France



Sheet- and film-type soft magnetic materials have been widely used to suppress unexpected noise in mobile and wearable devices using ferromagnetic resonance (FMR) losses [1][2]. The designs of these magnetic noise suppressors are mainly based on large-scale electromagnetic field simulations and &quot;trial and error&quot; experiences. In previous studies, the effect of the complex permeability of the magnetic sheet and film on circuit parameters of transmission lines was investigated by a simple magnetic circuit analysis using only the cross-sectional size and material parameters [3]. However, the effect on the reflection and the transmission coefficients have not been estimated quantitatively and the design guideline of the noise suppressor has not been clarified.&lt;br/&gt;In this paper, the estimation method of the reflection and the transmission coefficients of a transmission line with a noise suppressor is investigated including the effect of the complex permeability. A 95 μm-width microstrip line (MSL) with a Co-Zr-Nb film is discussed as a test bench. The electrical equivalent circuit parameters of the MSL with Co-Zr-Nb film were calculated by the magnetic circuit analysis and the characteristic impedance was estimated. The thickness of the Co-Zr-Nb film was determined considering impedance matching below 1 GHz range, where it was assumed that a signal frequency range, and the conductive noise suppression by the Co-Zr-Nb film at 3 GHz was estimated.&lt;br/&gt;Figure 1 illustrates the magnetic circuit in the cross-sectional view of the MSL with the Co-Zr-Nb film. The MSL was fabricated on low-temperature co-fired ceramic (LTCC) substrate with the thickness &lt;i&gt;h&lt;/i&gt;=100 µm and the relative permittivity of 9.8. The width, thickness and length of the signal line are &lt;i&gt;w&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;=95 μm, &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;=3 μm, and 10 mm, respectively. The Co-Zr-Nb film was fabricated using radio frequency (RF) sputtering and deposited on a SiO&lt;sub&gt;2&lt;/sub&gt; substrate. The film thickness &lt;i&gt;t&lt;/i&gt; was obtained by the magnetic circuit analysis and the electromagnetic simulation so that the characteristic impedance of the MSL with and without the film have a same value. The electrical equivalent circuit of the MSL with the Co-Zr-Nb film was obtained to calculate the characteristic impedance. The circuit consists of series impedance &lt;i&gt;Z = R + jωL&lt;/i&gt; = (&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;&lt;i&gt;+R&lt;/i&gt;&lt;sub&gt;e&lt;/sub&gt;&lt;i&gt;+R&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;) + &lt;i&gt;jωL&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and parallel conductance &lt;i&gt;Y = jωC&lt;/i&gt;, where &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;m &lt;/sub&gt;and &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; were calculated by the magnetic circuit analysis considering the effect of the complex permeability of the Co-Zr-Nb film. &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; and &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;e&lt;/sub&gt; were the resistance of the signal line including the skin effect and the increase of resistance due to the eddy current loss generated in the film [3], respectively. &lt;i&gt;C &lt;/i&gt;= 2 pF calculated by experimental value at 0.1 GHz [4].&lt;br/&gt;Figure 2(a) shows the estimated characteristic impedance &lt;i&gt;Z&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; = (&lt;i&gt;Z&lt;/i&gt;/&lt;i&gt;Y&lt;/i&gt;)&lt;sup&gt;0.5&lt;/sup&gt; with &lt;i&gt;t&lt;/i&gt; = 0.1-1 μm. Below 1 GHz, the impedance is roughly constant and the estimated impedance of the MSL with 1-μm-thick film is almost the same as the measured value of MSL without the film. Therefore, &lt;i&gt;t&lt;/i&gt; = 1 μm was used to calculate the reflection and the transmission coefficient.&lt;br/&gt;Figure 2(b) and (c) shows the reflection coefficient |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt;|, transmission coefficient |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;21&lt;/sub&gt;|, and the noise suppression &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;loss&lt;/sub&gt;/&lt;i&gt;P&lt;/i&gt;&lt;sub&gt;in&lt;/sub&gt; = 1-(|s&lt;sub&gt;21&lt;/sub&gt;|&lt;sup&gt;2 &lt;/sup&gt;+|s&lt;sub&gt;11&lt;/sub&gt;|&lt;sup&gt;2&lt;/sup&gt;) of the MSL with 1-μm-thick film obtained by the electrical equivalent circuit analysis. In the case with the film, |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt;| and |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;21&lt;/sub&gt;| were almost the same as the measured value within about 8 dB and 0.1 dB below 5 GHz, respectively. |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt;| increased up to 8 dB below 1 GHz but the value kept less than -25 dB. On the other hand, |&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;21&lt;/sub&gt;| decreased as the frequency increased because of the combination of FMR and Joule losses in each film at 3 GHz. &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;loss&lt;/sub&gt;/&lt;i&gt;P&lt;/i&gt;&lt;sub&gt;in &lt;/sub&gt;is maximized at 3 GHz.&lt;br/&gt;In summary, the reflection and the transmission coefficients of a transmission line with a noise suppressor were quantitatively estimated including the effect of the complex permeability using the magnetic circuit analysis using the cross-sectional size and material parameters. The thickness of the Co-Zr-Nb film was determined considering characteristic impedance matching. As a result, the reflection coefficient was lower than -25 dB below 1 GHz, and the conductive noise suppression was obtained at 3 GHz. Those results give a way to clarify the design guideline of the noise suppressors. This work was supported in part by JSPS KAKENHI Grant Number 20K04497. Part of this work was carried out under the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University.

**References:**

[1] S. Yoshida et al., IEEE Trans. Magn., Vol.37, No.4, pp.2401-2403 (2001).&lt;br/&gt;[2] K. Kondo et al., IEEE Trans. Magn., Vol.45, No.10, pp.4250-4252 (2009).&lt;br/&gt;[3] S. Muroga et al., J. Elec. Materi., Vol.48, No.3, pp.1342-1346 (2019).&lt;br/&gt;[4] T. Mikami et al., The 44th Annual Conf. Magn. Jpn, 14aD-11 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f49f11a1a0eaeda3f369b57ea16aa68b.jpg)
Fig.1 cross-sectional dimensions and magnetic circuit of a one kine MSL with Co-Zr-Nb film

![](https://assets.underline.io/uploads/markdown_image/1/image/c0f049207352d2aa4d74175eaaee669e.jpg)
(a) Charateristic impedance (b) S parameter (c) Input loss ratio&lt;br /&gt;
Fig.2 Transmission characteristics

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 Estimation of Noise Suppression in MSL with Co-Zr-Nb films Considering Impedance Matching

