France



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 δm&lt;sub&gt;x&lt;/sub&gt; on the time scales. And the spin wave transmission characteristics (Fig.1(d)) are obtained by probing the spectra intensity in &lt;i&gt;x&lt;/i&gt; 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 &lt;i&gt;y&lt;/i&gt; direction versus wave vector are obtained by a two-dimensional (2D) FFT of magnetization components δm&lt;sub&gt;x&lt;/sub&gt;. 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 k&lt;sub&gt;x&lt;/sub&gt;=0.015 rad/nm and k&lt;sub&gt;x&lt;/sub&gt;=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 k&lt;sub&gt;x&lt;/sub&gt;=0.164 rad/nm and k&lt;sub&gt;x&lt;/sub&gt;=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).&lt;br/&gt;2. R. Verba, M. Carpentieri and G. Finocchio, et al., Sci Rep, 6, 25018 (2016).&lt;br/&gt;3. Q. Wang, T. Brächer and M. Mohseni, et al., Appl. Phys. Lett., 115, 092401 (2019).&lt;br/&gt;4. A. V. Chumak, P. Pirro and A. A. Serga, et al., Appl. Phys. Lett., 95, 262508 (2009).&lt;br/&gt;5. S. Klingler, P. Pirro and T. Brächer, et al., Appl. Phys. Lett., 106, 212406 (2015).&lt;br/&gt;6. M. á. Kostylev, A. Serga and T. Schneider, et al., Appl. Phys. Lett., 87, 153501 (2005).&lt;br/&gt;7. F. Macia, F. C. Hoppensteadt and A. D. Kent, Nanotechnology, 25, 045303 (2014).&lt;br/&gt;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 m&lt;sub&gt;z&lt;/sub&gt; 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 δm&lt;sub&gt;x&lt;/sub&gt;.

INTERMAG 2021

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

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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.

