Magnon-Assisted Magnetization Reversal of Ni81Fe19 Nanostripes on Y3Fe5O12 with Different Interfaces

Magnetic bit writing by short-wave magnons without conversion to the electrical domain is expected to be a game-changer for in-memory computing architectures. Recently, the reversal of nanomagnets by propagating magnons was demonstrated. However, experiments have not yet explored different wavelengths and the nonlinear excitation regime of magnons required for computational tasks. We report on the magnetization reversal of individual 20 nm thick Ni81Fe19 (Py) nanostripes integrated onto 113 nm thick yttrium iron garnet (YIG). We suppress direct interlayer exchange coupling by an intermediate layer, such as Cu and SiO2. By exciting magnons in YIG with wavelengths λ down to 148 nm we observe the reversal of the integrated ferromagnets in a small external field of 14 mT. Magnons with a small wavelength of λ = 195 nm, i.e., twice the width of the Py nanostripes, induced the reversal at a spin-precessional power of only about 1 nW after propagating over 15 μm in YIG. Such small power value has not been reported so far. Considerations based on dynamic dipolar coupling explain the observed wavelength dependence of the magnon-induced reversal efficiency. For an increased power, the stripes reversed in an external field of only about 1 mT. Our findings are important for the practical implementation of nonvolatile storage of broadband magnon signals in YIG by means of bistable nanomagnets without the need of an appreciable global magnetic field.

Collective spin excitations in a magnetically ordered material are called spin waves (SWs)   or, in quantum-mechanical terms, magnons.By means of SWs, angular momentum is transferred without electrical charge motion, hence no Joule heating is generated.2][3] In magnonic applications, microwave signals are applied to integrated coplanar waveguides (CPWs) and excite coherent SWs in the adjacent magnetic layer.Grating couplers consisting of ferromagnetic nanoelements [Fig.5][6][7] They emit and detect magnons with wavelengths λ down to below 50 nm in ferrimagnetic yttrium iron garnet (YIG). 8,9Wang et al. explored the spin wave emission from a ferromagnetic stripe into YIG. 10They explained the strong spin-wave signal in the underlying YIG by prominent dipole-dipole interaction without assuming spin currents.Recently, it has been reported that dipolar SWs reversed 100-nm-wide ferromagnetic nanostripes deposited directly on YIG after propagating over 25 micrometers. 11The magnon-induced switching of Ni 81 Fe 19 (Py) nanostripes on YIG occurred in the linear excitation regime at low microwave power.However, the wavelength λ used for switching remote nanostripes was a few micrometers long.[14] In this work we report remote switching of 100-nm-wide Py nanostripes by magnons with λ down to 148 nm in YIG.We explore different interfaces and, both, the linear and nonlinear excitation regime.The Py nanostripes were integrated on an intermediate layer of either Cu or SiO 2 on YIG.Thereby we suppressed the direct exchange coupling 15 between Py and YIG.Using the identical nanostripe design, we compare our results to Ref. 11 in which an intermediate layer between Py and YIG was avoided.Using broadband spectroscopy [Fig.which we attribute to magnon-induced switching in a small opposing field.We analyze the power absorbed by the precessing spins in YIG and find that propagating magnons whose wavelength is twice the nanostripe width show the minimum power level of about 1 nW representing the highest reversal efficiency.Our findings go beyond earlier reports in that we (i) demonstrate experimentally that dynamic dipolar coupling between Py and YIG is sufficient for magnon-induced reversal, (ii) explain the wavelength dependent reversal efficiency, and (iii) report switching by propagating magnons with a wavelength of only 148 nm.(iv) Our BLS data reveal the magnon-induced reversal in the non-linear excitation regime which we attribute to parametrically pumped magnons.Our findings pave the way for future inmemory computation in linear and non-linear nanomagnonics with materials combinations which do not require direct exchange coupling between the magnetic elements.

