Spin-wave microscale RF delay lines for mid- and high-frequency 5G band

 View Online  Export Citation RESEARCH ARTICLE | OCTOBER 13 2025 Spin-wave microscale RF delay lines for midand highfrequency 5G band Kristýna Davídková  ; Khrystyna O. Levchenko ; Rostyslav O. Serha ; Florian Bruckner ; Morris Lindner; Carsten Dubs ; Michal Urbánek ; Dieter Suess ; Qi Wang ; Roman V. Verba ; Andrii V. Chumak J. Appl. Phys. 138, 143908 (2025) https://doi.org/10.1063/5.0286108 Articles You May Be Interested In 1D YIG hole-based magnonic nanocrystal Appl. Phys. Lett. (October 2025) Spectroscopy of the spin waves of a synthetic antiferromagnet grown on a piezoelectric substrate AIP Advances (March 2025) Spin-wave eigenmodes in direct-write 3D nanovolcanoes Appl. Phys. Lett. (March 2021) 03 December 2025 13:42:22 Spin-wave microscale RF delay lines for midand high-frequency 5G band Cite as: J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 View Online Export Citation CrossMar k Submitted: 18 June 2025 · Accepted: 23 September 2025 · Published Online: 13 October 2025 Kristýna Davídková, 1,2,a) Khrystyna O. Levchenko, 1 Rostyslav O. Serha, 1,2 Florian Bruckner, 1 Morris Lindner, 3 Carsten Dubs, 3 Michal Urbánek, 4,5 Dieter Suess, 1 Qi Wang, 6 Roman V. Verba, 7 and Andrii V. Chumak 1,b) AFFILIATIONS 1 University of Vienna, Faculty of Physics, Boltzmanngasse 5, Vienna, Austria 2 Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, Vienna, Austria 3 INNOVENT e. V. Technologieentwicklung, Prüssingstraße 27 B, Jena, Germany 4 Institute of Physical Engineering, Brno University of Technology, Technická 2, Brno, Czech Republic 5 CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno, Czech Republic 6 School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, China 7 V. G. Baryakhtar Institute of Magnetism of the NAS of Ukraine, 36-b Vernadskogo Blvd., Kyiv, Ukraine a) Author to whom correspondence should be addressed: kristyna.davidko[email protected]c.at b) Electronic mail: [email protected] ABSTRACT Delay lines (DL) are crucial components in communication systems, providing the required time delays for signal timing, synchronization, and processing. DLs providing nanosecond-scale delays are conventionally based on acoustic waves; however, they cannot operate conveniently in a high-frequency range (EU 5G high-band 24.25–27.5 GHz) required by a modern generation of 5G communication technologies to speed up data transfer. The proposed solution is to use DL based on spin-wave (SW) transmission, as SW devices allow for operation at high-frequency ranges and can be scaled down to a few μm2. In this study, we investigate SW-based DL at the microscale at the frequency ranges of 4, 9, and 25 GHz. The DL is based on SW transmission between a pair of 250 nm wide microwave coplanar waveguide transducers, each with a footprint of 2:25 100 μm2, and fabricated with varying mutual distances on a 97 nm thin yttrium iron garnet film. DLs are tested for in-plane SW modes (Damon–Eshbach and backward volume), and depending on the parameters, the extracted delay times are in the range of 6–165 ns. Furthermore, the insertion losses are extracted and compared to other DL concepts. Time-gating analysis of the measured transmission is performed, providing a detailed discussion of individual signal contributions to the measured spectra. Additionally, analytical theory is employed to compare the experimental delay times with analytical calculations and to predict how to adjust the device parameters to obtain variable time delays. © 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0286108 I. INTRODUCTION Communication systems urgently need to speed up data transfer due to the increasing number of active user devices every year. 1 Therefore, the aim of modern 5G technology systems is to move from standard frequency ranges (e.g., EU 5G low-band 694–790 MHz and mid-band 3.4–3.8 GHz) to high-frequency ranges (e.g., EU 5G high-band 24.25–27.5 GHz). However, moving to higher frequency ranges is challenging for many radio frequency (RF) devices, such as filters, limiters, and delay lines that are conventionally used at lower frequency ranges. 2 Delay lines (DLs) are two-port devices that delay signal transmission by a fixed amount of time to synchronize signals. This is crucial for error reduction in signal processing, timing, and phase Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-1 ©Author(s)2025 03 December 2025 13:42:22 shifting, especially in multi-band and multi-antenna systems used in modern 5G communication systems. 