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A magnonic directional coupler for integrated magnonic half-adders


Magnons, the quanta of spin waves, could be used to encode information in beyond-Moore computing applications, and magnonic device components, including logic gates, transistors and units for non-Boolean computing, have already been developed. Magnonic directional couplers, which can function as circuit building blocks, have also been explored, but have been impractical because of their millimetre dimensions and multimode spectra. Here, we report a magnonic directional coupler based on yttrium iron garnet that has submicrometre dimensions. The coupler consists of single-mode waveguides with a width of 350 nm. We use the amplitude of a spin wave to encode information and to guide it to one of the two outputs of the coupler depending on the signal magnitude, frequency and the applied magnetic field. Using micromagnetic simulations, we also propose an integrated magnonic half-adder that consists of two directional couplers and we investigate its functionality for information processing within the magnon domain. The proposed half-adder is estimated to consume energy in the order of attojoules.

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Fig. 1: Sample geometry and working principle of the directional coupler in the linear regime.
Fig. 2: Nonlinear functionality of the directional coupler.
Fig. 3: The operational principle of the magnonic half-adder.
Fig. 4: Modelling and characteristics of directional coupler 2.
Fig. 5: Operational principle of the magnonic half-adder.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We thank B. Hillebrands for support and valuable discussions. This research has been supported by ERC Starting Grant 678309 MagnonCircuits, FET-OPEN project CHIRON (contract no. 801055), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR-173 – 268565370 (Collaborative Research Center SFB/TRR-173 ‘Spin+X’, project B01) and DFG project no. 271741898, the Austrian Science Fund (FWF) through project I 4696-N and the Ministry of Education and Science of Ukraine, project 0118U004007. B.H. acknowledges support from the Graduate School Material Science in Mainz (MAINZ).

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Authors and Affiliations



Q.W. proposed the directional coupler and half-adder design, preformed the BLS measurements, carried out the evaluation and wrote the first version of the manuscript. C.D. provided the YIG film. M.K., B.H. and B.L. fabricated the nanoscale directional coupler. M.S., B.H. and M.G developed the BLS set-up. T.B. acquired the SEM micrograph. M.K. performed the VNA-FMR measurements. R.V. developed the analytical theory and performed the theoretical calculations. Q.W. and M.M. performed the micromagnetic simulations. F.C., C.A. and S.D.C. performed the benchmarking and calculated the parameters of the 7-nm CMOS half-adder. O.V.D. and T.B. discussed the interpretation and the relevance of the results. P.P. and A.V.C. led this project. All authors contributed to the scientific discussion and commented on the manuscript.

Corresponding authors

Correspondence to Q. Wang or A. V. Chumak.

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Extended data

Extended Data Fig. 1 Effect of far-field excitation by the U-shaped antenna.

SEM images of the a normal and b displaced waveguides. The red and blue dots show the μBLS measurement points. c, The spin-wave intensities for normal (red dot line), displaced waveguides (blue dot line) and thermal background (black dot line). The grey area shows the working frequency range in the paper.

Extended Data Fig. 2 Spin-wave spectra in the isolated waveguide.

a, The in-plane (black line) and out-of-plane (red line) field distribution created by the U-shape antenna. The schematic cross section of a U-shaped antenna is shown inset. b, The excitation efficiency as a function of spin-wave wavenumber. c, Spin-wave frequency as a function of spin-wave wavenumber. d, Spin-wave intensities are measured 4 μm far from the antenna for different excitation powers. The black line shows the analytical calculation of the spin-wave intensity. A SEM image of the isolated waveguide is shown on the top of Fig. 2d.

Extended Data Fig. 3 Reconfigurability of the directional coupler by an applied magnetic field.

a, The averaged spin-wave intensity for a frequency of 3.465 GHz as function of the external field for the first (blue circles) and the second (red squares) output waveguide of the directional coupler. b, Measured (circles and squares) and theoretically calculated (solid lines) normalized output spin-wave intensities at the first (blue) and second (red) output waveguide for different external fields. ce, Two-dimensional BLS maps of the spin-wave intensity for the different external magnetic fields: c, B1 = 56 mT, d. B2 = 53.2 mT, and e. B3 = 51.3 mT. The right panels show the BLS intensity integrated over the red dashed rectangular regions.

Extended Data Fig. 4 Modified half-adder with fan-out gate.

a-c, Operational principle and d truth table of two half-adders with shared inputs (corresponds to the half-adder with added fan-out logic gate).

Extended Data Fig. 5 Parametric amplification.

a, A schematic picture of the parametric amplifier. b, Output spin-wave intensity as a function of pumping current for different conditions.

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Supplementary Information

Supplementary Discussion, Figs. 1–5 and Table 1.

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Wang, Q., Kewenig, M., Schneider, M. et al. A magnonic directional coupler for integrated magnonic half-adders. Nat Electron 3, 765–774 (2020).

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