Results
We fabricated one-dimensional (1D) periodic arrays of Py nanostripes (gratings) on 113-nmthick YIG which was commercially available from the same supplier as in Refs. 7,16,17The stripes consisted of 20-nm-thick Py and were 100 nm wide.They are arranged with a period of p = 200 nm.The stripe lengths were consistent with Ref. 11 and alternated between 25 and 27 µm.The total width of a grating amounted to w GC = 10 µm.They were fabricated on YIG with a 5-nm-thick intermediate layer of either Cu (sample A) or SiO 2 (sample B).
We introduced the intermediate layers to intentionally modify the coupling between Py and YIG compared to Ref. 11 where Py had been deposited directly on YIG.The intermediate layers suppress the exchange coupling.Moreover, in sample B the SiO 2 spacer avoids the spin pumping mechanism thus allowing for only dipolar coupling between Py and YIG.In sample A, the Cu spacer thickness is smaller than the spin diffusion length 18 and a spin pumping related torque could occur in addition to dipolar coupling. 19In the following we denote the sample without an intermediate layer used in Ref.  20 The BLS microscopy was used to gain spatially resolved information about Py nanostripe reversal and explore the non-linear regime which was not achieved in Ref. 11 For obtaining the spectra ∆S 11 and ∆S 21 of sample A in Fig. 1(d) to (f) we applied H along the y-direction of sample C. We measured the scattering parameters in the following order: S 11 , S 21 , S 22 and S 12 .In the following we focus on spin waves which were excited at CPW1 and propagated to CPW2, i.e., we report spectra S 11 and S 21 , respectively.The spectra S 22 and S 12 showed consistent features when considering nonreciprocity and apply-ing an inverted magnetic history.We varied µ 0 H from -90 mT to +90 mT [indicated by the black horizontal arrow in Fig. 1 (Fig. 2) we adopted the methodology developed in Ref. 11 We evaluated VNA spectra taken at many different powers P irr and analyzed the field-dependent signal strengths of the first GC branch in the AP and P state.In such experiments, we applied i rf covering a broad frequency regime from about 10 MHz to 20 GHz.Assuming that the magnon mode for most efficient switching resided in this frequency regime, we obtained the minimum critical field values for reversal at a given P irr .At each value of P irr , we extracted the critical field values µ 0 H C1 and µ 0 H C2 that corresponded to 50% of the maximum signal strengths of the AP and P branches, respectively (symbols in Fig. 2).The difference (H C2 − H C1 ) reflected the distribution of switching fields of nominally identical Py nanostripes underneath the two CPWs.In sample A (Fig. 2a), the switching fields were distributed over a larger field range than in sample B (Fig. 2b) for P irr < −20 dBm.
We first consider the critical fields µ 0 H C1 extracted from the AP branches of both samples A and B. At low power, P irr ≤ -25 dBm, µ 0 H C1 is comparable within error bars in both samples.µ 0 H C1 decreases to 0 (±1) mT in sample A (B) when P irr ≥ -5 dBm (-10 dBm).We now focus on the critical fields of the P branch, i.e. µ 0 H C2 .For P irr < −20 dBm the critical field µ 0 H C2 is larger for sample A than for sample B (cf. Fig. 2a and 2b).µ 0 H C2 decreases as P irr increases up to -5 dBm.µ 0 H C2 is reduced to 2 mT in sample B when P irr ≥ -10 dBm and it maintains this small value at larger P irr .This is the smallest value so far detected for reversal of Py nanostripes on YIG induced by propagating magnons.This finding is one of the key achievements of this work.Near-zero critical fields were not be observed in Ref. 11 For comparison, in sample A, the critical field µ 0 H C2 is about 15 mT at −5 dBm.At the largest P irr , it has increased again (Fig. 2a) and reaches ≈ 22 mT.Considering Ref. 11 we attribute this increase in critical fields of Py nanostripes underneath CPW2 at high P irr to the nonlinear regime of magnon excitation underneath CPW1 with enhanced magnon scattering.Because of the scattering processes the magnon amplitudes after 15 µm are below the threshold for complete reversal of the nanostripe array under CPW2.The incomplete reversal at high power is observed for both samples A and C where spin pumping is allowed.
In sample B (Fig. 2b) we do not observe an increase in critical fields at large powers.Instead, we find the largest reduction in critical fields H C1 and H C2 in sample B. Here, a 5-nm-thick SiO 2 spacer rules out that spin pumping is relevant for the efficient magnon-induced reversal.
2][23][24] Our experiments highlight the importance of dynamic dipolar coupling between Py and YIG when developing a microscopic understanding of the magnon-induced reversal mechanism.
To quantify the power level at which a specific spin wave mode in YIG reversed nanos-  tripes we followed the concept of switching yield maps (Methods) introduced in Ref. 11 (Fig. 3).The samples were first saturated at -90 mT applied along the y-axis.Then, the field was gradually increased to +14 mT and kept constant.We provided powers P irr ranging from -25 to +6 dBm with +1 dBm steps within a 0.25-GHz-wide frequency window starting at a specific frequency f irr .After each power step and corresponding irradiation for 1 msec, the VNA power level was reduced to −25 dBm and the transmitted signal (S 21 ) was recorded as a function of frequency f sens ranging from 3 to 7 GHz. Figure 3 displays such datasets in panels (a) and (d) as well as gray-scaled switching yield maps performed at +14 mT for sample A (top row) and sample B (bottom row).The maps labelled by AP (P) branch in Fig. 3b and e (Fig. 3c and f) reflect the reversal of Py nanostripes under-neath CPW1 (CPW2) of sample A and B, respectively.From these maps, we extracted the critical power levels for magnon-assisted switching at CPW1 and CPW2 which we denote by P C1 and P C2 , respectively.In Fig. 4, we particularly display the critical power values extracted near the local minima indicated by arrows in Fig. 3  A and B at +14 mT, we require P C1 between 30 and 40 µW for the reversal of 50% of the nanostripes below CPW1 [red symbols in Fig. 4(a)].This power value is only about a factor of three larger than the one of sample C published in Ref. 11 [black symbol near 1.5 GHz in Fig. 4(a)].For all samples, P C1 and P C2 increase with increasing mode frequency.For the reversal underneath CPW1 by means of the GC mode k 1 + G (excited between 2.75 and 3.5 GHz) VNA powers P C1 of 400 to 800 µW are required.The reversal of Py nanostripes underneath CPW2 is achieved at a further increased power level P C2 of up to 2.5 mW.For sample C, P C2 was larger than 3 mW and not determined.