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Sheet- and film-type soft magnetic materials have been widely used to suppress unexpected noise in mobile and wearable devices using ferromagnetic resonance (FMR) losses [1][2]. The designs of these magnetic noise suppressors are mainly based on large-scale electromagnetic field simulations and "trial and error" experiences. In previous studies, the effect of the complex permeability of the magnetic sheet and film on circuit parameters of transmission lines was investigated by a simple magnetic circuit analysis using only the cross-sectional size and material parameters [3]. However, the effect on the reflection and the transmission coefficients have not been estimated quantitatively and the design guideline of the noise suppressor has not been clarified. In this paper, the estimation method of the reflection and the transmission coefficients of a transmission line with a noise suppressor is investigated including the effect of the complex permeability. A 95 μm-width microstrip line (MSL) with a Co-Zr-Nb film is discussed as a test bench. The electrical equivalent circuit parameters of the MSL with Co-Zr-Nb film were calculated by the magnetic circuit analysis and the characteristic impedance was estimated. The thickness of the Co-Zr-Nb film was determined considering impedance matching below 1 GHz range, where it was assumed that a signal frequency range, and the conductive noise suppression by the Co-Zr-Nb film at 3 GHz was estimated. Figure 1 illustrates the magnetic circuit in the cross-sectional view of the MSL with the Co-Zr-Nb film. The MSL was fabricated on low-temperature co-fired ceramic (LTCC) substrate with the thickness h=100 µm and the relative permittivity of 9.8. The width, thickness and length of the signal line are ws=95 μm, ts=3 μm, and 10 mm, respectively. The Co-Zr-Nb film was fabricated using radio frequency (RF) sputtering and deposited on a SiO2 substrate. The film thickness t was obtained by the magnetic circuit analysis and the electromagnetic simulation so that the characteristic impedance of the MSL with and without the film have a same value. The electrical equivalent circuit of the MSL with the Co-Zr-Nb film was obtained to calculate the characteristic impedance. The circuit consists of series impedance Z = R + jωL = (Rm+Re+Rs) + jωLm and parallel conductance Y = jωC, where Rm and Lm were calculated by the magnetic circuit analysis considering the effect of the complex permeability of the Co-Zr-Nb film. Rs and Re were the resistance of the signal line including the skin effect and the increase of resistance due to the eddy current loss generated in the film [3], respectively. C = 2 pF calculated by experimental value at 0.1 GHz [4]. Figure 2(a) shows the estimated characteristic impedance Z0 = (Z/Y)0.5 with t = 0.1-1 μm. Below 1 GHz, the impedance is roughly constant and the estimated impedance of the MSL with 1-μm-thick film is almost the same as the measured value of MSL without the film. Therefore, t = 1 μm was used to calculate the reflection and the transmission coefficient. Figure 2(b) and (c) shows the reflection coefficient |S11|, transmission coefficient |S21|, and the noise suppression Ploss/Pin = 1-(|s21|2 +|s11|2) of the MSL with 1-μm-thick film obtained by the electrical equivalent circuit analysis. In the case with the film, |S11| and |S21| were almost the same as the measured value within about 8 dB and 0.1 dB below 5 GHz, respectively. |S11| increased up to 8 dB below 1 GHz but the value kept less than -25 dB. On the other hand, |S21| decreased as the frequency increased because of the combination of FMR and Joule losses in each film at 3 GHz. Ploss/Pin is maximized at 3 GHz. In summary, the reflection and the transmission coefficients of a transmission line with a noise suppressor were quantitatively estimated including the effect of the complex permeability using the magnetic circuit analysis using the cross-sectional size and material parameters. The thickness of the Co-Zr-Nb film was determined considering characteristic impedance matching. As a result, the reflection coefficient was lower than -25 dB below 1 GHz, and the conductive noise suppression was obtained at 3 GHz. Those results give a way to clarify the design guideline of the noise suppressors. This work was supported in part by JSPS KAKENHI Grant Number 20K04497. Part of this work was carried out under the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University.

**References:**

[1] S. Yoshida et al., IEEE Trans. Magn., Vol.37, No.4, pp.2401-2403 (2001). [2] K. Kondo et al., IEEE Trans. Magn., Vol.45, No.10, pp.4250-4252 (2009). [3] S. Muroga et al., J. Elec. Materi., Vol.48, No.3, pp.1342-1346 (2019). [4] T. Mikami et al., The 44th Annual Conf. Magn. Jpn, 14aD-11 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f49f11a1a0eaeda3f369b57ea16aa68b.jpg)
Fig.1 cross-sectional dimensions and magnetic circuit of a one kine MSL with Co-Zr-Nb film

![](https://assets.underline.io/uploads/markdown_image/1/image/c0f049207352d2aa4d74175eaaee669e.jpg)
(a) Charateristic impedance (b) S parameter (c) Input loss ratio 
Fig.2 Transmission characteristics

poster

Spin wave logic devices are mainly based on the interference effect of spin waves. The phase modulation of spin waves has become the main direction of spin wave logic device design. SWs in Damon-Eshbach configuration in waveguide exhibits two types of mode: edge mode spin waves(E-SWs) and central mode spin waves (C-SWs)[1-3]. There has been much effort devoted to the development of a good deal of spin wave devices based on C-SWs such as phase shifters, logic gates, transistors, multiplexers, as well as majority gates. However, there are few researches of E-SWs in the waveguide. As well as known, the propagation of C-SWs in the waveguide is usually accompanied by the hybridization of multiple modes, which is not conducive to control the propagation characteristics of the spin waves precisely. Therefore, E-SWs may be more suitable for the design of spin wave devices. In this work, we propose a novel design of spin wave XOR gate based on edge-mode type spin wave, whose schematic is shown in Fig.1. We perform micromagnetic simulations using the MuMax3 software to study the phase shift characteristics and logic functionality in the structure[4]. The structure is composed of input waveguide, output waveguide and interference Y-type waveguide. The external field () of 1000 is applied parallel to the y-axis. The length, width and thickness of the narrow YIG waveguide are Li = 500 nm, W1= 50 nm, Tw = 10 nm, respectively. The length, width and thickness of the wide YIG waveguide are Lc= 3000 nm, W2= 400 nm, Tw = 10 nm, respectively. The distance between the Co element and the input wave guide is Le= 500 nm. The length and thickness of Co element are Lh = 970 nm, Tw = 10 nm, respectively. The gap between the YIG waveguide and the Co element is G =110 nm. The simulation results are shown in Fig. 2. The wavenumbers of E-SWs on both sides of Phase Shift Zone in YIG waveguide change after placing the Co element with high saturation magnetization on one side of YIG waveguide[5]. Therefore, π phase shift can be achieved by setting appropriate structural parameters. Based on this feature, this structure can realize the function of a spin-wave XOR logic gate. The local inhomogeneity of the effective field on one side of the YIG waveguide is the main reason for the phase shift. The stray field of the Co element causes this local inhomogeneity. Therefore, this phase shift is controllable by adjusting the stray field of the Co element. It can be changed by fine-tuning the Co magnetization direction through the SOT effect. Therefore, by applying an appropriate current on β-Ta, the operating frequency of the XOR gate can be broadened by utilizing the SOT effect[6]. In summary, we demonstrated a spin wave XOR gate based on edge mode type spin wave phase shifter. The operating frequency of the proposed XOR gate is a broadband rather than a specific frequency. The input and output signals are all encoded with the amplitude of SWs. The feature of proposed design is that the dipole field generated by Co element is used to shift the phase of the edge mode spin wave on one side of the YIG waveguide, so that the SWs on both sides have a phase difference.