2 In telecommunication systems, either photonic or acoustic DLs are conventionally used for on-chip signal processing applications. DLs based on photonic integrated circuits (PICs) 3–7 leverage the propagation of light through optical waveguides and offer several advantages, including broadband operation, performance up to THz frequency range, and small insertion losses. However, since on-chip PIC-based DLs provide delay times in the ps range, it remains challenging to simultaneously achieve tunability, longer delay times (at th ns range), and a small device footprint. 3,4 The synchronization requirements and delay compensations needed for 5G networks are from picoseconds to a few hundred nanoseconds. 8,9 Therefore, searching for a technology providing longer delay times is of interest. One of the suitable candidates are acoustic DLs based either on surface acoustic waves (SAWs) 10–18 or on bulk acoustic waves (BAWs). 19–22 SAW-based DLs can provide delay times in the range of a few ns up to several hundred ns. However, they can operate conveniently only in the low GHz range (approx. up to 3 GHz 11 ) because of the significantly increasing damping of acoustic waves with increasing frequency, resulting in high insertion losses. 12 Additionally, operating SAW DLs at higher frequencies requires proportionally smaller interdigitated transducers (IDTs), which poses significant challenges for conventional optical lithography techniques used for their fabrication. 13 Compared to SAW-based DLs, BAW-based DLs can provide significantly longer delay times in the range of a few hundred ns up to several hundred ms, and they can also operate at slightly higher frequency ranges (up to approximately 6 GHz). 23 However, BAW-based DLs suffer from complicated fabrication due to the high requirements for BAW isolation from the substrate and increasing damping with increasing frequency. 13 Therefore, it is of interest for the next generation of communication technology to search for a DL capable of operating in the high frequency range (around 25 GHz) and simultaneously providing longer delay times (in the ns range). One possible solution can be DLs based on spin-wave (SW) transmission, as they allow effective operation at high-frequency ranges with provided delay times in the ns range. Moreover, SW-based DLs are frequency flexible (the same device can operate at any frequency range defined by the external magnetic field), are easy to fabricate, and allow for device miniaturization. 2,24 Additionally, SW-based devices provide multifunctionality, meaning that a single SW device can simultaneously work as a delay line, filter, and power limiter. 24 Furthermore, the delay time can be precisely tuned by the choice of the magnetic material (sample thickness, saturation magnetization), antenna design (mutual distance between the antennas), and applied magnetic field, determining the frequency range and SW mode. 25–29 However, in the past, SW-based DLs have been investigated mostly at the macroscale, 30–36 in the centimeter and millimeter ranges, and in the low-frequency ranges (up to 5 GHz). Only recently, in 2023, Li et al. 37 demonstrated nanoscale spin-wave delay lines based on 100 nm thin YIG films, employing coplanar-waveguide (CPW) antennas with a width of 200 nm and a length of 30 μm. These devices, characterized in the Damon–Eshbach (DE) mode up to 14 GHz, exhibited delay times of 23, 47, and 96 ns at 10 GHz for propagation distances of 5 μm, 10 μm, and 20 μm, respectively. Nevertheless, the reported devices exhibit high insertion losses exceeding 50 dB, were not characterized in the desired highfrequency range up to 25 GHz, and were tested exclusively for the Damon–Eshbach mode. However, the backward volume mode is particularly relevant for 5G high-band applications, as it exhibits significantly lower insertion losses at 25 GHz compared to the Damon–Eshbach mode. 24 In this study, we investigate nanoscale DLs based on the spinwave transmission between a pair of 250 nm wide microwave CPW transducers, each with a footprint of 2:25 100 μm2, of different mutual center-to-center spacings, which are fabricated on the 97 nm thin yttrium iron garnet (YIG) film. The DLs are tested in a broad frequency range of 4, 9, and 25 GHz for both in-plane SW modes—Damon–Eshbach (DE, applied field is perpendicular to the SW propagation) and backward volume (BV, applied field is parallel to SW propagation). To extract the delay time, a time-gating analysis of the measured SW transmission is performed, providing a detailed discussion of the various signal contributions, including electromagnetic leakage, and explaining the oscillations in the measured SW spectra. The extracted delay times are compared with analytical calculations, and the possibility of obtaining variable delay times by tuning the device parameters (such as sample thickness, or using different SW modes) is discussed. Furthermore, the quantitative comparison of the extracted