of the ground lines and a part of the waveguide is shadowed, which leads to the deviation from a simple exponential decay in the measurement. As can be seen, the spin waves are excited locally at the CPW and they decay exponentially along the SWW. Because of the strong decay of the spin waves, the iSHE voltage is dominated by the spin waves in the vicinity of the CPW. As can be seen from Figure 3b, the spin-wave decay length δ initially increases with increasing frequencies as the decay becomes more shallow. However, for large frequencies, the decay becomes steeper. Around a frequency of 3.5 GHz, δ reaches its largest value of an amplitude decay length of about δ = 600 nm. This value is in reasonable agreement with the prediction δ ≈ 400 nm by the adopted analytical formalism presented in the Supporting Information, assuming the aforementioned values of α and Meff,B. It corresponds to a spin-wave amplitude lifetime of about 2 ns according to eq 3 in the Supporting Information. This lifetime is large in comparison to the value expected from a material system with similar values of Ms and α in the absence of PMA. This can be comprehended from the ellipticity contribution to the lifetime for the ferromagnetic resonance. The FMR lifetime58 is given by 1/τ = αγμ0(Hext + Meff/2) and thus a reduction of Meff due to the PMA significantly increases the lifetime at low magnetic fields. The obtained value of 2 ns is comparable to the lifetime in thicker ferromagnetic films on the order of tens of nanometers from metallic materials such as Ni81Fe19 or the half-metallic Heusler compound CMFS in the absence of pronounced interfacial damping.59,60 For larger frequencies, the decay length shows an unexpectedly strong decrease. This indicates the presence of a wave-vectordependent damping mechanism in the measurements. This is not incorporated into the analytical formalism, which might also explain why the maxima/minima in the measured spectra are not as well resolved as predicted. Ultimately, we would like to compare the iSHE detection to other detection methods: BLS detection (and other magnetooptical techniques like Kerr magnetometry) is local and the measured intensity depends on the local spin-wave density, which makes it a very powerful tool that does not require a large magnetic volume. In principle, it is possible to measure the phase-evolution of propagating spin waves directly by BLS, meaning that this method can give information on the wave amplitude and phase simultanously. In contrast, the maximum resolvable wave-vector is quite low (as mentioned above, 7238


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driving by Oersted fields is likely, and in our spin-wave rectification experiments the dominant driving force are Oersted fields. In both experiments, we find dominantly symmetric peak shapes. From this, we infer that the main detection mechanism in our Ta/CoFeB/MgO is the inverse spin Hall effect together with spin pumping. Symmetric peaks in ST-FMR have, however, also been observed in ultrathin CoFeB incorporated within a W/CoFeB/MgO layer which exhibits a large SMR. Thus, we cannot exclude an SMR contribution of spin-wave dynamics driven by SOTs in our STFMR experiments.65 Spin-Wave Rectification Spectroscopy (SWR). The setup for spin-wave rectification (SWR) measurements uses a similar principle than ST-FMR but with the important difference that the RF current is not applied to the magnetic waveguide but to a local spin-wave excitation source. This way, unlike ST-FMR, SWR provides information about spin waves with finite wavevector k. For their excitation, high-frequency probes are connected to nanometric shorted CPWs on top of the SWWs. They are connected to the RF source, which is modulated in amplitude by the LIA. The RF current provided by the generator creates a dynamic Oersted field around the CPWs. The LIA is connected to the leads of the SWWs. It is used to detect the rectified voltage which arises from the resulting spin-wave dynamics in the CoFeB. In the experimental geometry, where the magnetization is oriented along the short axis of the SWW, the torque by the CPWs and the rectification via the inverse spin Hall effect are maximum. Like in the ST-FMR measurements, the rectified voltage is detected as a function of the applied field for a given excitation frequency. The applied power of −1 dBm in the manuscript corresponds to the regime of linear excitation, whereas an increase of the power by about 2−3 dB leads to a deviation of the linear scaling of the measured voltage with the applied microwave power. Microfocused Brillouin Light Scattering Spectroscopy (BLS). A solid-state laser provides the reference light at a wavelength of 532 nm. The light is guided onto the sample by a microscope objective and focused down to a spot size of about 400 nm. Inelastically scattered light is recollected by the objective and guided into a 3 + 3-pass JRS Tandem Fabry Pérot interferometer,66 where it is analyzed with respect to frequency and intensity. The obtained BLS intensity at a given frequency is proportional to the number of inelastic scattering events of the light with magnons of this frequency in the probing spot. Thus, it is directly proportional to the local spinwave intensity. In the experiment concerning the spin wave decay lengths, the intensity is measured at different positions across the width of the SWW for each point along the wire. The intensity shown in the manuscript is given by the average of these measurement points.

