1D YIG hole-based magnonic nanocrystal

 View Online  Export Citation RESEARCH ARTICLE | OCTOBER 27 2025 1D YIG hole-based magnonic nanocrystal K. O. Levchenko  ; K. Davídková ; R. O. Serha ; M. Moalic ; A. A. Voronov ; C. Dubs ; O. Surzhenko ; M. Lindner; J. Panda ; Q. Wang ; O. Wojewoda ; B. Heinz ; M. Urbánek ; M. Krawczyk ; A. V. Chumak Appl. Phys. Lett. 127, 172401 (2025) https://doi.org/10.1063/5.0285098 Articles You May Be Interested In Tutorial: Simulating modern magnetic material systems in mumax3 J. Appl. Phys. (November 2023) Spin-wave self-imaging: Experimental and numerical demonstration of caustic and Talbot-like diffraction patterns Appl. Phys. Lett. (May 2024) Micromagnetic simulations of first-order reversal curves in nanowire arrays using MuMax3 AIP Advances (December 2019) 03 December 2025 13:46:32 1D YIG hole-based magnonic nanocrystal Cite as: Appl. Phys. Lett. 127, 172401 (2025); doi: 10.1063/5.0285098 Submitted: 12 June 2025 .Accepted: 28 September 2025 . Published Online: 27 October 2025 K. O. Levchenko, 1,a) K. Davídkov a, 1,2 R. O. Serha, 1,2 M. Moalic, 3 A. A. Voronov, 1,2 C. Dubs, 4 O. Surzhenko, 4 M. Lindner, 4 J. Panda, 5 Q. Wang, 6 O. Wojewoda, 5 B. Heinz, 7 M. Urb anek, 5 M. Krawczyk, 3 and A. V. Chumak 1 AFFILIATIONS 1 Faculty of Physics, University of Vienna, Vienna, Austria 2 Vienna Doctoral School in Physics, University of Vienna, Vienna, Austria 3 Department of Physics of Nanostructures, Adam Mickiewicz University, Pozna n, Poland 4 INNOVENT e. V. Technologieentwicklung, Jena, Germany 5 CEITEC BUT, Brno University of Technology, Brno, Czech Republic 6 Institute for Quantum Science and Engineering, HUST, Wuhan, China 7 Fachbereich Physik and Landesforschungszentrum OPTIMAS, RPTU, Kaiserslautern, Germany a) Author to whom correspondence should be addressed: [email protected] ABSTRACT Magnetic media with artificial periodic modulation—magnonic crystals (MCs)—enable tunable spin-wave dynamics and band structure engineering. Nanoscaling enhances these capabilities, making magnonic nanocrystals promising for both fundamental studies and applications. Here, we report on the design, fabrication, and characterization of one-dimensional YIG MCs with nanoholes (d150 nm) spaced a1lm apart. Microfocused Brillouin light scattering and propagating spin-wave spectroscopy, supported by TetraX and MuMax 3 simulations, reveal spin-wave transmission over 5 lm in the Damon–Eshbach configuration and the formation of pronounced bandgaps with rejection levels up to 26 dB. Detailed analysis of the spin-wave dispersion uncovered complex mode interactions, including two prominent anticrossings at 3.1 and 18.7 rad/lm, between which the spin-wave energy is predominantly carried by the n¼2 mode, enabling efficient transmission. The results advance the development of functional MCs and open pathways toward 2D magnonic nanoarrays and magnonic RF nanodevices. V C2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/).https://doi.org/10.1063/5.0285098 The field of magnonics explores the fundamental and applied potential of the spin waves (SW)—collective oscillations of magnetic moments in a magnetic material. The advantages offered by magnonics include high frequencies, tailored material parameters, 1 low-energy dissipation, and low power consumption, which have been successfully integrated into various prototype circuitry elements, 2,3 with selected concepts surpassing the performance of benchmark conventional devices. 4 Many of them (e.g., filters, 5 transistors, 2 and sensors 6,7 ) are realized based on magnonic crystals (MCs)—artificial magnetic materials with a spatially periodic variation of properties. 8–10 The growing potential of nanoscale magnonics for RF applications, including MCs, was highlighted in a recent review. 11 Similar to photonic crystals operating with light, MCs use the wave nature of their quasiparticles—magnons—to achieve propagation characteristics that are inaccessible by other means. 10,12 Key properties of MCs, such as the central frequency and bandgap width, can be tailored by adjusting (often simultaneously) (1) the use of different materials with suitable magnetic properties (e.g., saturation magnetization 13–16 ), (2) the choice of the periodic pattern, 17 and (3) external factors, such as the applied magnetic field 18 or temperature. 