**References:**

[1] K. Bernstein, R. K. Cavin, W. Porod. Proceedings of the IEEE, 98 (12), 2169–2184. (2010). [2] S. D. Bader, S. S. P. Parkin. Spintronics. Annu. Rev. Condens. Matter Phys. 1:71–88. (2010). [3] S. Saha, S. Barman, Y. Otani. Nanoscale, 7 (43). (2015). [4] A. Vansteenkiste, J. Leliaert, M. Dvornik. Aip Advances, 4 (10), 107133. (2014). [5] Zhizhi Zhang, M. Vogel, M. B. Jungfleisch. Physical Review B, 100 (17), 174434. (2019). [6] Zhiwei Ren, Shuang Liu, Lichuan Jin. Scientific Reports, 9, 7093. (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7861c719dce833d6266a597617c6796c.jpg)
Fig. 1. Schematic of SOT-based broadband spin wave XOR logic gate.

![](https://assets.underline.io/uploads/markdown_image/1/image/58470d5f026c8d4c0948a5abdc449f70.jpg)
Fig. 2. Diagram of spin wave propagation with current density of at 4.41GHz excitation frequency.

 Design of broadband XOR logic gate based on edge-mode type spin wave

In recently time the study of magnetostatic spin wave (MSW) propagation in ferromagnetic structures is of great interest [1,2]. In this work we experimentally and by micromagnetic simulation studied spin wave (SW) propagation in microwavegide with linearly varying width, formed from a yttrium iron garnet (YIG) film. The YIG film was grown on the gadolinium gallium garnet (GGG) substrate with a thickness of 500 μm. Magnonic waveguide with linearly varying width [3] was fabricated by the laser scribing technique from the YIG film. The scetch of structure is shown in Fig. 1 consists of segments: I - input waveguide with a length of 5 mm and a width of 2500 μm; II - waveguide with a smoothly varying width from 2500 μm to 200 μm, with a length of 10 mm; III - output waveguide 5 mm long and 200 μm wide. The thickness of the YIG film corresponded to 10 μm. The SW was excited by supplying a microwave signal to a microstrip antenna 30 μm wide, located in the I segment of the waveguide structure at a distance of 1500 μm from the starting of the waveguide. Studied srtucture was placed in external magnetic field with the magnitude H0 = 1200 Oe directed along the z-axis in order to excite a surface magnetostatic spin wave (MSSW). Micromagnetic modeling was carried out based on the solution of the Landau-Livshitz-Hilbert equation by the finite difference method. Also, when modeling the structure, regions with an increased attenuation parameter were introduced at the ends of the waveguide to get rid of reflections. Transmission and dispersion characteristics of the studied structure were experimentally measured using the microwave network analyzer E8362C PNA. The experimental measurement square of intensity spin wave was performed by the Brillouin light scattering (BLS) technique in backscattering configuration. A laser beam with a wavelength of 532 nm was focused to a spot of a diameter of 25 μm on the surface of magnonic waveguide with linearly varying width. Transformation of the beating pattern of the first and third transverse modes can be explained by mode decomposition from BLS map with amplitude resolution. the results of calculating the distribution of the magnetization of the MSSW in the linear and nonlinear modes, respectively, are shown. In this case, in a narrow region of the waveguide, a nonlinear process of three-magnon MSSW decay is observed. This confirmed by maps of dynamic magnetization distribution at frequencies equal to the frequency of the signal pumping frequency, obtained experimentally by BLS technique. This work was supported by the Russian Science Foundation (project no. 20-79-10191).

**References:**

[1] V. V. Kruglyak, S. O. Demokritov, D.Grundler, Journal of Physics D: Applied Physics, 43(26), 264001, (2010) [2] D. Sander, S. O. Valenzuela, D. Makarov, et. al., Journal of Physics D: Applied Physics, 50(36), 363001, (2017) [3] D. V. Kalyabin, A. V. Sadovnikov, E. N. Beginin, et. al., Journal of Applied Physics, 126(17), 173907. doi:10.1063/1.5099358, (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/90e17af846ce99b4d60dc5fe7b517c4c.jpg)
Fig.1 The scetch of studied structure with linearly varying width with marked segments.

 Linear and nonlinear spin-wave propagation in magnonic waveguide with linearly varying width

As one type magnetization dynamics excitations in magnetic materials, spin waves are providing a promising candidate as information carriers in the future spintronic logic and computing circuits and systems. Several concepts and building block for spin wave-based devices have been developed in recent years, including magnonic crystals, logic gates, transistor, multiplexers and wake-up receiver. The excitation and manipulation of magnetization dynamics is an essential part of all these spin wave-based devices. Electrical methods of magnetization dynamic excitation are conventionally used the magnetic field induced by a microwave antenna or spin torque oscillation induced by spin-polarized currents. However, these methods are generally introducing high Ohmic energy consumption due to the high current density, which contrary to the requirement for energy efficient spintronic devices. Furthermore, for practical applications, it is very desirable to use devices without permanent magnetic field bias. Motivated by these shortcoming, alternative approaches for the excitation of magnetization dynamics have been explored recently, include the effect of the voltage-controlled magnetic anisotropy, the elastic waves and strain pulse. A more comprehensive investigation of magnetization dynamics and spin wave excitation in nanoscale multiferroic heterostructures with perpendicular anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (i-DMI) has not yet been attempted. In this work, by means of a micromagnetic simulation combined with electromechanical to explore a promising way to excitation spin wave using voltage-controlled strain in a nanoscale multiferroic heterostructures with PMA and i-DMI. In this heterostructure, the excitation area is setting at the center of ferromagnetic nanostrip with an electrode underneath which can easily get a biaxial isotropy in-plane strain (Fig.1(a)). The relaxed profiles of the out-of-plane magnetization components along the center width direction with different DMI coefficient are demonstrated in Fig. 1(b). A SinC strain field pulse is applied locally at the excitation region to excite magnetization dynamics with a wide frequency range. The frequency spectra (Fig.1(c)) clear shown that two distinct resonance peaks around at 4 GHz and 13 GHz. It is worth mentioning, that all the spin dynamics excited by the strain fields are symmetric within the in-plane axis direction, that means only the odd values node are excited. The spin wave frequency spectra in terms of frequency versus propagation distance are obtained by an FFT of δmx on the time scales. And the spin wave transmission characteristics (Fig.1(d)) are obtained by probing the spectra intensity in x position 200 nm and 1000 nm, respectively. The propagation characteristics of spin wave studied in detail for different frequency, for example, the spin wave profiles generated and transferred by biaxial isotropy in-plane strain at 4 GHz, 4.5 GHz and 13 GHz are shown in Fig. 2(a)-(c). The dynamic magnetization profiles show that the spin wave phases front of these modes are perpendicular to the propagation direction. The dispersion characteristics in terms of the width position along the y direction versus wave vector are obtained by a two-dimensional (2D) FFT of magnetization components δmx. The results are shown in Fig. 2(d)-(f). At 4 GHz and 4.5 GHz, the width mode n=1 with a wave vectors kx=0.015 rad/nm and kx=0.037 rad/nm are present, respectively. Note, the mode n=0 with an extremely small amplitude is also observer. At 13 GHz, both n=1 and high order n=3 modes are present with wave vector kx=0.164 rad/nm and kx=0.059 rad/nm, respectively. To summarize, we analyzed the excitation of magnetization dynamics and spin waves via the magnetoelastic effect by applying locally biaxial isotropy in-plane strains, and we studied their propagation characteristics in non-uniformly magnetized ferromagnet waveguides induced by i-DMI. Our works show the potential of using strain with the presence of i-DMI as perspective for integrating spin waves emitter into future logic or computing devices and hinting at possible technological applications in strain controlled spintronic systems.

