Frequency selective tunable spin wave channeling in

Frequency selective tunable spin wave channeling in the magnonic network A. V. Sadovnikov, E. N. Beginin, S. A. Odincov, S. E. Sheshukova, Yu. P. Sharaevskii, A. I. Stognij, and S. A. Nikitov Citation: Applied Physics Letters 108, 172411 (2016); doi: 10.1063/1.4948381 View online: http://dx.doi.org/10.1063/1.4948381 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/108/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Formation of Bose–Einstein magnon condensate via dipolar and exchange thermalization channels Low Temp. Phys. 41, 801 (2015); 10.1063/1.4932354 Collective spin waves in a bicomponent two-dimensional magnonic crystal Appl. Phys. Lett. 100, 162407 (2012); 10.1063/1.4704659 Ferromagnetic and antiferromagnetic spin-wave dispersions in a dipole-exchange coupled bi-component magnonic crystal Appl. Phys. Lett. 99, 143118 (2011); 10.1063/1.3647952 Wide-range wavevector selectivity of magnon gases in Brillouin light scattering spectroscopy Rev. Sci. Instrum. 81, 073902 (2010); 10.1063/1.3454918 Observation of frequency band gaps in a one-dimensional nanostructured magnonic crystal Appl. Phys. Lett. 94, 083112 (2009); 10.1063/1.3089839

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APPLIED PHYSICS LETTERS 108, 172411 (2016)

Frequency selective tunable spin wave channeling in the magnonic network A. V. Sadovnikov,1,2,a) E. N. Beginin,1 S. A. Odincov,1 S. E. Sheshukova,1 Yu. P. Sharaevskii,1 A. I. Stognij,3 and S. A. Nikitov1,2 1

Laboratory “Metamaterials,” Saratov State University, Saratov 410012, Russia Kotel’nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia 3 Scientific-Practical Materials Research Center, National Academy of Sciences of Belarus, 220072 Minsk, Belarus 2

(Received 20 February 2016; accepted 18 April 2016; published online 29 April 2016) Using the space-resolved Brillouin light scattering spectroscopy, we study the frequency and wavenumber selective spin-wave channeling. We demonstrate the frequency selective collimation of spin-wave in an array of magnonic waveguides, formed between the adjacent magnonic crystals on the surface of yttrium iron garnet film. We show the control over spin-wave propagation length by the orientation of an in-plane bias magnetic field. Fabricated array of magnonic crystal can be used as a magnonic platform for multidirectional frequency selective signal processing applications in magnonic networks. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4948381]

Magnonic waveguide, formed from a stripe shaped magnetic film, is a building block of any complex integral magnonic network,1 acting as the transmission line between signal processing devices.2–6 To fabricate the topology of magnonic network7,8 the signal processing devices should be put together to create the integrated circuits, where the magnons carry the data. The most promising candidates to effective channelling of spin waves between the functional units of magnonic network are the spatially inhomogeneous magnetic structures.7,9 The control over the dispersion of spin-wave can be achieved, e.g., by the periodic patterning of the thin magnetic films. Periodic variation of the magnetic materials’ parameters allows the fabrication of magnonic crystals (MC), which can be widely used for spin-wave-based computing applications.8 MC can demonstrate a complicated magnonic band structure with a strong dispersion and anisotropy.10 It was demonstrated that in the binary component twodimensional (2D) magnetic lattices, the two stripe-like spinwave modes can form a spin-wave channel in a direction perpendicular to the applied field.10,11 This effect exists in the 2D bicomponent MC with nonuniform distribution of the internal magnetic field profile. The spatial and frequency filtering features of the MC have the straightforward advantages in the magnonic applications, some of which are discussed recently.8,12,13 Magnetic materials can be engineered to generate the anisotropy and dispersion, which open the possibility to non-diffractive spin wave propagation or selfcollimation.14 The most often used low-diffraction structures in optics are 2D photonic crystals (PCs) and waveguide array structure with the profile of refractive index, changed in the direction, perpendicular to wave propagation.14–17 The nondiffractive propagation in these structures is conceivable due to a flat constant-frequency contour within the isofrequency diagram, obtained from the dispersion relation. Theoretical and numerical prediction of spin-wave self-collimation was given in Refs. 18 and 19, where the spin wave channeling in a)