19 Different combinations of these properties produce a variety of MC designs, including waveguide19,20 and thin-film-based 12 structures; one-, 21–25 two-, 26,27 and three28,29 dimensional structures; and static, 14,15,17 dynamic, 18,30 and reconfigurable 19,31 MCs. The simplest and most efficient type of MC is a one-dimensional (1D) structure with geometric patterning. Typically, a 1D MC is fabricated from a waveguide, where patterning enables the structure to act as a wavevector-dependent, mode-selective system. 9,32 1D MCs can function as standalone devices or serve as building blocks for magnonic directional couplers, transistors, phase shifters, and other RF Appl. Phys. Lett. 127, 172401 (2025); doi: 10.1063/5.0285098 127, 172401-1 V CAuthor(s) 2025 Applied Physics Letters ARTICLE pubs.aip.org/aip/apl 03 December 2025 13:46:32 and data-processing components. 2 One of the fundamental works on this topic—a study on a geometrically patterned (notched) microscale Permalloy 1D MC—was realized by Chumak et al., 22 based on a theoretical model by Lee et al. 33 and numerical simulations by Ciubotaru et al. 34 The authors experimentally demonstrated the propagation of coherently excited SWs through a metallic MC; however, in such macrostructured waveguides, the SW dispersion is inherently multimode, 35 resulting in the simultaneous transmission of waves with different wavelengths at a fixed frequency. In MCs, this leads to bandgap (BG) edges being less defined, forming a gradual slope in the transmission spectra, 22 rendering their operating characteristics less favorable for applications. 36 To overcome this limitation, MCs based on nanowaveguides can be considered. The effects of downscaling on the SW spectra were explored by Wang et al. 37 and Heinz et al. 38,39 When the width of an yttrium iron garnet (YIG) waveguide is sufficiently small, exchange interaction dominates over dipolar one, leading to unpinning of SW modes. This alters the quantization condition and shifts higher-order width modes to higher frequencies, effectively providing a single-mode regime. 37 Nanoscale enables key advantages for applications, as shown experimentally by Davídkov aet al. 40 in a multifunctional tunable magnonic nanodevice, or numerically by Ge et al. 41 in magnon nanotransistor. In the latter, notably, authors propose to use MC for precise control of the SW propagation and frequency-specific filtering. While nanoscale MCs hold great promise, their potential remains largely unrealized due to the relatively recent advances in nanofabrication. Here, we report on the experimental realization of a nanoscale 1D waveguide-based MC, geometrically modulated with round holes. Based on our preliminary studies, MCs with optimized geometrical parameters were designed and fabricated. Then, a detailed analysis of the SW transmission in Damon–Eschbach (DE) configuration was performed with the means of propagating spin-wave spectroscopy (PSWS) across different frequency ranges, complemented by TetraX and MuMax 3 simulations of the dispersion relation. Finally, microfocused Brillouin light scattering (l-BLS) spectroscopy was carried out to demonstrate the spatial behavior of excitations in a single MC waveguide. Figure 1 presents a sketch of an individual MC waveguide with key parameters (a) and SEM image of a section of the entire fabricated structure (b). The crystal periodicity a¼1lm was selected to align with the maximum excitation efficiency of the antenna 42 (see the supplementary material). The waveguide’s width was designed as x¼300 nm to support a single SW mode in a specific range, e.g., 8–8.2 GHz (<5rad/lm) under a 262 mT bias field in DE and 10.3– 10.9 GHz in a backward volume configuration. After the fabrication, the width was around 320 nm, decreasing a single-mode window to around 100MHz frequency bandwidth under the same bias field. The total waveguide’s length of 190 lm was chosen to be significantly longer than the estimated SW decay length (15:8lm, see supplementary material Fig. S1) to ensure that SW energy is fully dissipated before reaching the waveguide ends and prevent any edge reflections from interfering with the main signal. The hole diameter d modulates the SW reflection efficiency and thus affects the width and depth of the rejection bands. 10 Based on our simulations of similar structures, d¼150 nm was estimated to provide the best ratio of minimized losses to well-defined BGs. The holes’pattern persisted along the whole waveguide. All structures were realized from an LPE-grown 100 nm-thick YIG/GGG ð111Þfilm 43,44 using e-beam lithography and ion etching. 