**References:**

1. J. Chen, J. Hu and H. Yu, iScience, 23, 101153 (2020). 2. R. Verba, M. Carpentieri and G. Finocchio, et al., Sci Rep, 6, 25018 (2016). 3. Q. Wang, T. Brächer and M. Mohseni, et al., Appl. Phys. Lett., 115, 092401 (2019). 4. A. V. Chumak, P. Pirro and A. A. Serga, et al., Appl. Phys. Lett., 95, 262508 (2009). 5. S. Klingler, P. Pirro and T. Brächer, et al., Appl. Phys. Lett., 106, 212406 (2015). 6. M. á. Kostylev, A. Serga and T. Schneider, et al., Appl. Phys. Lett., 87, 153501 (2005). 7. F. Macia, F. C. Hoppensteadt and A. D. Kent, Nanotechnology, 25, 045303 (2014). 8. R. Verba, M. Carpentieri and G. Finocchio, et al, Phys. Rev. Appl., 7 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/60743a42a0f49333363ec28086233b2e.jpg)
Fig. 1 (a) Schematic view of the investigated multiferroic heterostructures, the yellow color indicates the region where strain field is applied. (b) Equilibrium magnetization components mz across the width direction of nanostrip. (c) The spin dynamic characteristics obtained by integrating the perturbation over the excitation area. (d) The frequency spectra obtained from an FFT of the temporal evolution of perturbation magnetization in space.

![](https://assets.underline.io/uploads/markdown_image/1/image/934a1ea649c0d006edd041cd74d85817.jpg)
Fig.2 (a)-(c) Snapshots of the magnetization distribution pattern for different excitation frequency: 4 GHz, 4.5 GHz and 13 GHz, respectively. (d)-(e) Spin wave wavenumber distribution across the ferromagnet strip width computed by 2D FFT of the magnetization component δmx.

 Magnetization Dynamics and Spin Wave Excitation in Strain-mediated Multiferroic Heterostructures with the Interfacial Dzyaloshinskii-Moriya Interaction

In the last decade, peculiarities of spin-wave (SW) processes in diverse magnetic materials have opened new avenues in the field of magnonics. An increased research activity in this field is due to developing of novel microwave devices for analog signal processing and data transmission. Artificial spatially periodic magnetic media, called magnonic crystals (MCs), constitute one of the most promising building blocks for these applications [1]. In these crystals, the formation of spectral regions, band-gaps, with prohibited wave propagation is caused by Bragg scattering. Further advances in the field were achieved owing to a development of the dynamic MCs [2]. Promising functionalities of these crystals arise from the nonreciprocal behavior and dynamic controllability that provides altering of the band-gaps from full rejection to full transmission. Usually two types of the dynamic MCs are distinguished: the current- controlled and voltage-controlled ones. The first one originates from a spatial variation of a magnetic field induced by an electric current in the metal wires or periodic screens [3]. The mechanisms behind the second one are divided into the two types. These are a voltage-controlled perpendicular magnetic anisotropy in ferromagnetic-dielectric heterostructures [4] and a voltage-controlled variation of the ferroelectric layer permittivity in ferrite-ferroelectric structures [5]. Another way to produce a fully tunable MC is to use a laser radiation, which creates thermal landscapes and results in periodic modulations of the saturation magnetization [6]. Recently, our work [7] shows promising features of the metal-insulator transition (MIT) in the heterogeneous ferrite-vanadium dioxide structures. Such transition is characterized with an abrupt change of the VO2 conductivity (by four or five orders of magnitude) near the phase transition temperature at ultrafast timescales. Therefore, a combination of ferrite films with materials exhibiting the MIT allows one to exploit novel spin-wave phenomena that are of interest for enhancement of the functionality of the magnonic devices. The aim of the present work is to study the application of the MIT for controlling the microwave SW dynamics in the MC, which is composed of VO2 and grooved yttrium iron garnet (YIG) films (see Fig. 1a). The ferrite structure was fabricated in the form of the 3-cm-long and 2-mm-wide stripe of the 5.5-μm-thick single-crystal YIG film. This film had a saturation magnetization of 1985 G at room temperature. In order to produce a MC, the thickness of the YIG film was periodically modulated to a depth of 0.8 µm using a wet chemical etching. The periodic pattern consisted of 10 parallel grooves with a width of 65 µm spaced by 265 µm, so that a lattice constant was 330 µm. The film was epitaxially-grown on the gallium gadolinium garnet (GGG) substrates of 500-µm thickness. The films had the ferromagnetic resonance linewidth of 0.5 Oe at 5 GHz. A 0.55-µm-thick VO2 film was deposited on a silicon dioxide substrate with thickness of 500 µm by a reactive DC magnetron sputtering. This film demonstrates a MIT around 339 K, which manifests itself as a variation of the resistance from 148 kΩ down to 25 Ω with the temperature increase from 327 K to 348 K (see Fig. 1b). The VO2 sample has in-plane dimensions of 3x3 mm2. The composed YIG- VO2 structure was magnetized by a spatially uniform bias magnetic field of 1566 Oe applied parallel to the antennas providing the conditions for excitation of the surface SWs. To accomplish the measurements, the experimental waveguiding structure was placed in a temperature-controlled probe station providing monitored heating and cooling. The transmission characteristics of the structure were measured for different temperatures by the vector network analyzer. The experimental results are shown in Fig. 2. Near room temperature the resistance of the VO2 film is high. Therefore, the VO2 film has a negligible effect on the SW propagation in the YIG-VO2 bilayer in the experimental frequency range. In particular, at the initial temperature T = 327 K, the band-gaps are formed at the frequencies expected from the conventional Bragg analysis (see Fig. 2a). To analyze only the direct MIT impact on the original band structure of the MC, the SW carrier frequency was normalized by the cutoff frequency for the surface SW f⊥ [8]. This enables one to keep out of sight the frequency shifts of the band-gap positions due to changing of the YIG-film saturation magnetization. An increase of temperature up to T = 348 K provides a sharp drop of the VO2 resistance down to 25 Ω. It leads to a drastic change in the SW group velocity (see Fig. 2b). Therefore, the frequency bandwidth of the transmission characteristic is narrowed and becomes less than the frequency distance to the first-order band-gap. As a result, the band structure of the proposed MC is fully suppressed. A utilization of this phenomenon is practically beneficial because it enables one to control SW dynamics in the waveguiding structure. In particular, the low and high levels of microwave attenuation in the structures are determined by a high-resistance and low-resistance states of the VO2, respectively. As a result, the YIG-VO2 layered structure operates as a switch triggered by the MIT phase transition in the VO2 film. The reported study was funded by RFBR and JSPS, project # 21-52-50006.

