Reversing the magnetization of 50-nm-wide ferromagnets by ultrashort magnons in thin-film yttrium iron garnet

Spin waves (magnons) can enable neuromorphic computing by which one aims at overcoming limitations inherent to conventional electronics and the von Neumann architecture. Encoding magnon signal by reversing magnetization of a nanomagnetic memory bit is pivotal to realize such novel computing schemes efficiently. A magnonic neural network was recently proposed consisting of differently configured nanomagnets that control nonlinear magnon interference in an underlying yttrium iron garnet (YIG) film [Papp et al., Nat. Commun., 2021, 12, 6422]. In this study, we explore the nonvolatile encoding of magnon signals by switching the magnetization of periodic and aperiodic arrays (gratings) of Ni81Fe19 (Py) nanostripes with widths w between 50 nm and 200 nm. Integrating 50-nm-wide nanostripes with a coplanar waveguide, we excited magnons having a wavelength λ of ≈100 nm. At a small spin-precessional power of 11 nW, these ultrashort magnons switch the magnetization of 50-nm-wide Py nanostripes after they have propagated over 25 μm in YIG in an applied field. We also demonstrate the magnetization reversal of nanostripes patterned in an aperiodic sequence. We thereby show that the magnon-induced reversal happens regardless of the width and periodicity of the nanostripe gratings. Our study enlarges substantially the parameter regime for magnon-induced nanomagnet reversal on YIG and is important for realizing in-memory computing paradigms making use of magnons with ultrashort wavelengths at low power consumption.


Criteria for extraction of critical powers PC1 and PC2 from switching yield diagram experiment for device D1
The switching yield diagram is a plot of critical power needed to start and complete the switching of gratings beneath both the CPWs.This is calculated with the following strategy:  The device is saturated at -90 mT and the applied magnetic field is swept up to +10 mT (for D1).Median subtracted magnitude of ΔS21 is measured at Psens =-25 dBm and in a specific frequency window (fsens: 6 to 9.5 GHz), where the magnon modes are detected (black branches in figure S2a).Then, a specific magnon mode is excited at firr (here, 1.75 to 2 GHz) and for Pirr stepped from -25 dBm to +15 dBm.After every irradiation step Pirr, the magnitude of ΔS21 is measured at Psens =-25 dBm in the frequency window fsens. The criteria of extracting PC1 and PC2 are given by the disappearance of magnon modes and reappearance at a new frequency highlighted with blue and yellow brackets.
Figure S2: Procedure for determining the critical switching powers (PC1) and (PC2) from the S21 transmission data after exciting a magnon mode from 1.75 to 2 GHz at an increasing irradiation power (Pirr).The two black branches between 6.5 and 7 GHz as well as 8.5 and 9 GHz correspond to the spin wave modes sensed for Pirr below ~ -15 dBm.The integrated signal strength from fsens between 6.4 to 7 GHz (marked with blue dotted lines) was extracted and plotted as a function of Pirr in (b) showing the disappearance of the mode between Pirr = -25 dBm and -10 dBm.PC1 corresponds to Pirr at which the mode is at 50% of its maximum signal strength with respect to the minimum signal strength or noise floor.For the given S21 spectra, it is -14 dBm with an error bar of ± 1 dBm.On the contrary, a spin wave mode appears at 8 GHz for Pirr > 0 dBm.We apply a similar criterion but now for the increase in the signal strength for the branch highlighted in yellow dotted lines.The signal strength was extracted between 7.8 to 8.04 GHz and plotted in (c) as a function of Pirr.The critical switching power at which a new mode appears is denoted as PC2 and is given by 50% of maximum signal strength of the branch.
Here, it corresponds to 0 dBm with an error bar of ± 1 dBm.

Calculation of precessional power (Pprec) at PC1 and PC2 for device D1
The precessional power for a magnon mode with frequency firr excited at microwave power (Pirr) is given by: Pprec = (MAG(ΔS11) at firr) 2 × (Pirr), where, PC1 and PC2 are considered as Pirr and obtained from a switching yield diagram measurement as shown in the previous section.
MAG(ΔS11) = MAG(S11) at 10 mT -MAG(S11) at 0 mT The spectra S11 measured at 0 mT is subtracted from the Raw spectra measured at 10 mT to reduce the background signal.
The following plot shows reference subtracted ΔS11 spectra.
Pprec,1 was calculated with S11 spectra measured at -30 dBm, where, all gratings are antiparallel to YIG and the applied field direction.For Pprec,2, we use the spectra measured at -10 dBm.At this microwave power the gratings are completely switched beneath both the CPWs.

Theoretical model of magnetization reversal via curling
We have considered previous works [1-4] exploring the incoherent magnetization reversal of ferromagnetic wires and Py nanostripes.We use the following formula originally developed for an infinitely long cylinder to estimate the coercive field  for a nanostripe array following magnetization curling: [2,3] where  1.08 .

𝐵
is the effective demagnetization field acting on the nanostripe.The angle  is between the long axis of the cylinder and the applied magnetic field.The parameter  = 2 x 2.5 x lex represents the threshold diameter between coherent rotation and reversal by curling. is the equivalent diameter of a rectangular nanostripe.When   , the magnetization reversal mode is assumed to be curling instead of coherent rotation [2].
To calculate  , we considered ex = 5.7 nm from taken from [5] for permalloy.To calculate , we equated the cross-sectional area of a nanostripe in the device D4 (width height) with the cross-sectional area of a cylinder.An individual nanowire was 100 nm wide and 20 nm high.Hence, the equivalent diameter in D4 amounted to: which was larger than dC.= 28.5 nm.

𝐵
= - 0MS is determined as -101 mT using the effective demagnetization factor  = 0.1 given in the main text of the manuscript and 0MS = 1.01 T taken from [5] for permalloy.Figure S6 shows the expected angular dependent coercive field.In the manuscript we compare the calculated coercive field values with the measured data in Fig. 4(f).The stripes with width w = 50 nm and 200 nm fulfill the condition   for reversal via curling as well.

Figure S3 : 2 firr
FigureS3: Magnitude of ΔS11 spectra at 10 mT measured at -30 dBm and -10 dBm after subtracting the reference spectrum taken at 0 mT.The signal strength for both k1 and |G D1 -k1| modes were extracted and used to evaluate Pprec,1 and Pprec,2

Figure S4 :
Figure S4: Difference in critical switching fields extracted for the devices D1 and D2 consisting of 50-nm-wide and 200-nm-wide Py nanostripes, respectively.The data points correspond to the difference between HC1 and HC2 values extracted from ΔS21 spectra measured at -30 dBm and -5 dBm (Fig. 4 (d) and (e) in the main text).

H C2 H C1 5 .
Figure S5: Plot of median subtracted linear magnitude of S21 spectra of device D2 measured at -5 dBm.We do not resolve an AP branch.The onset of the branch P occurs at an applied field of around +5 mT 0H (mT)

Figure S6 :
Figure S6: Plot of HC as a function of field angle modelling magnetization reversal via curling.