layer of Al2O3 and Ta2O5. The Ta thickness is 5 nm, the thickness of the capping oxides is 1.5 nm (MgO), 2 nm (Al2O3), and 1 nm (Ta2O5), respectively. The used growth conditions ensure that the bottom Ta-layer grows in the βphase, resulting in a large spin Hall angle within the Ta layer.25,26 After an annealing step of the wafer at 250 °C for 1.5 h, the PMA is enhanced and leads to a transition to an out-ofplane magnetization of the CoFeB at thicknesses below approximately 1.2 nm. Around a CoFeB thickness of about 1.3 nm, where the ferromagnet is still in-plane magnetized, the trilayer is structured into spin-wave waveguides (SWWs) with a length of 10 μm and widths ranging from 500 nm to 5 μm by electron-beam lithography and ion-beam etching. Leads made from Ti/Au are defined at the short edges of the SWW. These are used for the measurement of the rectified DC voltage arising from magnetization dynamics in the wires.47,48 Subsequently, the SWWs are capped by a 30 nm thick layer of Al2O3 by means of atomic layer deposition. In a last series of steps, nanometric, shorted coplanar waveguides (CPWs) with different sizes are patterned on top of the SWWs by a combination of an electron beam-lithography and an optical lithography step and electron beam evaporation. The CPWs are made from a double layer of Ti/Au with thicknesses of 5 and 30 nm, respectively. They feature three different sizes (see main text) and the corresponding structures are patterned in rows along the gradient in the CoFeB thickness. The difference in the CoFeB thickness results in Meff,C ≈ 176 kA m−1 for structures with CPWs of type C, Meff,B ≈ 154 kA m−1 for type B and Meff,A ≈ 134 kA m−1 for type A. Spin Torque Ferromagnetic Resonance Spectroscopy (STFMR). For the spin torque ferromagnetic resonance (ST-FMR) measurements, the CoFeB SWWs are positioned between a pair of coils under an angle of 45° between the long axis of the SWW and the magnetic field within the film-plane. Using highfrequency probes, they are connected to a microwave generator via the capacitive part of a Bias-T. The generator provides an RF current with an output power of 0 dBm, leading to the excitation of magnetization dynamics in the SWW as the magnetic field is swept across resonance. This excitation is driven by the Oersted fields created by the current flow in the Ta layer and the spin orbit torques acting on the CoFeB layer simultaneously. To detect the rectified DC voltage created by these magnetization dynamics within the SWW, a lock-in amplifier (LIA) is connected to the inductive part of the Bias-T. The LIA is used to modulate the amplitude of the microwave generator at a frequency of 10 kHz to enhance the signal-tonoise ratio in the experiment. The rectified voltage is detected as a function of the applied field for a given excitation frequency. The quantitative analysis of the resonance peak shape of ST-FMR is rather involved. In general, anisotropic magnetoresistance (AMR) can give rise to an arbitrary peak shape. In addition, in ultrathin films adjacent to a heavy metal layer, the spin Hall magnetoresistance (SMR) can give rise to a significant contribution to the rectified voltage. SMR and AMR only give rise to a purely symmetric peak shape if the main driving force is SOTs. In contrast, if Oersted fields drive the magnetization dynamics, the symmetry of the resonance peak is determined by the relative phase between the microwave magnetic field and the oscillating currents. In addition to AMR or SMR rectification, the iSHE together with the spin pumping mechanism works particularly well in such ultrathin films and adds an additional, always purely symmetric contribution to the line shape.61−64 In out ST-FMR experiment, a significant

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b02458. Calculation of the spin-wave dispersion and lifetime as well as the excitation efficiencies in the presence of perpendicular magnetic anisotropy. Discussion of the amplitude of the measured voltages (PDF) 7239


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

T. Brächer: 0000-0003-0471-4150 Present Address

∥ (T.B.) Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany.

Author Contributions

T.B., U.E., O.B., and G.G. designed the experiments. T.B., S.A., and G.G. fabricated the samples. T.B. and M.F. performed the electrical measurements as well as the BLS measurements with help of T.M., T.F., and P.P. T.B. and P.P. derived the theoretical description of the spin-wave spectra. All authors discussed the results and were involved in writing the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Marine Schott for her assistance in sample preparation. M.F. acknowledges financial support from the French National Space Agency (CNES) and T. Fischer by the Deutsche Forschungsgemeinschaft (DFG) via the Graduate School Materials Science in Mainz (MAINZ) through the Excellence Initiative (GSC266). Financial support by the spOt project (318144) of the EC under the Seventh Framework Programme, by the DFG (Project B01 SFB/TRR 173 Spin+X) and by the Nachwuchsring of the TU Kaiserslautern is gratefully acknowledged.

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REFERENCES

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