**References:**

1. G. Csaba, Á. Papp, W. Porod, Phys. Lett. A 381 (17), 1471-1476 (2017). 2. A. V. Chumak, T. Neumann, A. A. Serga, et al., J. Phys. D, 42 (20), 205005 (2009). 3. A. A. Nikitin, A. B. Ustinov, A. A. Semenov, et al., Appl. Phys. Lett., 106 (10), 102405 (2015). 4. B. Rana, Y. Otani, Phys. Rev. Appl. 9 (1), 014033 (2018). 5. A. B. Ustinov, A. V. Drozdovskii, A. A. Nikitin, et al., Commun. Phys., 2, 137 (2019). 6. M. Vogel, A. V. Chumak, E. H. Waller, et al., Nat. Phys., 11 (6), 487 (2015). 7. A. A. Nikitin, A. A. Nikitin, A. B. Ustinov, et al., J. Appl. Phys., 128 (18), 183902 (2020). 8. D. D. Stancil and A. Prabhakar, Spin Waves: Theory and Applications (Springer, New York, 2009).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ca739c24f2f4ff5c7c3cb9981e08de80.jpg)
Fig. 1 (a) Sketch of the experimental structure. (b) Resistance-temperature curves of the VO2 film.

![](https://assets.underline.io/uploads/markdown_image/1/image/3fc0c7ff7c00b5d399bbccb47193937f.jpg)
Fig. 2 (a) Transmission characteristics and (b) group velocities of the surface SW.

 A novel approach for controlling spin-wave dynamics in magnonic crystals using metal-insulator switching of vanadium dioxide

Fano resonances generally appears in the interaction of subsystems with a continuous (continuum) and discrete spectrum of energy states and also observed in many physical systems: quantum and nanoscale [1], optical and microwave [2], plasmonic [3] . Systems of coupled Fano resonators [4], nonlinear effects [5], bistable and nonreciprocal properties are also being investigated. One of the promising approaches for the generation, transmission and processing of information signals is using spin waves (SW) as information carriers. By analogy with electronics, this area is called “magnonics” [6,7]. SWs characteristics can be modulated (amplitude, phase, frequency) and can propagate in waveguides based on various films of magnetically ordered materials. Currently, yttrium-iron garnet (YIG) is the magnetic material with the lowest losses (the smallest ferromagnetic resonance line width). Potentially, spin-wave excitations, due to their low damping in coupled waveguide-resonator systems, can also exhibit Fano resonances. However, unlike optical systems, systems based on magnetic materials have the following feature: the dependence of the equilibrium state of magnetic moments and, therefore, internal static magnetic fields on the geometric dimensions and shape of magnetic subsystems (waveguides and resonators), the magnitude and direction of the external magnetic field, anisotropy fields, etc. Here we study the characteristics of the Fano resonance in a coupled system of lateral magnonic stripes with piezoelectric layer and resonators depending on the geometric parameters of the systems, the magnitude of the coupling between them, and the electric field of the piezoelectric layer. Using micromagnetic simulation of spin-wave excitations and numerical integration of the coupled wave equation system, the transfer characteristics of the lateral system and the Fano resonance parameters are calculated. Micromagnetic modeling was carried out for the structure (see Fig. 1) based on a YIG film with a thickness of 10 μm and a saturation magnetization of 4πM0 = 1750 G. The structure consists of two tappered planar magnonic stripes with a widths w1 = 2500 μm and w2 = 200 μm. A system of resonators with a width of “w2” and a length of 500 μm is located between the stripes. A 200 μm-thick lead zirconate titanate (PZT) is used as a piezoelectric material. A 1 μm -thick titanium electrode is placed ("GND" in Fig. 1) on a top side of PZT, which does not have a significant effect on the propagation of SW in magnetic stripes. On the bottom side of PZT a 100 nm-thick titanium electrode. The entire structure is placed in an external uniform magnetic field, H0 = 1200 Oe, directed along the Z axis, which ensures efficient excitation of magnetostatic surface waves. To reduce parasitic SW reflections from the boundaries of microwave guides, layers (0 &lt;x &lt;0.6 mm and 6.0 &lt;x &lt;6.6 mm) with exponentially increasing dissipation parameters (ABL) were introduced. The features of exhibiting constructive and destructive interference of SWs under the conditions of Fano resonance are shown. An effective tuning of the strain of the piezoelectric layer and the effect of magnetostriction in lateral structure. This work was supported by the Russian Science Foundation Grant (#20-79-10191).

**References:**

[1] A.E. Miroshnichenko, S. Flach, Yu.S. Kivshar, Rev. Mod. Phys., Vol. 82, P. 2257—2298 (2010). [2] M. Galli, S. L. Portalupi, M. Belotti, L.C. Andreani, L. O’Faolain, and T. F. Krauss, Appl. Phys. Lett., Vol. 94, P. 10–13 (2009). [3] R. Ortuno, M. Cortijo, A. Martinez, J. Opt., Vol. 19, P. 025003 (2017). [4] B. Djafari-Rouhani, H. Al-Wahsh, A. Akjouj and L. Dobrzynski, Journal of Physics: Conference Series, Vol. 303, P. 012017 (2011). [5] M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, K. Karrai, Nature, Vol. 451, P. 311–314 (2008). [6] A.A. Grachev, S.E. Sheshukova, S.A. Nikitov, A.V. Sadovnikov, Journal of Magnetism and Magnetic Materials, Vol. 515, P. 167302 (2020). [7] A.V. Sadovnikov, A.A. Grachev, A.A. Serdobintsev, S.E. Sheshukova, S.S. Yankin, S.A. Nikitov, IEEE Magnetics Letters. Vol. 10. 5506405 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/be08bb31aa190e454ca6f32842716cae.jpg)