To compare different samples, it is instructive to consider the power values P C1,prec [Fig.We note that in sample B we observe nanostripe reversal by a further mode with wavelength λ = 148 nm corresponding to a wavevector k = (k 1 + G) 2 + k 2 PSSW1 (k PSSW1 is the first quantized magnon mode across the YIG thickness).When exciting this mode in the frequency range 4.75 to 5.25 GHz, we extract P C2,prec = 1.3 to 5.4 nW.These power values are increased compared to P C2,prec found near 3 GHz.For sample B, we observe the smallest spin-precessional power P C1,prec for reversal in Fig. 4(c) at 5.25 GHz.We explain the small value by the combined effect of magnon-induced reversal and microwave-assisted switching near the eigenresonance of the Py nanostripes underneath CPW1 before their reversal at +14 mT.For the nanostripes underneath CPW2 (P C2,prec ) the microwave-assisted switching does not play a role due their large separation from the CPW1 attached to the rf source.
In the following we apply micro-focus BLS to sample A [Fig. 5(a)] and gain spatially resolved information about the magnon modes that modify the magnetization vectors M Py of Py stripes.We do not evaluate absolute power values here as the BLS setup has not allowed for calibration, and CPWs were wire-bonded.We discuss BLS spectra reflecting the incoherent magnons excited thermally at room temperature.We compare spectra taken applying i rf at f irr = 4.3 GHz to CPW1 with a nominal irradiation power P irr of up to 39.8 mW (16 dBm) the red spectrum was obtained at the same position.Due to wire-bonded connections we expected the power in CPW1 to be a few dB lower than the nominal value.
The red spectrum is markedly modified compared to the black curve: the resonance peaks X and Y reduced to the noise level, and a higher frequency resonance Y' was resolved.The new peak in the red spectrum was consistent with the branch existing in the P configuration of the sample above the grey circle in Fig. 1(f).The microwave current applied to CPW1 with f irr = 4.3 GHz hence led to the reversal of Py nanostripes at the remotely located CPW2.
To investigate if heating of CPW1 by i rf initiated the reversal we followed the same measurement protocol as applied in Fig. 5(c) but changed the rf signal frequency to 1.25 GHz.
The signal i rf was applied for two hours, before taking the red spectrum in Fig. 5 and could explain the observed reversal.We note that the phase-sensitive voltage detection of the VNA experiment does not allow us to evidence the magnons created by parametric pumping because of their shifted frequency.We resolve them by BLS as presented in detail in Fig. S6.
We performed experiments also at 2 mT after initializing the sample at -84 mT.In Pos.We assume that at the small field the excitation of the k 1 mode was in the nonlinear regime as well, but additional parametric pumping did not take place at the small frequency.Instead, the amplitude of magnons decayed due to enhanced scattering and was below the threshold for reversal in Pos.2.2.The excitation of propagating magnons with a too high microwave power hence led to an incomplete reversal of nanostripes below CPW2.
This finding is consistent with the non-monotonous variation of critical fields with applied microwave power reported in Ref. 11 and as shown in Fig. 2. BLS studies on magnon-induced reversal in sample B are shown in Fig. S7 and support the findings reported for sample A.
We now discuss the roles of the intermediate (spacer) layers.The critical fields displayed in Fig. 2 indicate that the insertion of the Cu spacer between the Py and YIG increased the switching field distribution and the coercivity of individual Py nanostripes compared to the SiO 2 spacer.Our spatially resolved BLS data demonstrate that the precessing magnetiza-tion of allowed spin waves in YIG creates a torque leading to an irreversible change of the nanostripe magnetization.2][23][24] Still, the Cu spacer thickness is smaller than the spin diffusion length. 18In this case, forced spin precession in YIG and concomitant spin pumping into Py might introduce an additional torque. 19 noticed however significantly larger critical fields and a reduced switching efficiency at high power for sample A with Cu spacer compared to sample B with SiO 2 spacer.The data do not support the spin pumping effect to be relevant for reversal.Strikingly, we find the largest reduction in the critical fields H C1 and H C2 in sample B with the 5-nm-thick insulating spacer which avoids the spin-pumping torque.Thereby, we assume that dipolar coupling alone allowed for nanostripe reversal at a small power level.
In the following we discuss the possible origin for the observed variation of spin-precessional power for magnon-induced reversal.We focus on Fig. 4(d), where we exclude direct microwave-assisted switching of nanostripes by the applied rf signal.In sample B, we observe the smallest spin-precessional power when the propagating magnons exhibit a wavelength of 195 nm underneath the gratings. 7This value is (very close to) twice the width of a Py nanostripe.We argue that such a relation between the magnon wavelength and nanostripe width ensures the highest possible repetition rate by which a maximum in the dipolar stray field of a DE mode exerts a torque on the Py magnetization vector M Py .For a shorter magnon wavelength a partial cancellation of the dynamic dipolar field occurs underneath a nanostripe, and the dynamic dipolar coupling is reduced.For a long wavelength the repetition rate is small by which the maxima of the dynamic stray field pass by the nanostripe and produce the relevant torque.These considerations motivate the observed minimum in