38 To estimate the SW propagation length, multiple pairs of coplanar waveguide (CPW) antennas with varying spacings of 1, 2, 5, and 10 lm were fabricated. Considering the small excited magnetic volume and potentially weak PSWS signal, each separate MC structure included up to 100 conduits. Coplanar waveguides were used for coherent SW excitation and detection. Fabrication parameters matched the designed ones, apart from the conduits’width, as mentioned earlier, and the slight upward shift of the holes. An exemplary propagating SW spectrum, shown in Fig. 1(c),was measured on the 1D MC structure presented in Fig. 1(b).TheSW transmission S12 was recorded while applying a fixed microwave signal with 10dBm power to the structure under test in DE configuration (in-plane, k?Bext). The DE geometry was selected due to its higher excitation efficiency (compared to the backward volume, see the supplementary material), enabled by higher SW group velocity and stronger coupling to the in-plane antenna field. The measured complex propagating SW signal, recalculated to dB magnitude (red circles, motion direction indicated by arrow), was obtained while sweeping the magnetic field from 240 to 320mT in 20mT steps across FIG. 1. (a) Sketch of 1D waveguide-based MC periodically modulated with round holes. Spin waves excited by the CPW are shown in blue, while Bragg-reflected waves in red. Key parameters: x¼320 nm, waveguide’s width; a¼1lm, MC’s period; Na200, total number of periods; and d¼150 nm, diameter of the holes. (b) SEM image of the typical 1D MC fabricated from a 100 nm-thick LPE-grown YIG/GGG film, with key parameters as in (a). The number of waveguides per antenna is nwg ¼100, the distance between the antennas is 5 lm. (c) Spin-wave transmission signal S12 of MC shown at (b) for varying bias magnetic fields in a frequency range of 7.5–10.5 GHz. Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 172401 (2025); doi: 10.1063/5.0285098 127, 172401-2 V CAuthor(s) 2025 03 December 2025 13:46:32 7.5–10.5GHz frequencies. Reference background was subtracted as showninourearlierwork; 40 other frequency and power ranges are provided in the supplementary material. The obtained SW spectrum significantly differs from that of a plain film by displaying “bandgaps” or “rejection bands”—regions where propagation is prohibited and the signal’s magnitude drops due to the Bragg’s scattering of SW from the periodic holes 8–10 (nmck¼2asin h,wherenmc is an integer, kis aSWwavelength,andhis an incident SW angle). Only the SWs with wavenumbers ka¼6nmcp=asatisfy this condition. The BG frequency depends on the material parameters and MC spatial geometry and can be tuned by the applied magnetic field, while the number of gaps is defined by the Fourier distribution of spatial modulators. 10 Here, each hole introduces a sharp magnetic contrast (step-like function), generating multiple periodic bandgaps. Accordingly, in “transmission”or “propagation”bands, where the Bragg condition is not satisfied, SW energy is expected to propagate without interruption, aside from higher insertion losses compared to an unstructured waveguide. 10 Losses at the level of 80…85 dB are rather expected due to the low volume of magnetic material in structurally modulated nanowaveguides. For reference, in a similar experiment by Davídkov aet al. 40 on a 97 nm-thick unstructured YIG film, the PSWS signal displayed losses of 25…35dB at 10dBm power level. These losses can be further reduced up to four times through optimization of antennas’SW excitation efficiency. 45 Therefore, having a considerable number of the conduits within one MC structure was crucial for successful signal detection, despite increasing the risk of structural imperfections affecting the transmission. The results of TetraX 46,47 and Amumax 48 micromagnetic simulations (a fork of MuMax 349,50 ) are presented in Figs. 2(a)–2(c),respectively. The waveguide was modeled according to the geometry in Fig. 1(b) with the following YIG parameters: saturation magnetization Ms¼139 kA/m, exchange stiffness A¼3:7 pJ/m, uniaxial magnetic anisotropy Ku¼3:58 J/m 3 (?y axis), and Gilbert damping a¼104. Bias field Bext ¼262 mT was applied along the x axis. Mode profiles in Fig. 2(a) were calculated for the unstructured waveguide cross section at k¼0, considering only the first five (n¼5) modes due to the quadratic decrease in dynamic magnetization intensity with increasing n. The real part of the magnetization component myin the DE configuration is color-coded with red and blue (more in the supplementary material). In this work, the mode labeling deviates from the standard convention by including edge modes, where SWs are confined to the waveguide’s edges. These modes arise from