France



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].&lt;br/&gt;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].&lt;br/&gt;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.&lt;br/&gt;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, l&lt;sub&gt;1&lt;/sub&gt; = l&lt;sub&gt;1&lt;/sub&gt; = 2500 µm and width w = 500 µm. The exchange constant of the YIG film was assumed to be equal A&lt;sub&gt;ex&lt;/sub&gt; = 3.614&lt;sup&gt;-12&lt;/sup&gt; J/m and the saturation magnetization M&lt;sub&gt;0&lt;/sub&gt; = 1.39&lt;sup&gt;5&lt;/sup&gt; 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&lt;br/&gt;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 H&lt;sub&gt;0&lt;/sub&gt; = 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.&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;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)&lt;br/&gt;[2] A.V. Chumak, V.I. Vasyuchka, A.A. Serga, Nature Physics., Vol.11, p.453.&lt;br/&gt;[3] A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves, CRC-Press, London, New York. (1996)&lt;br/&gt;[4] A.A. Martyshkin, S.A. Odintsov, A.V. Sadovnikov, JETP Lett., Vol.110, No.8, pp.533–539 (2019)&lt;br/&gt;[5] V.E. Demidov, S. Urazhdin, S.O. Demokritov, J. Appl. Phys., Vpl.127, p.170901 (2020)&lt;br/&gt;[6] N. Thiery, V.V. Naletov, O. Klein, Phys. Rev. B. Vol.97, p.064422 (2018)&lt;br/&gt;[7] A.V. Sadovnikov, E.N. Beginin, S.A. Nikitov,Appl.Phys. Lett.,Vol.107, p.202405 (2015)&lt;br/&gt;[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 S&lt;sub&gt;21 &lt;/sub&gt;(b). Numerical result of effective wavenumbers (c).

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

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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).

poster

For ferromagnets, the adiabatic spin transfer torque (STT) causes current-induced spin-wave (SW) Doppler shift [1] whereas the non-adiabatic STT controls SW attenuation [2,3]. It was predicted [4] that the current-induced SW Doppler shift by the adiabatic STT is also present for antiferromagnets. In addition, a numerical study found a non-negligible non-adiabatic STT for antiferromagnetic domain walls [5], suggesting that electrical currents can control the attenuation of antiferromagnetic SWs. Recently, an experiment on GdFeCo ferrimagnets shows that the adiabatic torque in this material can be large [6]. Thus, the current-induced SW Doppler shift of compensated ferrimagnets is expected to be similar in magnitude to that of ferromagnets. Moreover, the same experiment [6] shows that the non-adiabatic torque in this material is also large. This large non-adiabaticity of spin current in compensated ferrimagnets is attributed to the enhanced spin mistracking [5-7], originating from the weakened spin dephasing in the antiferromagnetically aligned spin moments [8]. This unique STT characteristic of compensated ferrimagnets motivates us to investigate STT effects on ferrimagnetic SWs. In this work, we theoretically and numerically study the STT-controlled ferrimagnetic SW dynamics near the angular momentum compensation point. We show that the ferrimagnetic SW Doppler shift for right-handed SWs is opposite to that for left-handed SWs since they carry opposite spin polarizations. We also find that the SW attenuation is suppressed and the SW amplitude is even amplified when a sufficiently large non-adiabatic torque is exerted. Figures 1(a) and (b) respectively show the current-induced SW Doppler shift of the right- and left-handed SWs at the angular momentum compensation temperature TA (T2) when the current density Je = ±5 × 1012 A/m2 is applied. Symbols are numerical results and solid lines are theories, which are in good agreement. For the right-handed SW [Fig. 1 (a)] and wave vector k &gt; 0, a positive (negative) current decreases (increases) the SW frequency. On the other hand, for the left-handed SW [Fig. 1 (b)] and k &gt; 0, a positive (negative) current increases (decreases) the SW frequency. Therefore, the sign of Doppler shift of the right-handed SW is opposite to that of the left-handed SW, which originates from the opposite spin polarizations carried by left- and right-handed SWs. Figure 2(a) and (b) show the SW attenuation length as a function of the current density for β=10α, where β is the non-adiabaticity and α is the damping constant. The SW frequency (ω/2π) is 0.4 THz. Theoretical and numerical results are shown near the TA and T1 (T3) is the temperature which is below (above) TA. For a positive β, we find that the SW attenuation length of both right- and left-handed SWs increases when electrons move in the same direction with the SW propagation. In addition, when sufficiently large non-adiabatic torque is applied, the SW amplitude exponentially increases from the SW source.