poster

Spin waves (SWs) and their quanta magnons in the magnetic structures offer data transmission and data encoding capability in both amplitude and phase, providing an additional degree of freedom compared to their electronic counterparts. Most of the works in this field are focused on developing novel and energy efficient control mechanisms of SW by different means such as voltage [1], current [2], light [3], heat [4] etc., to use it in logic applications. However, this wave-based computation has the tremendous potential of parallel data processing. A multifrequency magnon network would allow parallel data processing within a single element, which is not possible in conventional transistor-based electronic logic. There are few reports about SW channeling in multiple paths in metallic ferromagnet [5][6]. In this work, we experimentally demonstrated a novel multifrequency SW device that can operate at multiple frequencies simultaneously using the shape anisotropy of the magnonic film. We have used yttrium iron garnet Y3Fe5O12 (YIG) as the magnonic material due to its extraordinarily low damping constant. A 145 nm-thick YIG film was grown on a (111)-oriented single crystalline Gd3Ga5O12 (GGG) substrate by pulsed laser deposition technique. Two patterned YIG waveguide with width w1 and w2 were fabricated by hot orthophosphoric etching at 160 °C temperature after photolithography as shown in Figure 1(a). w1 was maintained at 100 mm, whereas w2 was varied in the steps of 10, 20, 40, 60, 80, and 100 μm to implement a multichannel spin wave device. Subsequently, a system of two co-planner waveguide (CPW) made of 90 nm thick Au was integrated into the YIG film using dc magnetron-sputtering. The separation between the center lines of the exciting and detecting antenna (S) was designed as 200 μm. Another series of single channel SW device as shown as Figure 1(b) was fabricated by the similar procedure as Figure 1(a), where the width w of the devices was varied in the step of 10, 15, 25, 35, 45 60, 80, and 100 μm to investigate the contribution of shape anisotropy. For device characterization, we employed the microwave technique using the vector network analyzer (VNA). A dc-biased magnetic field ( μ0Hext = 25mT ) was applied in the in-plane direction and perpendicular to the SW propagation path, where magnetostatic surface SW (MSSW) was excited in the YIG film. To investigate SW propagation, we followed a similar approach as in the reference [7] The transmitted SW, scattering parameter S21 for a multichannel device (Figure 1(a)) has been shown in Figure 2(a)-(f). Figure 2(a) to (d) shows a single mode SW transmission with maximum propagation at f1= 2.15 GHz. However, Figure 2(e) and (f) shows the appearance of an additional SW propagation mode at f2= 2.06 GHz and f2= 1.92 GHz, respectively, along with the first mode at 2.15 GHz. Thus, it indicates that additional mode appears only when the width of the second waveguide has been shrunk beyond 20 μm, and it happens at a lower frequency than the first mode. To investigate the origin of the emergence of the second low frequency SW mode we have performed another set of the experiment where we have done the same measurement for the single channel SW device shown in Figure 1(b). Transmitted SW signals for these devices are shown in 2(g) to (n). We have found that the center frequency (indicated by arrow) of the transmission spectra has been moved from 2.25 GHz to 2.00 GHz when waveguide width has been changed from 100 mm to 10 mm. This frequency shifting can be attributed to the reduction effective magnetic field due to shape anisotropy induced demagnetizing field (Hd). When a magnonic film is micro structured as a bar, an Hd is developed inside the micro structured waveguide [8]. We have calculated this Hd as 3.2, 4.0, 5.3, 8.0, 15 and 32 mT for 100, 80, 60, 40, 20 and 10 μm waveguide respectively from Hd =t*4πMs/w, where t, Ms and w are the thickness, saturation magnetization and width of the waveguide, respectively. We have used Ms = 140 kA/m, which is the standard value for YIG film. This demagnetizing field reduces the effective magnetization based on the relation: Heff=Hext-Hd . According to the Kittle equation, the reduction of will result in the reduction of SW frequency, fFMR : fFMR=γ√Heff(Heff+Meff)/2π, where γ is the gyromagnetic ratio. As the width of the waveguide gets smaller, the demagnetizing field becomes larger, causing more reduction of Heff and SW frequency. These results provide us with a guideline that even by using same magnetic material operating under the same magnetic bias field, the resonant frequencies of the individual micron size magnets on a single chip can be tuned by varying the width of the magnet. In this work, combining such two different magnonic channel with the distinguishable anisotropic demagnetizing field has made it possible to make a multifrequency SW device for parallel data processing.

**References:**

[1] S. Choudhury, H. Takahashi, A. Barman, Sci. Adv. 2020; 6:eaba5457 [2] S. Sarker, H. Yamahara, H. Tabata, Appl. Phys. Lett. 117, 152403 (2020) [3] M. Vogel, A. V. Chumak, B. Hillebrands, Nat. Phys. 11, 487-491 (2015) [4] V. Castle, G.E.W. Bauer, Phys. Rev. B 96, 064407, (2017). [5] F. Heussner, B. Hillebrands, P. Pirro, Phys. Status Solidi RRL 2020, 14, 1900695 [6] K. Vogt, F.Y. Fradin, H. Schultheiss, Nat. Comm, 5:3727 (2014) [7] S. Sarker, H. Yamahara, H. Tabata, AIP Advances 10, 015015 (2020) [8] T. Manago, S. Yakata, T. Kimura, JJAP 52 (2013) 053001

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/27cafc7606015defe46e2dd9e20bfb9c.jpg)
(a) Optical image of multichannel SW device (b) Microscopic image of single channel SW device

![](https://assets.underline.io/uploads/markdown_image/1/image/41d800e831da93a8464b8ee58408f1f8.jpg)
Transmitted SW signal for in multichannel device for w1 = 100 μm and (a) w2 = 100 μm (b) w2 = 80 μm (c) w2 = 60 μm (d) w2 = 40 μm (e) w2 = 20 μm (f) w2 = 10 μm. Transmitted SW for single channel device for (g) w = 10 μm (h) w = 15 μm (i) w = 25 μm (j) w = 35 μm (k) w = 45 μm (l) w = 60 μm (m) w = 80 μm (n) w = 100 μm