nonuniform internal fields and dipolar interactions in finite-sized structures and are labeled here as n¼0;1. Among them, only the n¼1 mode could be excited due to its symmetric mode profile. However, it cannot be resolved in the experiment because of its low amplitude and group velocity. Due to lateral confinement, the profiles show only the width quantization components kx¼np=x, with the first width mode being n¼2. Under direct antenna excitation, only even width modes ðn¼2;4;…Þare efficiently excited, as odd ones ðn¼3;5;…Þhave no net dynamic magnetization averaged across the width. In practice, slight antenna nonuniformity can excite odd modes, albeit inefficiently. Notably, while the mode profiles appear overall unpinned in a cross section, pinning persists at the waveguide’sedges[seeFig. 2(a) n¼2], which introduces elastic scattering into higher-order width modes. This occurs because of the larger nanowaveguide’s width than required for a complete unpinning of the SW mode profile at the edges. 37,38 The dispersion relation of the MC is shown in Fig. 2(b).Toobtain it, the magnetization’s y-components were recorded as functions of position and time, followed by a discrete Fourier transform along both axes for each simulation cell. The absolute value of the resulting complex spectra was computed and summed over the xand z-axes to yield the final map. Black dashed lines correspond to the intersection of the estimated resonance conditions for Bragg scattering ka ¼6nmcp=awith micromagnetic simulation and experimental SW transmission [left panel of Fig. 2(c)]. To obtain it, “raw”data from Fig. 1(c) were subjected to “time gating” 51 post-processing (details in the supplementary material), improving the signal-to-noise ratio and increasing BG rejection efficiency through the elimination of main spurious signals. The highest signal amplitude originates from SWs with lower wavenumbers, driven by higher group velocity and efficient CPW excitation. Exceptions occur at anticrossing points, where mode hybridization leads to spatial localization and standing wave FIG. 2. (a) TetraX simulation of the mode profile amplitudes for the first 5 SW modes of the unstructured waveguide in DE geometry with parameters as shown in Fig. 1(b). The real part of the magnetization dynamic component myis calculated for the waveguide cross section at k¼0. (b) MuMax 3 micromagnetic simulation of the 1D MC dispersion relation. (c) SW transmission S12 at bias field 262 mT after “time gating”post-analysis vs TetraX-simulated dispersion of a uniform waveguide in DE configuration. Gray squares indicate the intersection of the wavenumbers ka¼6nmcp=aat the bandgap frequencies with the TetraX-simulated dispersion (crimson solid line), while black squares –the intersection of dispersion with the MuMax 3 /experimental data, as shown by the gray solid (c, right panel) and black dashed (b, c) projection lines. Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 172401 (2025); doi: 10.1063/5.0285098 127, 172401-3 V CAuthor(s) 2025 03 December 2025 13:46:32 formation, resulting in a transmission drop below 140 dB. Six distinct BGs were identified in a spectrum: five arising from the hole-induced gaps between the antennas (k¼3:1rad=lm, nmc ¼1; ::; 5) and two anticrossings (k3.1 and k18.7 rad/lm), the first coinciding with the structural gap. These anticrossings were revealed with TetraX dispersion simulation [Fig. 2(c) right panel] for the modes nmc ¼2and3 of the unstructured waveguide (crimson solid and peach dotted lines, respectively). Gray squares mark intersections of the BG wavenumbers ka(thin solid gray lines) with the TetraX simulation of a WG dispersion, while black squares mark the intersection of dispersion with the experimental data/MuMax 3 results (black dashed lines). The rejection efficiency of the bandgaps is between 12.6 and 26.1 dB. The dispersion reveals that the investigated 1D MC operates predominantly in a single-mode within the frequencies 8.08–8.17 GHz (<3.1 rad/lm). Reducing the waveguide width to approximately 280nm is expected to eliminate mode anticrossings, while further narrowing to 250 nm would expand the single-mode frequency range sevenfold to 7.91– 8.56 GHz (up to 12 rad/lm; see the supplementary material). We can also assume that within the linear regime, the majority of the SW energy is effectively carried by n¼2 mode in the range 8.2–9.16 GHz (3.1–18.7 rad/lm), since the edge modes n¼0, 1 and the odd mode n¼3 are not excited effectively. Both the MuMax 3 and TetraX simulations of an individual waveguide