 Voltage-controlled Fano resonances in irregular magnonic structure

Investigations of the transfer of spin momentum in planar and multilayer magnetic structures make it possible to reveal that spin waves (SW) could potentially be used as data carriers in low energy computing devices [1]. Properties of spin-wave transport in three-dimensional (3D) magnonic networks [2] are determined by the dipole and exchange interactions and can change significantly with a change in the parameters of the medium, such as variation in the direction and magnitude of the equilibrium magnetization caused by elastic deformations, modification of substrate properties by the laser light [3]. The present work is devoted to the development of the ideas of the directed branching of SW in 3D structures. In this work, we propose a magnonic structure with the possibility of spin-wave transport in both the lateral and vertical directions. In this case, the effects of collimation of a spin-wave beam in arrays of magnonic-crystal structures make it possible to use the periodic properties of the medium to control the SW propagation length at frequencies near the non-transmission band of an individual magnonic crystal. For this, a system of lateral spin-waveguide channels separated by a periodic structure was fabricated on the surface of each film. Fig. 1 (a) shows a schematic view from above of each single magnonic crystal structure (YIG1 and YIG2) which are placed one above the other. Films of yttrium iron garnet (YIG), which are grown on a gallium-gadolinium garnet (GGG) substrate, were separated by a vertical gap of g in the direction of the z axis. A system of waveguides (S1 , S2 , S3 and S4 ) of equal width w = 200 µm is formed from the YIG film, S1 and S2 are oriented parallel to each other, S3 and S4 were placed above them in such a way that the resulting structure was two systems of lateral stripes S1 - S2 and S3 - S4. The thickness of the YIG films for both structures was t = 10 µm. The length of the coupling area is L=4 mm (see Fig.1a). Thus one can consider the single MCS as a lateral array of microwave guides separated by periodic sequence of grooves with a length in y-direction a = 100 µm period of D = 200 µm in the direction of the y axis on the surface of YIG films. The groove width along the x axis is d = 50 µm, the groove thickness in the direction of the z axis was s = 1 µm. Fig.1(b) shows a schematic diagram of the structure and demonstrates the geometric dimensions including the primitive cell of a magnonic crystal (MC) (on the right part of Fig. 1b). The experimental study was performed, with samples of a magnonic-crystal structure based on thin films of yttrium iron garnet that were made by laser scribing based on a precision laser cutting system based on a fiber laser ”MiniMarker2-20A4”. In the input section of the lower film S1 , there is a microstrip antenna with a width of 30 µm, to which a microwave signal was applied to efficiently excite the MSSW [34]. The structure was placed in an external magnetic field H0 =1200 Oe, as in the numerical simulation. Input and output transducers are attached to the YIG film (see Fig. 1(a)) at a distance of 4 mm from each other. The uniform static magnetic field H0 = 1200 Oe was applied in the plane of the waveguide along the x-direction for the effective excitation of the guided MSSW. Transmission and dispersion of MSSW were experimentally measured using PNA-X Keysight Vector Network Analyzer(VNA). First, the measurement of the transmission response for the one layer MCS was performed. The solid line in Fig. 5(a) shows the measured MSSW intensity for the MCS. A well pronounced forbidden bands where spin waves are not allowed to propagate is clearly observed for the frequencies of f1 = 5.1 GHz and f2 = 5.193 GHz. These two gaps in the magnetostatic suface waves spectra are typical for the system of coupled magnonic crystal, where two gaps are formed at the Bragg resonance condition for the symmetric and anti-symmetric modes. For single MCS structure we use the formalism where we can also consider the two coupled magnonic crystal waveguides separated by the array of grooves. In this case the formation of two gaps in spin-wave spectra can be explained also with the symmetric and antisymmetric modes as in Ref. [4]. Next we measure coupled MCS place one above the other with the gap of g = 80 µm. In the present structure we have four eigenmodes and each of them can satisfy the Bragg condition forming the band gaps. The microwave measurement of the fabricated two layer MCS shows that one more forbidden frequency band has been added to the two bandgaps at the frequency f3 = 5.15 GHz (see Fig. 5(a)). From the experimentally measured phase shift for the MSSW, the dispersion characteristic of MC was obtained (fig.5(b)). The dispersion measurement reveals that the frequency f3 corresponds to the Bragg wavnumber kB . This work was supported by the Russian Foundation for Basic Research under Project 19-37-90079

**References:**

1. V. V. Kruglyak, S. O. Demokritov, D. Grundler, J. Phys. D: Appl. Phys. 43 (2010) 264001. 2. E. Beginin, D. Kalyabin, P. Popov, A. Sadovnikov, A. Sharaevskaya, A. Stognij, S. Nikitov, “3D Magnonic Crystals” In G. Gubbiotti (Eds) “Three-Dimensional Magnonics”, Jenny Stanford Publishing, 2019. 3. A. V. Sadovnikov, E. N. Beginin, S. E. Sheshukova, Y. P. Sharaevskii, A. I. Stognij, N. N. Novitski, V. K. Sakharov, Y. V. Khivintsev, S. A. Nikitov, Route toward semiconductor magnonics: Light-induced spin-wave nonreciprocity in a yig/gaas structure, Phys. Rev. B 99 (2019) 054424. 4. M. Morozova, A. Y. Sharaevskaya, A. Sadovnikov, S. Grishin, D. Romanenko, E. Beginin, Y. Sharaevskii, S. Nikitov, Band gap formation and control in coupled periodic ferromagnetic structures, Journal of Applied Physics 120 (2016) 223901.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2349ae2fcd65e0aec36c812c4ac45501.jpg)
(a)Concept of the bilayer magnonic crystal structure;

![](https://assets.underline.io/uploads/markdown_image/1/image/3e015877e23ba6dfe23901460242a834.jpg)
(a) transmission characteristics, measured with signal network analyzer for one MCS and two layer of MCS;(b)experimentally measured dispersion for one layer MCS and two layer of MC

 Collimated spin-wave beams in a three-dimensional multilayer magnon-crystal arrays near the bandgap frequencies

With the development of technologies for the manufacture of magnetic structures, within the framework of the direction of magnonics, the mechanisms and methods of excitation and control of spin waves (SW) in magnetic materials are being actively studied [1, 2]. One of the key problems in the development of spin-wave devices is associated with the damping of spin waves [3]. A record low level of SW attenuation can be achieved when using films of yttrium iron garnet (YIG) [3]. At the same time, in YIG, it is possible to excite and propagate SWs with a wavelength from tens of nanometers to a few millimeters [2]. Improvement of the technological process of manufacturing thin YIG films made it possible to create multilevel micro- and nanostructures for the implementation of magnon networks [4], on the basis of which it is proposed to create an element base for information signal processing devices [5-6]. The use of the effects of spin-wave interference and amplitude-phase coding is a promising way to create an magnon networks for processing information signals in a wide frequency range [7]. The paper proposes and investigates a variant of vertical spin-wave transport based on orthogonally coupled magnetic microwave guides. With the help of numerical and experimental studies, the features of the transmission of the spin-wave signal at orthogonal coupling of the waveguide sections have been revealed. To describe the physical processes causing the propagation of a spin-wave signal in an irregular structure, we used the method of numerical micromagnetic simulations based on a numerical solution of the Landau–Lifshitz–Gilbert equation [8]. Magnetic films are formed from yttrium-iron-garnet (YIG) waveguides (Fig. 1) with thickness of t = 10 µm, l1 = l1 = 2500 µm and width w = 500 µm. The exchange constant of the YIG film was assumed to be equal Aex = 3.614-12 J/m and the saturation magnetization M0 = 1.395 A/m. To reduce SW reflections from the boundaries of waveguides in the numerical simulation, regions ABL (absorbing boundary layers) with an exponentially increasing dissipation parameter. Fig.2a shows the results of calculating the spectrum of the spin-wave signal in orthogonal magnonic waveguide. The drop in signal power at the output by 5 dB is associated with attenuation in the YIG For experimentally investigation were fabricated by laser scribing a continuous YIG film epitaxially grown on a substrate of gadolinium gallium garnet (GGG). The waveguides were magnetized by a uniform field H0 = 1150 Oe, directed along the short symmetry axis of the waveguides for efficient excitation of a magnetostatic surface spin wave. Spin wave transmission characteristics were acquired using two 30 µm wide microstrip antennas positioned on either end of the waveguides. The input antenna’s dynamic magnetic field couples to the YIG’s magnetization, exciting spin waves propagating along the waveguide. The efficiency of spin wave propagation was measured using a vector-network-analyzer. The results from the characterization of the waveguides are shown in Fig.2b. Fig. 2c shows the result of calculating the effective wavenumbers in the frequency range of the MSSW excitation. It can be seen that the phase incursion and the effective wavenumber begin to increase with increasing frequency, which corresponds to the case of MSSW. Proposed spin-wave transport in orthogonal vertical junction makes it possible to implement functional processing of information signals (frequency filtering and phase correction) during signal transmission in a wide frequency range. This work was supported by the Russian Science Foundation Grant (#20-79-10191).