Conclusions
We reported magnon-induced reversal in Py/YIG hybrid structures with different intermediate layers.We quantified and compared the power values for magnon-induced switching.
Reversal of 100-nm-wide Py stripes was achieved by means of propagating magnons with wavelengths ranging from 148 nm to 7222 nm.Their excitation was realized both in the linear and non-linear regime.The non-linear parametric pumping was evidenced by local BLS microscopy.In an opposing field of 14 mT a spin-precessional power of the order of 1 nW was enough to reverse the up to 27 µm long Py nanostripes after magnon propagation over 15 µm.The absence of interlayer exchange coupling due to a spacer layer between Py and YIG led to nanostripes with partly enhanced coercive fields compared to Py stripes directly integrated on YIG.The enhanced coercive fields are advantageous in terms of a nonvolatile memory of magnon signals.Importantly, with increasing power, we achieved a reduction of switching fields of nanostripes to (nearly) zero mT.Our results promise that nonvolatile magnon-signal storage in magnetic bits is feasible for wave-logic circuits and neural networks performing computational tasks at different magnon frequencies.Considerations based on dynamic dipolar coupling suggest that the power for magnon-induced storage might be minimized when the width of the magnetic bit equals half the wavelength of the magnon.C. Switching yield maps.To build switching yield maps (Fig. 3) we have followed the methodology described in Ref. 11 To get µ 0 H C = 14 mT by the emission of the magnon mode k 1 (in Ref. 11 this field H C was labelled H C2 .)We required (−12 ± 1) dBm (63.1 µW) at CPW1.We compare this value to 58.4 µW needed in Ref. 11 .The separation between CPW1 and CPW2 was larger by 20 µm in Ref. 11 compared to the present samples.However the previously reported critical field was only +28 mT compared to +40 mT in Fig. 1(d).This larger coercive field of nanostripes with the Cu underlayer used here might explain that a similar power level for reversal was needed though the propagation length of magnons was shorter.To characterize the critical power levels featuring the switching at CPW1 (CPW2) we focus on the frequency branch 4.5÷4.7 (3.9÷4.1)GHz of the S 11 (S 21 ) spectra (cf.Fig. 3).
To evaluate the critical precessional power P C,prec we first extract the minimum critical power P C for the same frequency.The overall irradiation frequency f irr range is divided into subintervals of 250 MHz width.We record P C and the frequency sub-interval δf P C that achieves