showed good agreement with the experiment, considering the cumulative PSWS signal from 100 conduits. The minor misalignment, along with the appearance of multiple weakly defined gaps, is associated with fabrication imperfections. Defect-related variations in hole positioning and etching parameters between different waveguides, as well as within a single waveguide, cause reflections with slightly different amplitudes, phases, and wavelengths, leading to multiple Bragg conditions across the structure(s). This results in SW reflections at slightly different wavevectors and the appearance of a few closely spaced bandpass peaks in the transmission spectrum [e.g., Figs. 2(c) and 3(b)]. After PSWS, coherently excited SWs were probed by l-BLS spectroscopy. 52,53 An in-plane external field of l0Hext ¼238.6 mT was applied along the CPW antenna, ensuring uniform magnetization in DE configuration. Spectral analysis of the scattered light was performed using a 6-pass tandem Fabry–P erot interferometer and a kLaser ¼457 nm 54 blue laser. Unlike PSWS, l-BLS enables probing SW propagation within a single MC nanowaveguide. Figure 3 shows the SW signal, measured 5lm away from the CPW antenna (inset) on an MC with identical structural parameters to that analyzed by PSWS. Measurements were performed by sweeping the excitation frequency fext ¼77:8GHz in Df¼0:01 GHz steps at a constant 10dBm power. The SW signal in the form of BLS detector intensity (counts, Stokes part) is presented as a 2D map [Fig. 3(a)], where each y axis point corresponds to the integrated BLS counts at respective fext,and as a 3D intensity map [Fig. 3(b)], where the y axis shows the full range of measured frequency fat each excitation fext; signal intensity color-coded as the z axis. BLS measurements were performed at the waveguide’s center. While sweeping the microwave frequency, four periodically spaced passbands were observed (red and green areas in the 3D map), with the first signal appearing at 7.05 GHz and subsequent bands spaced by approximately 0.19 GHz. For clarity, adjacent peaks were Lorentzian-fitted (gray-shaded areas), with the first peak, corresponding to the passband center, located at 7.09 GHz. Regions dominated by the background BLS counts (blue areas on the 3D map) represent five BGs measured 4.5 structural periods from the excitation antenna within a single MC waveguide. The diminishing BLS counts and the appearance of two-three separated peaks in the vicinity of 7.09 and 7.48GHz indicate structural imperfections. Finally, we investigated the SW transmission in the passband and bandgap regions by sweeping the laser position from 0 to 5 lmaway from the antenna in 100 nm step. Figure 4 demonstrates the maximum BLS intensity at the passband excitation frequency fext ¼7:04 GHz (red circles) and at the bandgap frequency fext ¼7:2GHz (blue squares). The passband signal is an order of magnitude stronger than that of a bandgap, confirming the SW filtering. Linear fitting reveals a smaller slope for the bandgap signal (light-blue dots) compared to the passband (orange dashes), indicating suboptimal excitation efficiency and enhanced signal dissipation due to holes beneath the antenna. In conclusion, we demonstrated efficient SW propagation in nanoscale one-dimensional YIG magnonic crystal modulated with FIG. 3. BLS signal intensity of the propagating SW as a function of coherent excitation fext (x axis) in a form of: (a) 2D graph, where each y axis point corresponds to the integrated BLS counts over the respective excitation frequency fext; (b) a 3D intensity map, where the y axis shows the full range of measured frequency fat each excitation frequency fext, and BLS signal intensity (log scale) is color-coded at z axis. Gray-shaded areas are fitted with a Lorentzian, with the peak frequency highlighted. Measurements were performed 5 lm away from the coplanar waveguide’s antenna (inset). FIG. 4. BLS signal intensity of the propagating spin wave as a function of a laser scan position 0–5lm from the antenna (x axis); each y axis point corresponds to maximum BLS counts at the respective passband (red) or bandgap (blue) excitation frequency. Applied Physics Letters ARTICLE pubs.aip.org/aip/apl Appl. Phys. Lett. 127, 172401 (2025); doi: 10.1063/5.0285098 127, 172401-4 V CAuthor(s) 2025 03 December 2025 13:46:32 holes. PSWS and BLS investigations revealed well-defined magnonic passbands and bandgaps with a rejection efficiency up to 26 dB, corresponding to Bragg scattering from the periodic holes. Single-mode operation is achieved below the