**References:**

[1] V.V. Kruglyak, S.O. Demokritov, D. Grundler, J.Phys. D: Appl. Phys., Vol.43, p.264001 (2010) [2] A.V. Chumak, V.I. Vasyuchka, A.A. Serga, Nature Physics., Vol.11, p.453. [3] A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves, CRC-Press, London, New York. (1996) [4] A.A. Martyshkin, S.A. Odintsov, A.V. Sadovnikov, JETP Lett., Vol.110, No.8, pp.533–539 (2019) [5] V.E. Demidov, S. Urazhdin, S.O. Demokritov, J. Appl. Phys., Vpl.127, p.170901 (2020) [6] N. Thiery, V.V. Naletov, O. Klein, Phys. Rev. B. Vol.97, p.064422 (2018) [7] A.V. Sadovnikov, E.N. Beginin, S.A. Nikitov,Appl.Phys. Lett.,Vol.107, p.202405 (2015) [8] A. Vansteenkiste, J. Leliaert, B. Waeyenberge, AIP Advances, Vol.4, p.107133 (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1078ae873129af68926d5e8c6cd3e260.jpg)
Schematic view of the orthogonal magnetic waveguide

![](https://assets.underline.io/uploads/markdown_image/1/image/2ec69ac00f12d23ff39ef2bbad677fb3.jpg)
Numerical results of transmission spectrum of the input signal (red) and output (blue) (a). Experimental transmission characteristics S21 (b). Numerical result of effective wavenumbers (c).

 Surface spin wave propagation in the orthogonal vertical junction of YIG-based magnonic waveguide

An existance and stability of discrete breathers in the monoaxial chiral helimagnet with Dzyaloshinskii-Moryia (DM) interaction and easy-plane anisotropy are investigated. We focus on the phase of forced ferromagnetism when the magnetic system is subjected to an external magnetic field directed along the chiral axis. The intrinsic breather modes have high frequencies above the maximum frequency of the spin-wave spectrum and are excited at the Brillouine zone boundary. We modify the numerical algorithm suggested in Ref. [1] to find the nonlinear solutions and show that these localized modes are characterized by a sign-changing ordering of transversal spin components. The discrete breathers in a finite-size system may be categorized by number of embedded kink-antikink pairs forming a regular breather lattice (Fig. 1). The DM interaction supresses amplitude of these modes and lowers their symmetry by allowing only excitations with an odd envelope function with respect to the center of the system. The energy of the discrete modes demonstrates a linear dependence on number of bound kink-antikink pairs. Floquet stability analysis [2] is employed to examine stability of the breather modes depending on their frequency and external parameters, such as strengths of the external magnetic field and the local anisotropy. The work is supported by the RFFI grant (project 20-02-00213).

**References:**

[1] S. Rakhmanova and D. L. Mills, Phys. Rev. B, Vol. 54, p. 9225 (1996). [2] J. M. Khalack, Y. Zolotaryuk, and P. L. Christiansen, Chaos, Vol. 13, p. 683 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a5dd98070fa917c77840aa75e5a7e638.jpg)
Spatial distribution of spin moments (blue arrows) in a spin chain with different numbers of kink-antikink pairs. Cases without DM interaction: (a) n = 1, (b) n = 2, (c) n = 3; and with an account of the DM interaction: (d) n = 1, (e) n = 2, (f) n = 3.

 Discrete breathers and their stability in a finite-size monoaxial chiral helimagnet

In the last two decades, the rapid development of broadband communication systems is the cause of the creation of the ultrashort pulse (USP) sources. In optics, there are various methods for USP generation, one of which was given the Nobel Prize in Physics [1]. Nowadays, some optical methods for USP generation start to be used in the microwave range to generate both the USPs of "giant" amplitude [2] and the multisoliton complexes consisting of bright and dark spin-wave envelope solitons [3]. Recently, a new method for the ultrashort dark pulse generation was proposed [4]. It is based on the use of three-wave nonlinear spin-wave interactions and a nonlinear amplification. Using this method, the generation of microwave dark multisoliton complexes was obtained. Each multisoliton complex consists of some dark parametric pulses of submicrosecond duration that contains the trains of dark incoherent spin-wave envelope solitons possessing a subnanosecond duration. The characteristics of such patterns are controlled by a variable attenuator that is managed by the nonlinear loss of a magnetostatic spin wave (MSW), propagating in an irregular magnonic waveguide. Dynamic control of the MSW loss can be realized with the help of direct current (DC) [6,7]. If DC flows in a wire conductor located on the ferromagnet surface, then the internal magnetic field is locally changed in the ferromagnet. This causes a change not only in the MSW dispersion, but also in its linear loss. Dynamic control of the MSW loss by means of DC underlies the operation of a dynamic magnonic crystal (MC) [7]. The dynamic MC is a ferromagnetic medium, the internal magnetic field of which is periodically changed in space by DC. By analogy with photonic crystals, a periodic change in the parameters of the medium is the reason for the forbidden zones (FZs) formation. At FZs frequencies, the MSW linear loss undergo a significant change. Dynamic control of the MSW loss can also be realized for a static MC, if a DC-controlled local inhomogeneity is created on the surface of a periodic structure. This will make it possible to control not only the MSW loss at the frequencies of the FZs, but also the FZ location in the MSW spectrum. In this work, it is demonstrated the dynamic control of the loss and FZs of the static MC due to a local change in the MC internal magnetic field. In addition, the static MC with dynamic control of the loss and FZs is used in a feedback loop of an active ring resonator to manage a duty cycle of the chaotic dark parametric envelope solitons.The parametric wave model with nonlinear amplification is used to explain the experimental results. As shown in Fig.1a, the MC, contained in the feedback loop of the active ring resonator, is a periodic structure of crests and grooves that are formed on the surface of an yttrium-iron garnet film with a thickness of 10 μm. The crests and grooves have the same width of 100 μm. An external bias field H0=356 Oe is applied tangentially to the surface of the MC and directed along to the input and output microstrip lines. Such field configuration supports a magnetostatic surface spin wave (MSSW) propagation. The strength of the bias field is chosen so that three-wave nonlinear spin-wave interactions are allowed for the MC. A wire conductor connected to a DC source is placed along the longitudinal symmetry axis of the MC. Depending on the polarity of the DC, the MC internal magnetic field can either increase or decrease. As shown in Fig.1b, such changes of the internal magnetic field lead to the management of both the linear and nonlinear MSSW loss. In addition to the MC, the generator contains an amplifier stage, consisting of a klystron amplifier and two transistor amplifiers, that are necessary to compensate the loss. The output transistor amplifier of the stage operates in the output power saturation mode, and the other two amplifiers operate in the linear amplification mode. In addition, a resonant frequency of the klystron amplifier is tuned to a frequency located near the center frequency of the MC first FZ. This is necessary in order to realize the amplitude and phase conditions for signal generation. A generated microwave signal is fed through the directional couplers to the inputs of a spectrum analyzer and a real-time oscilloscope for analysis and processing. In Fig.2, the dark parametric soliton modes obtained both experimentally and calculated on the basis of the parametric wave model with nonlinear amplification are presented. The presented in Fig2a experimental results show that a change in the DC polarity leads to a change in the duty cycle of the generated chaotic dark parametric solitons. A similar effect is observed in a numerical experiment (see Fig2b), if the frequency of the parametrically excited spin waves is detuned from the half value of the MSSW frequency. This work was supported by the Russian Science Foundation (Project No.19-79-20121).

