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

*Session Co-Chair: Oleksandr Dobrovolskiy, University of Vienna*

*Session Co-Chair: Qi Wang, Universitat Wien*

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Multifrequency Spin Wave Device for Parallel Data Processing using Micro Structured Yttrium Iron Garnet Thin Films

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