first anticrossing (<3.1 rad/lm) within a 100 MHz bandwidth and can be further enhanced by narrowing the waveguides. Between the first and second anticrossings (1 GHz bandwidth, 3.1–18.7 rad/lm), most SW energy is carried by the n¼2 mode, enabling effective SW transmission. While nanoscaling increases insertion losses and structural defects affecting the spectra, simulations confirm these to be only technical constraints. Future fabrication improvements are expected to firmly establish 1D YIG-based MCs as promising platforms for low-energy, high-frequency RF applications and magnonic computing. See the supplementary material for details on the fabrication process, analytical calculations performed in MATLAB, micromagnetic simulations using Amumax and TetraX, and the PSWS setup description. Additional content also includes PSWS responses across various frequency ranges and microwave powers, time-gating post-analysis for signal-to-noise enhancement, and extended data from l-BLS measurements. The research is funded by the Austrian Science Fund (FWF) project ESP 526-N TopMag (10.55776/ESP526) and by FWF IMEC (10.55776/PAT3864023). M.M. and M.K. acknowledge Grant by the National Science Center of Poland (NCN) No. UMO–2020/37/B/ ST3/03936 and 2023/49/N/ST3/03538. The work of M.L. was supported by the German Bundesministerium f€ ur Wirtschaft und Energie (BMWI) under Grant No. 49MF180119. B.H. acknowledges funding by the European Research Council within the Starting Grant No. 101042439 “CoSpiN.”M.U. acknowledges the support of the Grant Agency of the Czech Republic, Project No. 23-04120L. O.W. acknowledges Project No. CZ.02.01.01/00/22 008/0004594 (TERAFIT). The CzechNanoLab project funded by MEYS CR (LM2023051) is acknowledged for supporting sample fabrication at the CEITEC Nano Research Infrastructure. The authors thank Barbora Koraltan and Sabri Koraltan for the valuable discussions. AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions K. O. Levchenko: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (lead); Project administration (lead); Software (equal); Validation (lead); Visualization (lead); Writing –original draft (lead); Writing –review & editing (equal). K. Davídkov a: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing –review & editing (equal). R. O. Serha: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing –review & editing (equal). M. Moalic: Formal analysis (equal); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing –review & editing (equal). A. A. Voronov: Formal analysis (supporting); Investigation (equal); Methodology (equal); Software (equal); Writing –review & editing (equal). C. Dubs: Funding acquisition (supporting); Methodology (equal); Resources (equal); Validation (equal); Writing –review & editing (equal). O. Surzhenko: Methodology (equal); Writing –review & editing (equal). M. Lindner: Funding acquisition (supporting); Methodology (equal); Writing –review & editing (equal). J. Panda: Methodology (equal); Writing –review & editing (equal). Q. Wang: Methodology (equal); Validation (equal); Writing –review & editing (equal). O. Wojewoda: Methodology (supporting); Validation (equal); Writing –review & editing (equal). B. Heinz: Funding acquisition (supporting); Validation (equal); Writing –review & editing (equal). M. Urb anek: Funding acquisition (supporting); Methodology (supporting); Resources (equal); Validation (equal); Writing –review & editing (equal). M. Krawczyk: Formal analysis (equal); Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Resources (equal); Software (equal); Validation (equal); Writing –review & editing (equal). A. V. Chumak: Conceptualization (supporting); Formal analysis (equal); Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Resources (lead); Supervision (supporting); Validation (supporting); Writing – original draft (supporting); Writing –review & editing (supporting). DATA AVAILABILITY The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1 T. B€ ottcher, M. Ruhwedel, K. O. Levchenko, Q. Wang, H. L. Chumak, M. A. Popov, I. V. Zavislyak, C. Dubs, O. Surzhenko, B. Hillebrands, A. V. Chumak, and P. Pirro, Appl. Phys. Lett. 120, 102401 (2022). 2 A. V. Chumak, A. A. Serga, and B. Hillebrands, Nat. Commun. 5, 4700 (2014). 3 G. Talmelli, T. Devolder, N. Tr€ ager, J. F€ orster, S. Wintz, M. Weigand, H. Stoll, M. Heyns, G. Sch€utz, I. P. Radu et al.,Sci. Adv. 6, eabb4042 (2020). 4 Q. Wang, M. Kewenig, M. Schneider, R. Verba, F. Kohl, B. Heinz, M. Geilen, M. Mohseni, B. L€ agel, F. 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