**References:**

1. D. Strickland and G. Mourou, Opt. Commun., Vol.55, p.447 (1985). 2. N.S. Ginzburg, G.G. Denisov, M.N. Vilkov, and et al., Phys. Plasmas, Vol.24, p.023103 (2017). 3. S.V. Grishin, B.S. Dmitriev, O.I. Moskalenko, and et al., Phys. Rev. E, Vol.98, p.022209 (2018). 4. A.S. Bir, S.V. Grishin, O.I. Moskalenko, and et al., Phys. Rev. Lett., Vol.125, p.083903 (2020). 5. M. Tsoi, A.G.M. Jansen, J. Bass, and et al., Phys. Rev. Lett., Vol.80, p.4281 (1998). 6. S.O. Demokritov, A.A. Serga, A. Andre, and et al., Phys. Rev. Lett., Vol.93, p.047201 (2004). 7. A.V. Chumak, T. Neumann, A.A. Serga, and et al., J. Phys. D: Appl. Phys., Vol.42, p.205005 (2009).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/191173d877ed2fc4ea8c44926e431f0f.jpg)
Fig.1 (a) Block diagram of the dark parametric soliton active ring resonator based on direct current-controlled magnonic crystal. (b) Dependences of the MSSW loss on the input power, measured at the MC FZ frequency at various values and polarity of DC.

![](https://assets.underline.io/uploads/markdown_image/1/image/2807bd8f2d795d58d447a183b7d44cb9.jpg)
Fig.2 Sequences of the dark parametric envelope solitons obtained (a) experimentally and (b) calculated by the model. In (a), the pulses are obtained for two DC polarities: +320 mA (top panel) and -200 mA (bottom panel). In (b), the pulses are obtained for two values of the SW frequency detuning: 10-25 Hz (top panel) and 10-315 Hz (bottom panel).

 Direct Current Control of the Chaotic Dark Parametric Solitons in a Magnonic Crystal Active Ring Resonator

Nowadays, the Wireless Power Transfer (WPT) presents itself as a new option to charge batteries, in order to eliminate the respective cables and gain mobility, convenience and ease for the user. One of the WPT techniques uses the Coupled Magnetic Resonance (CMR). This technology is capable of transmitting electromagnetic energy from a power source (transmitter coil) to an electric load (in the receiver coil) through a gap in the air and the variation and oscillation of magnetic fields [1]. Metamaterials (MM’s) are typically conductive elements such as copper, gold and silver [2]. They present unnatural magnetic properties, obtained from their internal arrangement, which allow them to obtain a negative refractive index, making them perfect lens. Thus, they are used between the coils to increase the efficiency of WPT. Veselago called the MM's as left-handed materials (LH materials) because the propagation of electromagnetic waves with the electric and magnetic fields and propagation vector forms a left-handed triad when compared to conventional materials. He predicted several behavioral phenomena that occur in LH media such as the reversal of the Doppler effect and the Snell's law and negative refraction [3]. In this work, since the technique chosen was that of strong resonant magnetic coupling, where the magnetic characteristic of the evanescent field prevails, we opted to use a structure with MNG characteristics (Mi-negative Medium, ε &gt; 0, μ &lt;0), which can be obtained from the Split Ring Resonators (SRR's). If the magnetic field H is perpendicular to the plane of the rings, in order to induce resonant currents in the loop and generate equivalent magnetic dipole moments, this MM exhibits plasmatic permeability as a function of frequency [4]. The main goal is to propose a metamaterial topology that allows a horizontal misalignment between transmitter and receiver coils, resulting in a more efficient system. The system was simulated on CST® Studio software. The transmitter and receiver coils are flat and have 7 loops, width of 2.49 mm, spacing of 1.0 mm, inner radius of 22 mm and outer radius of 47 mm. These coils are in a FR4 substrate with dimensions of 100 x 100 x 1.5 mm. The distance between the coils ranged from 4 cm to 10 cm without misalignment. The transmitter coil has an alternating voltage source (Vmax of 100 V) and the receiver has a resistor of 100 Ω as load. This same system was simulated with a metamaterial slab placed at half way between the coils. The metamaterial slab has the dimensions of 100 x 150 x 1.5 mm, and 12 unit cells arranged in a 4x3 array with two copper Split-ring resonators (SRR’s) with height of 0.02 mm, width of 1.63 mm, and spacing of 1.47 mm, and 2 capacitors of 47 nF. The system was designed and computed for a resonance frequency of 1 MHz. The best results were at 4 cm with the MM slab, where there was an increase of 77.32% in the efficiency (12.23% to 23.46%), 24% in the maximum voltage (67.19 V to 83.42 V) and current (671.89 mA to 834.20 mA), 54% in the power (45.14 W to 69.59 W). Figure 2 shows the efficiency of the system, at 4 cm, simulated with a horizontal misalignment between the coils, with and without metamaterial. Although the system is very sensitive to the misalignment, it still presents a better efficiency compared to no MM setup. After introducing the MM slab, there was an increase in the efficiency of 55.63% (13.14% to 20.45%) in 1 cm, 52.72% (10.81% to 16.51%) in 2 cm and 49.41% (7.67% to 11.46%) in 3 cm of misalignment. Even with 2 cm of misalignment, the system with MM is more efficient than the one without it (16.51 to 13.23%). Thus, the MM was able to increase efficiency in wireless power transfer even with horizontal misalignment between coils.

**References:**

[1] D. C. Corrêa, U. C. Resende and F. S. Bicalho, "Experiments With a Compact Wireless Power Transfer System Using Strongly Coupled Magnetic Resonance and Metamaterials," in IEEE Transactions on Magnetics, vol. 55, no. 8, pp. 1-4, Aug. 2019. [2] X. Wang, Y. Wang, Y. Hu, Y. He and Z. Yan, "Analysis of Wireless Power Transfer Using Superconducting Metamaterials," in IEEE Transactions on Applied Superconductivity, vol. 29, no. 2, pp. 1-5, March 2019. [3] D. Smith, J. B. Pendry; Reversing light negative refraction. Physics Today, 57, pp. 37-45, 2009. [4] C. Caloz.; T. Itoh; T. Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. The Engineering Approach. [s.l.] Wiley, 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2fbd97c45539a51f7b042db4481bbc6.jpg)
Fig. 1 – Efficiency comparison without misalignment

![](https://assets.underline.io/uploads/markdown_image/1/image/3c7c8a96fe9a7c72453d1acd4bf36f6b.jpg)
Fig. 2 - Efficiency comparison with misalignment between coils

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