1Figure 1 :
Figure 1: (a) Schematic device with the two CPWs, Py stripes (gratings) and microwave tips connected to a VNA.A current i rf at frequency f irr is injected into CPW1.The generated field h rf excites magnons.Sketches of the (b) anti-parallel (AP) and (c) parallel (P) magnetic configuration of Py nanostripes and YIG.Color-coded spectra ∆S 11 (left) and ∆S 21 (right) taken as a function of field from -90 mT to +90 mT on sample A for powers P irr of (d) −30 dBm, (e) −15 dBm, and (f) 0 dBm.The horizontal arrow in (d) indicates the magnetic field sweep direction.We display ∆S, i.e., the difference of scattering parameters S that are taken at subsequent field values.Intense and dark colors indicate magnon resonances.Labels and symbols highlight specific resonances and critical fields.The black (red) vertical lines indicate 24 mT (40 mT).In (f, right) the AP branch is not resolved indicating H C1 is (close to) zero.

Figure 2 :
Figure2: For samples (a) A and (b) B the critical fields µ 0 H C1 and µ 0 H C2 realizing 50% of the maximum signal strengths of the two relevant magnon branches are shown as a function of P irr .The error bar refers to fields needed to achieve 30% and 70% of the maximum signal strengths of branches AP and P.

Figure 3 :
Figure 3: (a) Mag(S 21 ) recorded on sample C (Cu spacer) between f sens = 3 and 7 GHz at +14 mT with a power of -25 dBm after applying a microwave signal with f irr = 1.75 GHz to CPW1 for increasing power P irr .Switching yield maps at +14 mT for sample C displaying color-coded (b) Mag(S 11 ) and (c) Mag(S 21 ) integrated as a function of f sens for the AP and P branch respectively.The frequency integration range for the P branch is highlighted by the red dashed lines in (a).To extract the switching yield map for the AP branch, the first GC mode branch in the Mag(S 11 ) spectrum is used.Panels (d) to (f) show the corresponding dataset for sample B (SiO 2 spacer).Arrows indicate local minima in the power threshold inducing stripe reversal by specific magnons discussed in the text.