 Multifrequency Spin Wave Device for Parallel Data Processing using Micro Structured Yttrium Iron Garnet Thin Films

Nonreciprocity is a vital, unique, and fundamental signal transmission characteristic widely required in a large number of RF, microwave and millimeter-wave circuit, and module applications, which include communication systems, radar, and measurement equipment. Without any doubts, the nonreciprocal properties are indispensable for the development of emerging circuits and systems such as the highly anticipated in-band full-duplex transceiver systems The recent development of nanotechnology in combination with the increased interest in the properties of artificial crystals brought back the topic of spin-wave (SW) nonreciprocity and its potential application in functional devices. The surface spin waves (SSWs) propagating in a ferromagnetic film along the direction perpendicular to a tangentially applied magnetic field H0 (Damon-Eshbach geometry) [1] possess nonreciprocal properties. Recently, of great interest is the study of the properties of spin waves during their propagation in magnetic waveguide structures of micro and nano scale. In this case, the main attention is paid to the use of spin waves (STs) as carriers of information signals, since it is possible to implement a number of signal processing devices based on the principles of magnonics [2], taking into account the possibility of coding the signal using both amplitude and spin phase the waves. As is known, the properties of SW spin waves are determined by the dipole and exchange interactions in magnetic media and can change significantly with changing medium parameters, for example, the magnitude and direction of the magnetization field [3]. In this paper, we consider structures consisting of laterally coupled YIG micro- and nanowaveguides that can be used as basic elements for creating various devices of functional magnonics: waveguides, filters, couplers. It also explores the possibility of controlling the propagation modes of spin waves by adding a metal layer. The structure of a directional coupler with metal layer on it is schematically shown in Fig. 1. Two parallel waveguides with length Lc = 8 mm, width w1 = w2 = 200 μm and thickness t 10 μm are placed laterally parallel with a gap d0 = 15 μm. Metal layer placed above it on distance d. The numerical modelling of this structure is performed using the micromagnetic simulation and finite element method with the following parameters of an Yttrium Iron Garnet (YIG) film: saturation magnetization Ms = 1.4*105 A/m, exchange constant A = 3.5 pJ/m and Gilbert damping alpha = 2*10-4. A external magnetic field Bext = 1200 Oe is applied along the long axis of the waveguides (x-direction in Fig. 2). The results of numerical simulation by the finite element method are presented on Fig.2. Figure 2(a) shows the dependence of the coupling length of the MSSW on the frequency in the case of the positive and negative directions of wave propagation along the structure. The wavelength depends on the frequency of the wave, which propagates in the negative direction. The lines show the normalized value of the pumping lengths when the distance between the metal and the surface of the microwave ovens changes from 10 μm to 90 μm. It can be seen that at a distance of d = 30 μm at a frequency of 5.6 GHz, the largest difference is observed, about 9 times, between the pumping length of waves propagating oppositely to each other in the structure under study. At the same time, it can be said that at a distance of more than 90 μm, the influence of the metal has practically no force over the entire frequency range of the MSSW wave, which can propagate in this structure under the considered parameters. This work was supported by the Russian Science Foundation (20-79-10191)

**References:**

1. R. W. Damon and J. R. Eshbach, J. Phys. Chem. Solids 19, 308 (1961). 2. S.A. Nikitov, A.R. Safin, D.V. Kalyabin, A.V. Sadovnikov, E.N. Beginin, M.V. Logunov, M.A. Morozova, S.A. Odintsov, S.A. Osokin, A.Yu.Sharaevskaya, Yu.P. Sharaevsky, A.I. Kirilyuk Phys. Usp. 63 945–974 (2020) 3. A. V. Sadovnikov, E. N. Beginin, S. A. Odincov, S. E. Sheshukova, Y. P. Sharaevskii, A. I. Stognij, S. A. Nikitov, Applied Physics Letters 108 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a929c59507eb2da2039e24ebb5da6935.jpg)
(a)Schematic view of lateral magnonic stripes 
with metal layer; (b)view on stucture along x-axis 
(along wave propogation)