insertion losses is presented and compared to other DL devices. To explain the different delay times and insertion losses observed for the two spin-wave modes, calculated dispersion relations, group velocities, lifetimes, and decay lengths are provided for both modes. II. NANOSCALE SW-BASED DELAY LINES The DL devices consist of CPW transducers and a magnetic film. As a magnetic medium, the 97 nm thin liquid phase epitaxy (LPE) grown YIG film on h111igallium gadolinium garnet (GGG) is used because of favorable damping characteristics, 38 resulting in long propagation distances of spin waves. On top of the YIG layer, the microwave transducers are fabricated using PMMA resist and e-beam lithography, followed by metal evaporation (10 nm Ti, 320 nm Cu, 20 nm Au) and lift-off. The fabricated transducers consist of three fingers, each 250 nm wide with 750 nm spacing, and a length of 100 μm. The center-to-center distance between the transducers is 3, 7:5, and 52:5μm, and their total thickness is 350 nm; see Fig. 1. The microwave transducers are connected via picoprobes and coaxial cables to the vector network analyzer (VNA), which generates and detects microwave signals (electromagnetic waves, EM). For characterization of DLs, propagating spin-wave spectroscopy (PSWS) 24,39,40 is used. The principle is the following: the DL device is located in the external magnetic field, and the microwave current generated by the VNA is sent to the input transducer. The microwave current creates an alternating magnetic field around the transducer, which interacts with the magnetic moments in the magnetic layer beneath. If the frequency of the microwave current matches the SW dispersion relation (determined by the external magnetic field and material parameters, see Appendix A), spin waves are generated, and they propagate in the magnetic film. When they Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-2 ©Author(s)2025 03 December 2025 13:42:22 reach the output transducer, the alternating magnetic field (created by magnetic moment precession) induces a voltage in the output transducer, which is detected by the VNA. The transmitted SW signal can be represented by the scattering parameter S21, which is the ratio of the detected and generated signals. The time delay Tdis determined by the SW group velocity vg and the distance Dbetween the transducers, Td¼D vg :(1) The SW group velocity is a derivative of the SW dispersion relation vg¼2π@f @k, (2) which is calculated from the analytical model of Kalinikos and Slavin, 41 see Appendix A. III. MEASUREMENTS AND DATA ANALYSIS We characterize the fabricated DLs described in the previous section using the time-gating analysis. 37,42–46 SW transmission is measured using VNA in the frequency domain, 24,39,40,42,47,48 and then the inverse Fourier transform (IFT) is applied to convert the measured data into the time domain. This emulates propagation of a very short pulse (with the duration being the inverse frequency band accounted for in the calculations—see Appendix B) and allows for distinguishing all the possible contributions to the transmission. The analysis of a finite-length pulse propagation is discussed later. In the time domain, we identify and extract the signal of interest, a peak whose amplitude corresponds to a specific delay time Td. To gain deeper insight into the time-domain data, the Fourier transform (FT) of the signal of interest (extracted peak with annulled surroundings) is applied to convert this signal back to the frequency domain for comparison with the original data. This time-gating analysis enables the identification of the individual signal contributions and their origin in the measured transmission, allowing for further optimization of SW devices by eliminating unwanted signal components. Please note that the time-gating analysis is applicable only to time-invariant linear systems. Moreover, in many cases, the SW signal in the measured transmission is very weak, particularly in a few-nanometer-thick structured YIG films. The standard procedure to eliminate parasitic signals (e.g., electromagnetic leakage) typically involves subtracting the reference transmission (measured at different magnetic fields) from the transmission of interest, which is both time-consuming and prone to inaccuracies. Compared to this standard method of background subtraction, time-gating is highly efficient in finding the signal of interest in the measured transmission spectrum in the frequency domain. The time-gating analysis of all signal contributions in the transmission spectra measured using transducers with a center-tocenter distance of 7:5μm, at 71mT in DE mode is shown in Fig. 2. The VNA parameters used are input power 30 dBm, bandwidth 1 kHz, frequency step 200 kHz, and no averaging. The measured SW transmission in the frequency domain (original raw data) at 3–5 GHz is plotted in gray in the bottom row in Fig. 2(a). The IFT of the measured (raw) data in the time domain is also plotted in gray in the middle row in Fig. 2(a). The signal of interest in the time domain is highlighted in color for each column, and its FT is plotted in the same color in the frequency domain. In the following text, the individual signal contributions, depicted in the top row in Fig. 2(a), are described. †The first column I. The fastest signal that is detected by the second VNA port is the electromagnetic leakage, i.e., the crosstalk between the transducers. 