**References:**

[1] V. Vlaminck, and M. Bailleul, Science 322, 410 (2008). [2] S.-M. Seo, K.-J. Lee, H. Yang et al., Phys. Rev. Lett. 102, 147202 (2009). [3] K. Sekiguchi, K. Yamada, S.-M. Seo et al., Phys. Rev. Lett. 108, 017203 (2012). [4] A. C. Swaving and R. A. Duine, Phys. Rev. B. 83, 054428 (2011). [5] H.-J. Park, Y. Jeong, S.-H. Oh et al., Phys. Rev. B 101, 144431 (2020). [6] T. Okuno, D.-H. Kim, S.-H. Oh et al., Nat. Electron. 2, 389 (2019). [7] J. Xiao, A. Zangwill, and M. D. Stiles, Phys. Rev. B 73, 054428 (2006). [8] J. Yu, D. Bang, R. Mishra et al., Nat. Mater. 18, 29 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5fd8ead22f3106e5bc7cef3e01990321.jpg)
Fig. 1. Current-induced Doppler shift of (a) right- and (b) left-handed SWs in a ferrimagnet at the angular momentum compensation temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/de38b5665d8a3e2df3174fa9069220ef.jpg)
Fig. 2. The SW attenuation length for (a) right- and (b) left-handed SWs as a function of the current density.

 Current-induced spin-wave Doppler shift and attenuation in compensated ferrimagnets

Magnon valve effect (MVE) and magnon junction effect (MJE) which show the spin-dependent magnon transmission through ferromagnetic insulator (FMI) /spacer [S = nonmagnetic metal or antiferromagnetic insulator (AFMI=AFI)]/ferromagnetic insulator (FMI) sandwiches have been experimentally reported by our group [1-3]. It opens a door for promising applications in magnonics. However，the MJE is still not well interpreted, such as its physical origin and the optimized structure of AFMI spacer. It is intuitively regarded that the AFMI spacer would effectively modulate the magnon transmission and a high switching on-off ratio of magnon flow can be expected after a wise choice of the spacer, which would be proven in this work. Here, we study in theory magnon transmission through sandwich structure of FMI|AFI|FMI by atomistic spin model simulation [4]. We reproduced the MJE observed in experiments and proposed a magnon selection rule induced magnon blocking effect (MBE) to explain it. More importantly, following the proposed mechanism, different kinds of AFI spacers were evaluated. It showed that magnon transmission could be remarkably changed by the AFI spacers with various FMI configurations. This works on the MBE can provide significant and meaningful information for both the fundamental physics and the appealing applications of magnon junctions.

**References:**

[1] H. Wu, and X. F. Han* et al., Phys. Rev. Lett. 120, 097205 (2018). [2] C. Y. Guo, C. H. Wan, and X. F. Han* et al., Phys. Rev. B 98, 134426 (2018). [3] C. Y. Guo, C. H. Wan, and X. F. Han* et al. Nat. Electron. 3, 304–308 (2020). [4] Z. R. Yan, C. H. Wan and X. F. Han*, Phys. Rev. Appl. 14, 044053 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/623bd53887b1d15f4775ef1bf710eeb4.jpg)
Fig. 1. Magnon junction structure and space dependence of magnon potential. (a) Magnon potential (|Mz|) as function of layer (x) of P state (solid line), AP state (short dot) and FMI1|AFI system (green line). (b) Separated channel dependent |Mz| from (a): ↑|↑|↑ (black line), ↑|↓|↑ (red line), ↑|↑|↓ (blue line) and ↑|↓|↓ (green line). (c and d) Schematics of spin dependent magnon blocking of P and AP state respectively. Spin-up (spin-down) lattices can only accommodate right- (left-) circularly polarized magnons. While only right-circularly polarized magnons are favored in FMI with upward magnetization, both left- and right-circular polarizations are permitted in AFMI owing to two spin-opposite lattices. This selection rule thus makes the MBE occur when magnons try to diffuse into a spin lattice, which does not support their polarization.

 Magnon Blocking Effect in Antiferromagnet Spacered Magnon Junction

The spin wave (magnon) have many excellent properties that are unavailable in electron-based spintronic devices, which could drastically reduce the power consumption of spintronic devices[1-4]. Magnon valves[3] and magnon junctions (MJs)[4] based on yttrium iron garnet (Y3Fe5O12, YIG), with the structures YIG/Au/YIG and YIG/NiO/YIG, respectively, have been fabricated. Here we report a magnetoresistance effect that occurs in a platinum layer deposited on a magnon junction consisting of two insulating magnetic YIG layers separated by an antiferromagnetic nickel oxide spacer layer. The resistance of the platinum layer is found to depend on the magnetization of the YIG layer in direct contact with it (an effect known as the spin Hall magnetoresistance), but also the magnetization of the adjacent YIG layer in the junction; the resistance of the platinum layer is higher when the two YIG layers are aligned antiparallel than when parallel[5]. We assign this behaviour to a magnonic nonlocal spin-Hall magnetoresistance (MNSMR) in which spin-carrying magnon propagation across the junction affects the spin accumulation at the metal interface and hence modulates the spin Hall magnetoresistance. The effect could be used to develop spintronic/magnonic devices that have spin transport properties controlled by an all-insulating magnon junction and are thus free from Joule heating.