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the out-of-plane magnetized 2D MC was demonstrated. When the spin-wave beam, having the same frequency corresponding to the flat isofrequency curve, propagates in the artificially fabricated magnetic medium, the wavenumber components of the beam propagate with almost equally directed group velocities. Thence the spin-wave beam almost does not spread in transverse section. For the typical planar magnonic application, the static magnetic field is applied in the plane of the film.7,8 This is related with the possibility for functional magnetic devices to operate at the values of magnetic field lower than the magnetization saturation of the ferromagnetic material.20 Dispersion management of the in-plane magnetized 2D MC cannot provide the true condition of the flat isofrequency curve in the wide range of the wavenumbers as it prevails in the case of the out-of-plane magnetization, which is accompanied with the isotropic dispersion. In this letter, we propose a magnonic crystal array (MCA) that supports self-collimation in the frequency range of magnonic forbidden gap. We present the results of experimental study of MCA fabricated on the surface of yttrium iron garnet (YIG) film. By using space-resolved BLS technique, we have demonstrated multichannel collimated spin-wave propagation in the MCA. An almost fully collimated spinwave beam was visually observed in the array of magnonic waveguides, formed between the adjacent one-dimensional (1D) magnonic crystals on the surface of YIG film. The control over the spin-wave propagation distance in each channel can be achieved by the variable orientation of an in-plane bias magnetic field. The proposed array of the magnonic crystals can be used as a non-diffractive frequency selective spinwave bus due to the flexibility for integration of MCA in the functional magnonic circuits. The schematic of the experimental setup is shown in Fig. 1(a). MCA was fabricated from the single-crystalline ferrimagnetic YIG film with saturation magnetization of M0 ¼ 139 G. Magnetic waveguide of wm ¼ 3.5 mm width was produced using the laser scribing.12,21,22 The array of grooves with the period of L ¼ 200 lm was fabricated at YIG

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FIG. 1. (a) Schematic of the experimental setup. Inset: the photograph of the MCA fragment; (b) transmission characteristics, measured with signal network analyzer for MC (blue curve) and MCA (red curve). Inset: detailed frequency region of the magnonic forbidden zone; (c) experimentally measured dispersion for the MC (blue line) and MCA (red line). Calculated dispersion for MCA (green dotted line). Inset: isofrequency curves for spin waves. Yellow area is the guide for the eye to show the frequency and wavenumber region of the magnonic forbidden zone of the MC.

surface using the precise ion-beam etching. The width of each groove is wg ¼ 500 lm, the groove depth is 1 lm, and the length is lg ¼ L=2 ¼ 100 lm. The distance between grooves in x-direction is wd ¼ 500 lm. This structure on the surface of YIG film forms three channels, separated by 1D MC’s. The sample has a length of 30 periods in y-direction. The only four periods in x-direction allow to consider this structure as the MCA with the linear waveguiding channels rather than as the 2D square-lattice MC. As a reference, we fabricated a conventional MC, which is similar to the structure with the array of MC’s but with the value of wd ¼ 0. In this case, the width of the groove is equal to the width of YIG film wg ¼ wm. The 50 X-matched microstrip delay line with the 30 lm width and 4 mm length microwave transducers was used for the excitation of spin waves in the MCA. Input and output transducers are attached to the YIG film (see Fig. 1(a)) at a distance of 8 mm from each other. The uniform static magnetic field H0 ¼ 1185 Oe was applied in the plane of the waveguide along the x-direction for the effective excitation of the guided magnetostatic surface waves (MSSW).23,24 Transmission and dispersion of MSSW were experimentally measured using E8362C PNA Microwave Network Analyzer. First, the measurement of the transmission response for the reference MC