![](https://assets.underline.io/uploads/markdown_image/1/image/761c698d6d8beeaa6c1766edccc9c3fd.jpg)
(a)Frequency dependence of the coupling length of the MSSW, with opposite directions of wave propagation along x-axis; (b) dependance of normalized 
coupling length of gap between waveguides and metal layer

 Nonreciprocal spin-wave propagation in lateral magnonic stripes

The study of physical principles that determine the possibility of using spin waves (SW) to create information signal processing devices based on magnonics principles is of great interest [1]. Microstructures based on the iron-yttrium garnet (YIG) can be used in the processing of spin-wave signals due to the low attenuation. To control the properties of SW propagating, the method of structuring YIG films and creating irregular micro- and nanoscale waveguides, including structures with broken translational symmetry, can be used [2]. In this work, the numerical simulations and Brillouin light scattering technique results of the unidirectional spin wave propagation in latelal nonidentic magnonic crystals was shown(MC) [3,4]. In Figure 1 present the structure was made up of two MC waveguides (MC1 and MC2) with different width, oriented along the direction of the y axis. Each MC waveguide represents a structure with grooves 1 microns deep, repeating with a period of D = 200 microns. The length of sections of microwave structures with a periodic system of grooves is 5 mm. The width of magnon crystals MC1 and MC2 along the z axis were 500 μm and 200 μm, respectively. The value of lateral gap d between MC1 and MC2 was 20 μm. The structure was placed in an external magnetic field with the magnitude H0 = 1300 Oe directed along the z-axis in order to excite a surface magnetostatic spin wave (SMSW). By the means of Brillouin light scattering technique, we obtained 2-D intensity maps of the spin wave propagating in the structure for case spin wave excitation on MC1 . The possibility of unidirectional coupling of SW propagating in MCs near the frequency boundary of the transmission zone is demonstrated. Based on the results of micromagnetic modeling, the mechanism that accompanies the observed mode of intermode coupling in the lateral system of nonidentical MCs is determined, and the spatial-frequency signal separation modes are studied. The proposed device can act as spin-wave unidirectional coupler for planar interconnecting element for magnonic conduits operating in a regime of single mode propagation in one of the MCs. As results we demonstrate the perspective system of nonidentical magnonic crystals as a building block for integrated magnonic circuits for the concept of spin-wave signal processing units for logic gates such as demultiplexer, directional coupler and signal splitter. Experimental strucrure and was performed by the Russian Foundation for Basic Research (project no. 20-37-90020). Micromagnetic simulation was performed by Grant of the President of RF (No. MK-1870.2020.9).

**References:**

[1] V. V. Kruglyak, S. O. Demokritov, D. Grundler, Journal of Physics D: Applied Physics Vol. 43, P.260301 (2010) [2] A. V. Sadovnikov, C. S. Davies, V. V. Kruglyak, at al., PHYSICAL REVIEW B. Vol. 96, P. 060401(R) (2017) [3] A. V. Sadovnikov, V.A. Gubanov, S.E. Sheshukova, at.al.,Physical Review Applied, 9(5) (2018) [4] A. V. Sadovnikov, A. A. Grachev, A. A. Serdobintsev, at al., IEEE Magnetics Letters, 1–1 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a23efc808f3bb4570c013365c71273b1.jpg)
Fig.1 Scheme of the uniditectional spin-wave coupler.

 Unidirectional spin-wave coupler based on YIG nonidentical magnonic crystals.

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

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.

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

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