3 PFigure 4 :
Figure 4: For samples A (red), B (blue), and C (black, magenta) the critical powers (a) P C1 and (b) P C2 , (c) P C1,prec and (d) P C2,prec are depicted for irradiation frequencies f irr in half-logarithmic graphs.In (a) we label magnon modes by k 1 , k 1 + G and k 1 + G + k PSSW1 .In (d) the values of sample C (magenta symbols) are scaled by a factor ρ to correct for the different propagation path length and decay of magnon amplitudes between CPWs (Methods, paragraph C).Connecting lines are guide to the eyes.

4
(c)] and P C2,prec [Fig.4(d)] which quantify the power absorbed by the spin-precessional (prec) motion in YIG at the emitter CPW (Methods).These values consider that only part of the rf power applied by the VNA is absorbed by the spin system and converted into magnons.These values, taken at the same field, allow us to compare the different samples independent of the individual efficiency of microwave-to-magnon transduction.In case of the long-wavelength modes k 1 existing near 2 GHz in samples A and B, we observe reversal at power levels P C1,prec between 4 to 10 nW [Fig.4(c)].P C2,prec for modes k 1 is only slightly larger attributed to a weak decay of the magnon mode between emitter and detector CPW.At larger excitation frequencies f irr between 3 and 3.5 GHz corresponding to the first GC mode resonance k 1 + G, power values P C1,prec are smaller by up to two orders of magnitude compared to modes k 1 in Fig.4(c).Here, sample B realizes the smallest values P C1,prec down to about 0.5 nW.Note that despite larger coercivities in sample A the magnon-induced reversal underneath CPW1 via mode k 1 + G is realized at a smaller power than in sample C with the direct interface between Py and YIG.A similar small value of about 1 nW is found in Fig.4(d) for reversal underneath CPW2, suggesting a weak decay of magnon amplitudes after a path of 15 µm.The key finding of Fig.4(d) is that the mode k 1 + 1G in sample B is most efficient in terms of P C2,prec and nanostripe reversal underneath CPW2.Considering its intermediate layer to be an insulator (SiO 2 ) the dipolar coupling between magnons in YIG and Py provides the torque for the reversal.

1 Figure 5 :
Figure 5: (a) Sketched cross-section of the device (top).The CPW lines (yellow) are on top of the stripes (dark grey) which have been fabricated on YIG (green).In BLS we detected thermally excited magnons in Pos.2.1 (microscopy image) and 2.2.(b) Magnon dispersions in the thin YIG at 24 (solid lines) and 2 (dotted lines) mT calculated via the Kalinikos-Slavin formalism for two limiting configurations, i.e.Damon-Eshbach (blue lines) and backward volume (red lines) configuration.The horizontal dashed green line indicates 1.25 GHz which is below (inside) the magnon band at 24 mT (2 mT).Magnon spectra in Pos 2.1 at 24 mT before (black) and after (red) applying i rf to CPW1 for P irr = 16 dBm with (c) 4.3 GHz and (d) 1.25 GHz.Labels X, Y and Y' indicate characteristic resonant modes.