49 The electromagnetic leakage creates the background in the frequency domain, and it is of interest to reduce it as much as possible to have the best signalto-noise ratio for the SW signal. †The second column II. After the electromagnetic leakage, the main SW signal takes place. Compared to electromagnetic leakage, the SW signal is slower as it propagates at a speed of the SW group velocity (in this case vg¼598 m=s) from the input to the output transducer. This propagation defines the delay time Td, which is extracted from the measured data as Td¼13:6+3:2 ns. The theoretical delay time T d,determined by the distance between the transducers and the SW group velocity [see Eq. (1)], is T d¼12:5 ns and agrees well with the experimental one. The SW signal maximum (27dB) is 29dB larger than the median value of the electromagnetic leakage (56 dB) extracted at the frequency range of the SW signal (3.8–4.3 GHz). FIG. 1. SEM images of SW-based DLs consisting of microwave transducers on the YIG film. The lengths of the transducers are 100 μm, and both signal (S) and ground (G) conductors are 250 nm wide and 750 nm apart from each other. The center-to-center distance Dbetween the transducers is (a) D¼3μm, (b) D¼7:5μm, and (c) D¼52:5μm. Spin-wave propagation between the input and output transducers and the signal conversion between electromagnetic (EM) and spin-wave (SW) signals are indicated in (c). Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-3 ©Author(s)2025 03 December 2025 13:42:22 †The third column III. The next signal contribution appears as an interference of two signals. We see a pronounced beating in the time domain with a period ΔT2 ns, as evidenced in the zoomed-in signal profile in Fig. 2(d). The reconstructed spectrum of this signal of interest contains two peaks, one at the same frequency position as the main SW peak discussed just above (around 4 GHz) and the second at about 4.5 GHz. Frequency separation between the peaks Δf0:5 GHz gives the period of beating in the time domain ΔT¼1=Δf. Both of these peaks originate from the SW signal. The frequencies (f) and wavenumbers (k) of the generated spin waves in the measured transmission [gray curve in Fig. 2(c)] are determined by the intersection of the SW dispersion relation [black curve in Fig. 2(c)] and transducer excitation spectra Jexc [blue curve in Fig. 2(c)]; see Appendix A for more details. The main SW signal contribution in the measured data is from the first peak in the excitation spectra at k¼3:1rad=μm(wavelength λ¼2:026 μm), and the side contribution is from the second peak ks¼9:3rad=μm(λs¼0:675 μm). The SW group velocities differ within the main peak (vg¼598 m=s) and side peak (vg,s ¼316m=s). Theoretical delay for shorter SW (secondary peak) is T d, s ¼D=vg,s ¼23:8 ns, close to the measured one Td¼29:5+4:5ns. Thus, the signal from the second peak in the excitation spectra is the SW signal at a smaller wavelength that propagates as a common one-way from the excitation toward the detection transducer. The nature of the signal at the FIG. 2. (a) In the top row: Different signal contributions—the electromagnetic leakage (the curved arrow in I.), the SW signal with small wavenumbers that undergo reflections from the transducers (straight arrows in II., III., IV., and V.), and the SW signal with large wavenumbers (double-arrow in III.). In gray, the bottom row: Measured SW transmission using the transducers with the distance of 7:5μm in DE mode. In gray, the middle row: The IFT of the measured transmission to the time domain. In color: The signal of interest in the time domain is highlighted in color, and its FT with the annulled background back to the frequency domain is highlighted in the same color. In columns: The individual signal contributions are highlighted and compared to the original data in each column. (b) The interference of two signals causes the oscillations in the measured SW transmission (in gray). The signal contributions in the time domain are highlighted in light green for the main SW peak and in dark green for the side SW peak. (c) The SW transmission (in gray) occurs at the frequency range that matches the intersection of the SW dispersion relation (in black) and the transducer excitation efficiency (in blue). The arrows symbolizing the individual signal contributions in (a) are assigned to the first and second peaks in the excitation spectra. (d) The details of the interference of two SW signals with different wavenumbers in the time domain in III. The distance between two maxima in the time domain (2 ns) corresponds to the distance in frequency between the main and the side SW signal, as highlighted in dark cyan in (c). Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-4 ©Author(s)2025 03 December 2025 13:42:22 main excitation peak is more nontrivial. To match theoretical delay time with the experimental one, we need to assume that the signal propagates the doubled distance, i.e., T d¼2D=vg¼25:0ns. Thus, the signal from the first peak of the excitation spectra originates from the SWs that travel from the excitation transducer toward the detection transducer and back. We assume that this signal contribution is present in the measured transmission due to the interference of this reflected SW signal with the electromagnetic leakage signal that is being generated at the emitting transducer and detected at the output, as we are operating at the continuous-wave (CW) mode. Because the two aforementioned delay times are similar, the interference occurs, see Fig. 2(d). Both discussed contributions are weak compared to the main SW peak (column II)—24:5dB smaller for the second excitation peak contribution and 28:2dB smaller for the double reflected signal. †The fourth and the fifth columns IV. and V. In the fourth and fifth columns, the SW signals with two and three reflections from the transducers are highlighted. Its theoretical delay times T d¼3D=vg¼37:5 ns and T d¼4D=vg¼50:0 ns agree reasonably with the experimental one Td¼41:0+5:2 ns and Td¼53:0+3:1 ns. The differences between the contributions from the signals with two reflections (48 dB) and three reflections (61 dB) from the transducers are 21 and 24 dB compared to the main SW signal maximum (27 dB). We assume that, also in this case, the SW signal with three reflections is present in the measured transmission due to the interference with the electromagnetic leakage when reaching the emitting transducer. Based on this analysis, the main SW signal exceeds the electromagnetic leakage by 29dB, the side peak from the second excitation maxima by 24:5 dB, and the contribution from two reflections on the transducers by 21 dB. Therefore, despite the presence of these parasitic signals, the DL performance remains good, with a margin exceeding 20 dB. Moreover, this time-gating analysis is particularly useful for understanding the original data measured in the frequency domain (in gray). Both the main and the side SW signals exhibit some oscillations; see Fig. 2(b). These oscillations are caused by the interference of two signals. To explain their origin, an IFT must be performed simultaneously for two signals of interest with an annulled background. The oscillations observed in the main SW peak arise when the IFT is calculated from the superposition of the SW signal propagating once between the transducers and the signal undergoing three round trips between them. These contributions in the time domain are highlighted in light green in Fig. 2(b). For certain applications, such as SW-based filters, it is essential to minimize these oscillations to achieve a well-defined peak shape, ideally as close as possible to a rectangular profile. The oscillations originate from SW reflections at the interface between the metal transducers and the YIG film, and can be suppressed by introducing an insulating layer between the transducers and the film. However, a trade-off arises: while a thicker insulating layer reduces the reflections more effectively, it also decreases the efficiency of SW excitation and detection due to the increased separation from the YIG film. Alternatively, parasitic reflections can be mitigated by fully metallizing the YIG film in DE mode 35,50 and employing the “inverse approach,”in which the entire surface is covered by metals except for the antenna gaps. Another potential strategy is the use of antennas with a gradual increase in thickness, enabling the SWs to adapt progressively and thereby reducing reflections through a smoother transition in wavenumber. The oscillations in the side peak are caused by the interference between the SW signal originating from the second peak in the excitation spectrum and the electromagnetic leakage, as highlighted in dark green in Fig. 2(b). While the electromagnetic leakage interferes with all signal components, pronounced oscillations appear