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was performed. The solid blue line in Fig. 1(b) shows the measured MSSW intensity for the MC. The frequency f0 ¼ 5:222 GHz of ferromagnetic resonance is depicted with the gray vertical dashed-dotted line. A well pronounced stop band where spin waves are not allowed to propagate is clearly observed for the frequency of f2 ¼ 5:333 GHz. The frequency width of the first band gap is DfB ¼ 0:05 GHz at the level of 35 dB. From the experimentally measured phase shift for the MSSW, the dispersion characteristic of MC was reconstructed (see blue curve in Fig. 1(c)). The frequency f2 ¼ 5:333 GHz corresponds to the Bragg wavenumber ky ¼ kB ¼ p=L ¼ 157 rad/cm. We plot the isofrequency contours for the in-plane magnetized YIG film for three values of frequency f0, f1, and f2 on the inset in Fig. 1(c). The microwave measurement of the fabricated MCA shows that the first forbidden frequency band is clearly distinguishable at the transmission response (see red curve in Fig. 1(b). The dispersion measurement (see red curve in Fig. 1(c)) reveals that this frequency corresponds to the Bragg wavenumber kB as in the case of MC measurement. The fabrication of the waveguiding channels at the surface of YIG film leads to the growth of transmission of spin-wave in the MCA by 18 dB at the central frequency of forbidden zone f2 (red curve) relative to the MC (blue curve, see the inset in Fig. 1(b)). This can be explained using the simple formalism of the coupled waves, which is typically implemented to analyze the dispersion of conventional MC.25,26 The efficiency of the forward and backward wave coupling is decreased with the increase in the distance wd between the adjacent MC inside the MCA. This leads to the decrease in the reflection coefficient of MSSW propagating along the y-axis. To demonstrate the distribution of the dynamic magnetization in the MCA, the Brillouin light scattering (BLS) technique in the backscattering configuration was used. By moving the probing laser spot over the sample surface, the BLS technique enables measurements of the spatial maps of the spin-wave intensity with the resolution of 25 lm. The detected BLS intensity I is proportional to the square of the dynamic magnetization. Figure 2 represents the result of two dimensional 4 3:5 mm2 mapping of the sample area, where the periodic structure is fabricated. At the frequency f1 ¼ 5:3 GHz, the spatial profile of BLS map corresponds to the typical result of width modes beating24,27,28 for the YIG waveguide of the width of wm ¼ 3.5 mm (Fig. 2(a)). The estimated half-period of the beating of first and third transverse modes27 is about 3.5 mm in the frequency range of f1 < f < f2 . This is in a good accordance with the BLS map (Fig. 2(a)), where the transverse size of spin wave beam29 is decreased at y ¼ 3 mm. The distribution of the magnetization squared is almost not affected by the array of MCs on the surface of YIG. The distribution of spin wave intensity changes as the frequency reaches the forbidden band. At the frequency of f2, the spatial map of magnetization, shown in Fig. 2(b), demonstrates the channeling of spin-wave. Confinement of spin-wave in the x-direction in each channel of width wd is clearly seen. In the central channel, denoted by “CH2” in Fig. 2(a), the spin-wave beam propagates almost non-divergent over the distance of 3 mm, while in two adjacent channels (along the lines x 0:7 mm (“CH1”)


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FIG. 3. Pseudocolor logarithmic map of the BLS intensity in the section y ¼ 2.0 mm as a function of frequency. Gray horizontal dotted lines depict the edges of the adjacent waveguides of width wd. Vertical dashed line is the guide for the eye to show the central frequency of the first magnonic forbidden zone of the MC. The frequency f0 is depicted with the vertical dasheddotted line.

FIG. 2. Normalized colour-coded BLS intensity map (left panels) and transverse (along x-axis) profile of magnetization squared at different y-coordinates at / ¼ 0 for frequencies: f1 ¼ 5:3 GHz (a), f2 ¼ 5:33 GHz (b), and at / ¼ 15 for frequency f2 (c).

and x 2:8 mm (“CH3”)), the spin-wave collimation allows the beam to propagate over the distance of about 2 mm. Collimation allows for a wave to travel in a medium along one particular dimension without a significant dispersion in any orthogonal dimensions. To prove the collimation of spin-wave, we plot the transverse distribution of magnetization squared at the different distances from the input transducer (see right panels of Fig. 2). The crosstalk effect of the adjacent waveguiding channels30 is negligible due to the relatively high distance between the channels wd. Two main factors define the attenuation of spin waves propagating along the channel between MC’s: the damping of spin-wave in YIG and the evanescence of spin-wave beam. Latter is correlated with the etching depth and the value of L=ðL lg Þ (see Ref. 18). To show that the frequency selective collimation of spinwave is associated with the frequency range of the 1st forbidden zone, we performed the spatially resolved measurement of the spin-wave intensity along the line y ¼ 4.0 mm in the frequency range from 5.15 GHz to 5.5 GHz. The results of these measurements are shown in Fig. 3. In the frequency range f0 < f < f2 DfB =2, the intensity of spin-wave is allocated in the center of the MCA structure approximately in the range 0:4 < x < 2:6 mm. As the frequency reaches the frequency range of band gap f2 DfB =2 < f < f2 þ DfB =2, three spin wave beams are observed in three channels inside the MCA. As the frequency increases, the confinement of spin-wave is vanishing, and the spatial BLS map represents the results of