Figure 6 :
Figure 6: (a) Optical image when positioning the laser at Pos. 2.2.(b) Magnon spectra taken in Pos.2.2 at 24 mT before (black) and after (red) applying i rf to CPW1 with f irr = 4.3 GHz.The reversal of Py nanostripes by magnons k 1 + G is evidenced.Magnon spectra in (c) Pos.2.1 and (d) Pos.2.2 before (black) and after (red) applying i rf with f irr = 5 GHz at CPW1.The black (red) arrows highlight characteristic modes (changes).Thermal magnon spectra in (e) Pos.2.1 and (f) Pos.2.2 before (black) and after (red) emitting magnons with k 1 by applying i rf with f irr = 1.25 GHz at CPW1.In all these experiments the irradiation power was P irr = 16 dBm.The legends list relevant parameters and highlight the parametric pumping (p.) experiments.
(d).The red spectrum is found to contain the identical resonances as the black spectrum, i.e., M Py was not changed by applying an rf signal at 1.25 GHz.We explain the different spectra (red) in panels (c) and (d) of Fig. 5 by the dispersion relation of YIG at 24 mT displayed in Fig. 5(b).At f irr = 1.25 GHz (green dashed line), magnons are not emitted into YIG as all allowed magnon bands reside at higher frequencies.This is different for f irr = 4.3 GHz.Here, a Damon-Eshbach (DE) mode is allowed and excited at CPW1.It propagates to CPW2 as evidenced by the transmission spectra shown in Fig. 1.The allowed mode is the grating coupler mode k 1 + G with λ = 195 nm.The characteristic resonance Y' in the red spectrum of Fig 5(c) evidences the reversal of Py nanostripes in Pos.2.1 by the propagating magnon mode.In Pos.2.2 located a few micrometers further away from CPW1 (Fig. 6a),we detected a modified spectrum (red) at 24 mT as well (Fig.6b).Hence, the reversal of Py nanostripes was induced in both gaps by the short-wave magnon mode k 1 + G excited at CPW1 at f irr = 4.3 GHz.When applying a microwave signal with f irr = 5 GHz to CPW1 (after again initializing sample A at -84 mT), we observed modified spectra (red) taken at Pos. 2.1 [Fig.6(c)] and Pos.2.2 [Fig.6(d)].Note that the directly excited grating coupler mode did not exist at 5 GHz.Still, the finding is different from the experiment conducted with f irr = 1.25 GHz in Fig.5(d).We attribute the observed reversal of Py nanostripes to magnons which were excited by parametric pumping at CPW1 (Supplementary information).Their frequency reads f m = f irr /2 = 2.5 GHz, which was above the k 1 resonance (f k 1 = 2.3 GHz) at 24 mT and inside the allowed magnon band for propagation.Such magnons hence reached CPW2

2. 1 [
Fig.6(e)] we observed that the magnon spectrum (red) was modified after applying i rf with f irr = 1.25 GHz.At 2 mT, spin waves at this small frequency were allowed [dotted lines in Fig.5(b)] and possessed a wave vector k 1 with λ = 7222 nm.Excited at CPW1, the magnon mode changed the Py nanostripes underneath CPW2 at Pos. 2.1, but not at Pos. 2.2 [Fig.6(f)].

Fig. 4 (
Fig. 4(d) as a function of f irr , i.e., magnon wavelength.The slightly increased power levels needed for reversal in sample A incorporating the Cu spacer might indicate that additional spin pumping or an eddy current effect reduced the total torque.Further studies on stripes with different spacer layers and of e.g.different lengths and widths are needed to engineer

MethodsA.
Sample fabrication.Devices are fabricated on 113-nm-thick YIG originating from the same wafer.The YIG had been deposited by liquid phase epitaxy on a 3-inch wafer and purchased by the company Matesy GmbH in Jena, Germany.The spacer is fabricated by DC sputtering of 5-nm-thick Cu on YIG.Then 20-nm-thick Py (Ni 81 Fe 19 ) is deposited via electron beam evaporation on the YIG.The gratings were written with electron beam lithography (EBL) using hydrogen silsesquioxane (HSQ) as negative resist and then transferred into the Py/Cu by ion beam etching.We etch both layers of Py and Cu.CPWs are fabricated via lift-off processing after EBL and Ti/Au (5 nm / 120 nm) evaporation.For sample B, the SiO 2 layer is deposited by e-beam evaporation and the following steps to fabricate stripes and CPW are unchanged.B. Broadband VNA spectra.The broadband spectroscopy data ∆S αβ (α, β = 1, 2) are obtained by nearest-neighbor subtraction of raw linear magnitude signals, i.e. ∆S αβ (f, H i ) = S αβ (f, H i+1 ) − S αβ (f, H i ).The magnetic field step is 2 mT.The linear magnitude signal Mag(S αβ ) is obtained from the quadrature sum of real (Re(S)) and imaginary (Im(S)) parts of median-subtracted signals.Re(S) (Im(S)) is obtained by the raw real (imaginary) part after removing at each measured frequency its median value across all applied magnetic fields.