only when the SW signal is comparable to or smaller in magnitude than the electromagnetic leakage. Therefore, for SW devices, it is crucial to minimize electromagnetic leakage as much as possible, thus achieving a better signal-to-noise ratio and avoiding unwanted oscillations in the signal of interest. Electromagnetic leakage can be reduced by optimizing the transducer design, particularly the transducer pads used for contacting the picoprobes. A real device is operating with finite-length pulses 51 (units up to tens of nanoseconds) that have relatively narrow frequency spectra rather than a wide uniform spectrum in the whole measurement band (which mimics in our case a pulse of just 0:5ns length, as we take 2 GHz band into consideration). To analyze transmission of such pulses, we consider a normalized 10ns long Gaussian pulse [Fig. 3(a)] and 5 ns long square pulse [Fig. 3(e)]atthecarrierfrequency of 4.1 GHz. The calculations are done in a standard way— the pulse frequency spectra [blue curves in Figs. 3(b) and 3(f)]are multiplied by the amplitude-frequency characteristics of the delay line, which is nothing else than the measured frequency-dependent SW transmission in continuous mode [gray curves in Figs. 3(b) and 3(f)]. The resulting spectra of the transmitted signals [dark blue curves in Figs. 3(c) and 3(g)] are then converted back to the time domain using IFT, where they are compared with the original data; see Figs. 3(d) and 3(h). From this comparison, it is visible that the second peak (at about 30 ns delay) is suppressed for both excitation pulses (Gaussian and square), because the second excitation maximum in the antenna spectrum lies outside the signal bandwidth and therefore does not contribute to the transmission. Also, the oscillations of the transmitted signal are suppressed for the same reason. The suppression of the second peak is more pronounced when using the Gaussian pulse, as there are no side products in the frequency domain compared to the square pulse; see blue curves in Figs. 3(b) and 3(f). Other peaks, with a delay of about 41 and 53 ns, are still there, meaning that these peaks originate from the SW signal that undergoes multiple reflections. At the same time, these side peaks are at least 10 times in amplitude (i.e., 20 dB) smaller than the main one. In addition, the main peak distortions and dispersion spreading are weak. These two features prove that the SW-based DL is able to operate in the ns-pulse regime, preserving the welldefined pulse structure and delay time. To construct an effective SW-based DL, it is essential to suppress both electromagnetic leakage and signals arising from SW reflections at the transducers. The desired signal for DL application is the SW signal from the main peak, which propagates only one-way from the excitation to the detection transducer, and is more than 20 dB larger than the other contributions. In the following text, we focus solely on this main SW signal. Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-5 ©Author(s)2025 03 December 2025 13:42:22 We performed systematic measurements using the fabricated DLs with different center-to-center distances between the transducers. The measured SW transmissions for both SW modes and all investigated frequency ranges are plotted in gray in Fig. 4(a). The IFT of the measured SW transmission to the time domain is also plotted in gray in Fig. 4(b). The signal of interest in the time domain is highlighted in color (green for DE and red for BV). The FT of this signal is plotted in the same color in the frequency domain in Fig. 4(a). The signal of interest is the main SW signal that propagates from the excitation transducer toward the detection transducer. It is a pure SW signal with no electromagnetic leakage and no contributions from other SW signals, such as the reflected ones or those with different wavelengths. The delay time Tdis extracted from the normalized SW amplitude at the peak maxima. The signal amplitude in the time domain is normalized for better peak visibility. This analysis, shown in Fig. 4(b), clearly demonstrates that SW-based microscale DLs work in the broad frequency range up to 25 GHz, providing different delay times depending on the transducer distance and SW mode. The comparison of the SW delay time in the time domain for both SW modes is shown in Fig. 5(a). The delay times are extracted from the measurements in Fig. 4(b) for all investigated frequency ranges and SW modes, except the DE mode at 25 GHz, as no SW signal was found in the time-domain spectrum. The experimental delay times (solid lines) are compared with the theoretical delay times (dashed lines) obtained from analytical calculations using the Kalinikos–Slavin 41 model, as described in Appendix A. The