the transverse mode beating modulated with the ripple, which is the result of the numerous reflections of spin wave. Since the self-collimation in the MCA structure manifests itself in the frequency range corresponding to the frequencies inside the band gap, the MCA can exhibit the spatial-frequency selective regimes for spin-wave. It should be noted that when the input signal is applied to the microstrip antenna, defined as “Pout” in Fig. 1(a), the effect of spin-wave channeling vanishes, that is caused by the concentration of MSSW energy close to the opposite surfaces of the film for the reversed propagation directions.23 By means of finite-element method (FEM), the straightforward solution of system of Maxwell equations was performed for 3D geometry of the MCA.31 The simulation was performed for one period of MCA. The periodic boundary conditions were used in the y ¼ 0 mm and y ¼ 0.2 mm sections. We have performed FEM simulation to find the eigenmode profiles and wavenumbers for wave propagating in the MCA. To compute the spatial distribution of magnetization at the fixed frequency, we take into account only the 1st width mode. The distribution of the absolute value of Hz component of the wave is shown in Fig. 4. The profile of the first transverse mode at the frequency of the f1 is depicted in Fig. 4(a) (right panel). As seen from Fig. 4(b), the field profile of the 1st width modes changes as the frequency approaches to f2. When the frequency is outside the bandgap, the confinement of spin-wave vanishes. The finite-difference time-domain (FDTD) micromagnetic simulation32 of the transmission of MSSW over the MC and MCA at the frequency of Bragg resonance f2 shows that the ratio of the transmission of spinwave power in the MC and MCA is about 18 dB, which corresponds to the data of the microwave experiment (Fig. 1(b)). FDTD simulation is performed also to verify the collimation in the MCA structure. Figure 5(a) illustrates the channeling of spin-wave at the frequency of f2. The non-diffractive propagation of spin-wave in the MCA is conceivable also due to a relatively flat area of constant-frequency contour in the isofrequency diagram (Fig. 1(c)) at ky kB . By the variation of the orientation of applied dc magnetic field (angle /) at the fixed frequency f2, the control over spinwave propagation length in magnonic channels is possible.


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FIG. 4. FEM calculation results of the 1st eigenmode profile in MCA at the frequency of f1 (a) and f2 (b).

The divergence of the collimated beam is insensitive to the small variation of the value of the angle /. Figure 2(c) shows the spin wave distribution when magnetic field is applied at / ¼ 15 . The propagation length of collimated spin wave beam in channel “CH1” is considerably larger rather than in “CH2” and “CH3.” We analyze the angular dependencies of the spin wave transmission with micromagnetic simulation technique.32 Figure 5(b) verifies the control over a propagation length in the spin-wave channels at / ¼ 15 . This behaviour is consistent with the work,17 where the self-collimation effect is studied for the 2D silicon photonic crystal in infrared wavelength at large incident angles over a broad wavelength range. To demonstrate the redistribution of the spin-wave power in the magnonic channels at different values of /, we calculate the integralÐ value of spin-wave intensity in n-th channel (Cn) as Tn ¼ x2Cn IðxÞ dx. The influence of 1st width mode, excited by the microstrip, evidently results in the nonequal distribution of power in each channel (Fig. 4(c)). Thus, the transmission of spin waves in 2nd channel is four times larger than in 1st and 3rd channels at / ¼ 0. Rotating the magnetic field enabling the controllable manipulation of spinwave propagation over the magnonic channels. These results are supported by the experimental data, depicted with the closed markers in Fig. 5(b) for the angles 0 ; 5 ; 10 , and 15 . Several individual scans over the area of interest were performed and then averaged. Therefore, MCA offers an alternative to the present spatial-frequency selective magnonic devices such as coupled magnetic stripes30 or T-shaped magnonic waveguide.4 In conclusion, we have demonstrated the spatialfrequency channeling of spin waves in magnonic crystal array with the in-plane magnetization. The spin wave can be spatially divided in three adjacent wave beams, when the wave number of propagating wave corresponds to the Bragg wavenumber and the frequency lies within magnonic bandgap. We have shown that in the designed and fabricated structure spin

FIG. 5. Micromagnetic simulations of the spin-wave propagation in the MCA. Distribution of dynamic magnetization squared in logarithmic scale are shown for different angles of magnetic field orientation: / ¼ 0 (a) and / ¼ 15 (b). Black rectangles denote the etching area on the surface of YIG film. (c) Dependencies of the spin-wave transmission on the in-plane angle of magnetic field orientation. Open symbols denote the simulation results, and closed symbols correspond to the experimental data.

wave propagates without diffraction at large distance. The control over a propagation distance in the spin-wave channels can be implemented by the orientation of the magnetic field. This was explained by the frequency selective collimation of spin-wave, which is confirmed by numerical simulations. This effect requires a fabricated magnonic channels in 2D structure to act as a waveguide on the surface of magnetic film. Collimated spin wave beams can be used as the signal carrier in the magnonic platform for applications such as signal multiplexing. Array of magnonic crystals offers new flexibility for spin-wave guiding control in planar magnonic devices. We gratefully acknowledge the contributions of S. V. Grishin. This work was supported partially by the Russian Foundation for Basic Research (Nos. 16-37-60093, 16-3700217, and 15-07-05901), Yu.P.S. and E.N.B. acknowledge the support from the Grant from Russian Science Foundation (No. 16-19-10283), S.A.N. acknowledges the support from the Grant from Russian Science Foundation (No. 14-1900760), A.V.S. and S.E.S. acknowledge support from the


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Scholarship of the President of RF (SP-313.2015.5) and Grant of the President of RF (MK-5837.2016.9). 1

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