**References:**

[1] H. Wu, and X. F. Han*et al., Phys. Rev. B 93 (2016) 060403(R) [2] C. Y. Guo, C. H. Wan, and X. F. Han* et al., Appl. Phys. Lett. 114,192409(2019). [3] H. Wu, and X. F. Han*et al., Phys. Rev. Lett. 120(9),097205(2018). [4] C. Y. Guo, C. H. Wan, and X. F. Han* et al., Phys. Rev. B 98, 134426 (2018). [5] C. Y. Guo, C. H. Wan, X. F. Han* et al. Nat. Electron. 3, 304–308 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/abfdb962e8fb1138aac4c3b433b030ce.jpg)

 A nonlocal spin Hall magnetoresistance in a Pt layer deposited on a magnon junction

One of the main research directions in magnonics focuses on the excitation of short wavelength SWs (SWs). Recently, a few approaches have been proposed, but with some limitations like the lack of an efficient source of SWs, which further limits the development of magnonic applications. We propose a system (Fig 1.) that generates a local excitation of SWs in a thin ferromagnetic waveguide with the help of a nanodot that possesses perpendicular magnetic anisotropy. Our idea is to use the confined SW modes in the nanodot pumped by a global microwave magnetic field directed along the magnetization of the waveguide, which will emit propagating SWs due to direct static and dynamic coupling with the waveguide. Two study cases are put against each other: a nanodot inscribed with a skyrmion and a nanodot in a fully saturated state along out-of-plane direction. The system can function with several combinations of magnetic materials. The waveguide has to be ferromagnetic and present a low enough damping so that the SWs can propagate over a significant distance, which is why Permalloy is an ideal candidate having one of the lowest Gilbert damping [1]. The waveguide is magnetically saturated along its length and is separated from the nanodot by a spacer of 1.5 nm. It is 384 nm wide and 4.5 nm thick, and a few micrometers long with absorbing boundary conditions at its edge both extremities to avoid any kind of back-propagating SWs. The nanodot must have a specific geometry and size, as it requires a strong enough interfacial Dzyaloshinskii-Moriya Interaction to allow for the formation of a skyrmion. For this reason, the nanodot is made of Pt/Co/Ir circular layers with a diameter of 300 nm to create a strong shape anisotropy which allows the presence of a metastable state such as a skyrmion in its core. When relaxing this system, an imprint of the skyrmion is created in the waveguide, meaning the magnetization below the nanodot will deviate from their saturated magnetization along the x axis because of the dipolar coupling with the skyrmion. In the same way, the waveguide will influence the magnetization inside the nanodot and affect the shape of the skyrmion. In our example, the skyrmion’s core expends and becomes egg shaped under the influence of the waveguide. Confined skyrmions present a wide range of different resonant modes [2] when excited by an external magnetic field. Such modes are also present here and influence the shape of the resulting imprint which will start oscillating along with the skyrmionic modes acting like an antenna. This complex movement of both halves of the imprint, alternating phases and amplitude is what generates the coherent and efficient propagating SWs. Interestingly, only asymmetrical SWs can be created this way, but modifying the material parameters or the geometry will cause the imprint to change shape which allows us to tune the efficiency of the antenna for specific microwave frequencies. In the case of a fully saturated nanodot with the same magnetic parameters as the one with the skyrmion, the created imprint is less visible because of the simpler magnetic texture. It leads to a very inefficient coupling for a narrow range of frequencies compared to the broadband SW excitations (Fig 2.) that a skyrmion can generate. We found that the propagating SWs can be excited in a broad frequency band from a few to a dozen GHz with wavelengths that can be shorter than 100 nm. Furthermore, our studies look for the magnetic parameters and geometry that would be most suitable for an efficient conversion of global electromagnetic radiation to short wavelength SWs. The work was supported by National Science Centre of Poland, Project SHENG No. UMO-2018/30/Q/ST3/00416.

**References:**

[1]: Zhao, Yuelei, et al. Scientific reports 6 (2016): 22890. [2]: Kim, Joo-Von, et al. Physical Review B 90.6 (2014): 064410.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4340c8d482e1f2ff739851984370476.jpg)
Fig 1. The system used in the micromagnetic simulations: the Permalloy waveguide ( 12 µm x 384 nm x 4,5 nm ) and the Pt/Co/Ir nanodot ( 300 nm x 1.5 nm ), separated by a 1.5 nm thick spacer.

![](https://assets.underline.io/uploads/markdown_image/1/image/cb301d6acf52e6837d77f506c4aed181.jpg)
Fig 2. The dispersion relation of the SWs generated by the skyrmion and waveguide system. This was calculated using the Fast Fourier Transform of the time- and space-resolved magnetization of the waveguide under a global magnetic field.

 Excitation of short wavelength spin waves in a ferromagnetic conduit with a microwave pumped perpendicularly magnetized nanodot

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

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