applied magnetic fields used in the calculations, together with the group velocities, calculated using Eq. (2), and extracted at k¼3:1rad=μm, are depicted in Table I. The theoretical delay times T d, calculated using the corresponding group velocity and transducer distance [Eq. (1)], and the experimental delay times Tdare depicted in Table I for all investigated distances Dbetween transducers, frequency ranges, and SW modes. From Fig. 5(a) and Table I, it is visible that the analytical calculations agree well with the delay times extracted from the measurements. As expected, the larger the distance between the transducers, the longer the delay time. With increasing frequency, the delay time increases for DE and decreases for BV. This is because the group velocity increases for DE and decreases for BV with increasing frequency; see Fig. 6(b) in Appendix A. The comparison of the insertion losses of the presented DL devices is shown in Fig. 5(b) and Table I. The values are extracted from the raw data at the peak maxima. As expected, the insertion loss increases with larger transducer distance due to damping during spin-wave propagation. This trend holds for all cases, except for the BV mode at a distance of 3 μm, which exhibits a slightly higher insertion loss than at 7:5μm. The deviation can be attributed to imperfections in the fabricated transducers. To explain the frequency dependence of the insertion losses, three factors must be considered: the SW group velocity, lifetime, and the efficiency of excitation and detection by the transducers. The SW lifetime is inversely proportional to frequency and decreases for both SW modes, see Fig. 6(c) and Table I. In the case of DE mode, the group velocity also decreases with increasing frequency [see Fig. 6(b)], which leads to larger insertion losses at higher frequencies. In contrast, for the BV mode, the spin waves are getting faster with increasing frequency [see Fig. 6(b)]. However, this increase in group velocity is not enough to compensate for the decrease in the lifetime, and the decay length for the BV mode also FIG. 3. (a)–(d) Calculated 10 ns Gaussian pulse: (a) normalized time-domain waveform; (b) pulse spectrum (blue) with measured SW transmission (gray) using the transducers with the distance of 7:5μm in theDE mode; (c) product of pulse spectrum and transmission (dark blue) vs transmission (gray); (d) inverse Fourier transform (IFT) to the time domain of the transmission (gray) and the product (dark blue). (e)–(h) Calculated 5 ns square pulse: panels analogous to (a)–(d). Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-6 ©Author(s)2025 03 December 2025 13:42:22 decreases with increasing frequency; see Fig. 6(d) and Table I. Nevertheless, the impedance matching improves for the BV mode with increasing frequency, as it can be derived from the theoretical model presented by Bruckner et al. 52 In both cases, the combination of these three factors explains the observed trends: with increasing frequency, the insertion losses increase for the DE mode and decrease for the BV mode, indicating that operation in the BV mode is more favorable at higher frequencies. The comparison of DL characteristics—material dimensions, transducer size and spacing, operating mode and frequency, delay time, and insertion loss—is presented in Table II. Compared to macroscale YIG devices with millimetre-scale samples and transducer lengths, the insertion loss of the present device is higher (by 14.2 dB relative to Fetisov et al. 33 ); however, the YIG film is more than 160thinner than in Ref. 33. In contrast, relative to the nanoscale YIG devices of Li et al., 37 the presented DL exhibits a substantially lower insertion loss (by 27 dB). Acoustic DLs (SAW/ BAW) generally achieve lower insertion losses but can conveniently operate only in the low-frequency range. In general, the insertion losses of the presented DL devices are higher than 20 dB; however, if the DL device were used at a single frequency, the signal would exhibit a 20 dB margin over the background. The insertion loss can be significantly reduced—potentially down to 3 dB 2 —by optimizing the transducer design 52–55 and by increasing the thickness of the YIG film. IV. DISCUSSION As there is a good match between the experimental results and the analytical theory (summarized in Appendix A), the theory can FIG. 4. (a) In gray: Measured spin-wave (SW) transmission using the transducers with center-to-center distance of 3 μm (first row), 7:5μm (second row), and 52:5μm (third row). The SW transmission is measured at 4, 9, and 25 GHz with a frequency span of 2 GHz for both Damon–Eshbach (DE) and backward volume (BV) modes. The VNA parameters used: power 30 dBm, bandwidth 1 kHz, frequency step 200 kHz, and no averaging. The applied magnetic fields are depicted in Table I.In color: the Fourier transform of the signal of interest extracted in the time-domain in (b) with annulled surroundings, back to the frequency domain (highlighted in color, green for DE and red for BV). (b) In gray: The inverse Fourier transform of the measured SW transmission in (a) to the time domain. The SW amplitude in the time domain is normalized for better signal visibility. In color: The signal of interest (SW signal) is highlighted in color. The time delay Tdis extracted at the SW signal maxima. Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-7 ©Author(s)2025 03 December 2025 13:42:22 be implemented to predict and optimize the DL parameters to achieve specific delay times. †To achieve shorter delay times, the simplest approach is to position the transducers as close to each other as possible; see Fig. 5(a). However, this approach has practical limitations, making it essential to explore strategies to maximize the SW group velocity. For dipolar spin waves (at large wavelengths), the group velocity increases with both the magnetic film thickness and the saturation magnetization. Doubling the thickness of the magnetic film results in an approximately twofold higher SW group velocity, thereby reducing the delay time by half. The only drawback is the increase in bulkiness of the device. The saturation magnetization of single-crystalline YIG films can be increased by substituting Nd and Pr ions; however, such substitutions drastically increase the damping. Therefore, a more effective approach to increase saturation magnetization would be the replacement of the iron ions on the octahedral lattice sites with diamagnetic ions such as Sc and In. 56,57 Another approach can be to use magnetic materials with higher damping, such as nanocrystalline YIG films, whose magnetization can be increased by doping with rare earth ions 59 or using different magnetic materials with higher saturation magnetization, such as CoFeB or NiFe. However, this would lead to a decrease in signal magnitude as a result of the enhanced damping compared to the single-crystalline YIG films. Nevertheless, this effect might be less pronounced when the propagation distance between the transducers is very small. For exchange spin waves (at short wavelengths), an increase in group velocity can also be achieved with Ga-substituted YIG (Ga:YIG), which exhibits substantially higher vgowing to its enhanced exchange stiffness, despite its lower Ms. 58 To further increase the group velocity, it is preferable to use the DE mode when operating in a lower frequency range and to use the BV mode in a higher frequency range; see Fig. 6(b), which agrees well with the results obtained in Ref. 24. An option to increase the SW group velocity for the DE mode is to add a metalized surface to the YIG film. 35,50 †To achieve longer delay times, there are two solutions: (i) to place the transducers further away from each other [see Fig. 5(b)]or (ii) to operate at a lower SW group velocity. Both the solutions FIG. 5. (a) Experimental delay time (solid line) extracted from Fig. 4(b), and theoretical delay (dashed line) time calculated using Eq. (1). (b) Insertion losses obtained from the maxima of the SW transmission bands. All values are calculated/extracted for Damon-Eshbach (DE, in green) and backward volume (BV, in red) for distances between the transducers of 3, 7.5, and 52:5μm. TABLE I. Overview of the key parameters characterizing SW-based delay lines for Damon–Eshbach (DE) and backward volume (BV) modes at 4, 9, and 25 GHz. The table lists the applied magnetic fields B, calculated group velocities v g , SW lifetimes τ, decay lengths δat k= 3.1 rad/μm; the theoretical delay time T dderived from the calculated group velocity and the center-to-center distance between the transducers D; and the experimental delay times T d and insertion losses IL extracted from measurements for transducers with distances of 3, 7.5 and 52.5 μm. 4 GHz 9 GHz 25 GHz DE BV DE BV DE BV D(μm) B(mT) 71 87 244 255 807 823 v g (m/s) 598 308 298 429 145 508 τ(ns) 192 173 89 86 32 32 δ(μm) 115 54 26 37 5 16 3T d(ns) 5.0 9.8 10.1 7.0 20.8 5.9 T d (ns) 6.0 ± 2.0 8.6 ± 4.0 9.7 ± 3.5 7.3 ± 2.7 18.0 ± 3.8 6.5 ± 2.2 IL (dB) 23.7 34.8 22.9 30.3 33.3 28.1 7.5 T d(ns) 12.5 24.4 25.2 17.5 51.9 14.8 T d (ns) 13.6 ± 3.2 24.5 ± 7.3 26.7 ± 4.8 18.2 ± 3.5 46.5 ± 3.1 15.1 ± 2.9 IL (dB) 27.1 36.9 25.7 31.0 34.0 26.8 52.5 T d(ns) 87.8 170.7 176.3 122.5 363.2 103.4 T d (ns) 82.0 ± 14.1 154.5 ± 21.8 158.4 ± 14.9 111.5 ± 16.7 …95.0 ± 9.8 IL (dB) 36.4 52.4 40.7 48.0 …44.5 Journal of Applied Physics ARTICLE pubs.aip.org/aip/jap J. Appl. Phys. 138, 143908 (2025); doi: 10.1063/5.0286108 138, 143908-8 ©Author(s)2025 03 December 2025 13:42:22