Magnonics, which main idea is the utilization of spin waves propagating in media with spontaneous magnetic order (ferromagnetics, antiferromagnetics, etc.) for digital and analog signal processing, is a promising and fast-developing research field. To the date, many important milestones were already achieved, in particular, key building blocks of magnonic logic – logic elements of different design and operational principle have been developed and experimentally realized [1, 2]. The next crucial step in the development of magnonics systems is the integration of different logic gates and auxiliary elements (e.g., amplifiers, normalizers, etc.) into a magnonic circle, leaving all the signals in the magnonic band, without transformation into electric or other signals, which are the largest source of energy losses. A nice approach for the solution of this task was found in Ref. [4], where nanoscale spin-wave directional coupler is studied. Directional coupler shows great potential to be a universal element of magnonic circles, as it can perform different operation: guiding spin wave at the waveguide intersection, power splitting and combining, frequency demultiplexing, etc. Moreover, using nonlinear operation mode of a direction coupler it become possible to develop all-magnonic half-adder [5] – first all-magnon integrated scheme.

All the previous works on spin-wave directional couplers consider dipolar interaction between nearby placed waveguides as a source of the coupling. Although this approach has already allowed for the creation of real submicron-sized device [5], further improvement of dipolar-based direction couplers is rather questionable, since dipolar interaction weakens when spin wave becomes shorter (i.e., with increase of spin wave frequency), as well as with a decrease of the waveguide thickness.

In this work, we, using micromagnetic simulations and analytical calculations, demonstrate an alternative approach of exchange-based coupler, in which two waveguides are coupled via a ferromagnetic spacer having direct exchange contact with the spacer. As it is shown in Fig. 1, exchange coupling can drastically, more than in one order, reduce the so-called “coupling length” – the length at which spin-wave energy is fully transferred from one waveguide to another, and, therefore, allows for the development of efficient nanoscale directional coupler with high working frequencies. It may appear, that the strongest the coupling, the better, so that usage of the same ferromagnetic material for the waveguides and spacer may be the best way. However, it is not true, as with an increase of the strength of the spacer the reflection from the coupler input increases drastically. We found two main sources of this reflection: (i) increased averaged wavenumber of symmetric and antisymmetric collective modes in the coupler, which could be overcome by local dispersion modification, and (ii) mismatch of spatial profiles of spin waves in isolated and coupled waveguides, which limits reasonable strength of the spacer up to about 10-20 % of the waveguide materials (in saturation magnetization and exchange stiffness).

This work was partially supported by NAS of Ukraine and National Research Foundation of Ukraine (grant # 2020.02/0261).

Fig. 1. Coupling length in CoFeB-based spin-wave directional coupler with different fillings in between CoFeB waveguides: air gap (dipolar coupling only), weak ferromagnet having saturation magnetization and exchange stifness 0.1 or 0.2 of those of CoFeB, and permalloy Ni80Fe20 (Py), as the function of spin-wave frequency. Width and thickness of CoFeB waveguides, as well as the distance in between them aer equal to 7 nm.

References
[1] A. Khitun, M. Bao, and K. L. Wang,.” Magnonic logic circuits”. J. Phys. D. Appl. Phys., vol. 43, p. 264005, 2010.
[2] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, “Magnon spintronics”, Nat. Phys., vol. 11, p. 453–461, 2015.
[3] A. N. N. Mahmoud, F. Vanderveken, F. Ciubotaru, C. Adelmann, S. Cotofana, and S. Hamdioui, “N-bit data parallel spin wave logic gate”.2020 Design, Automation & Test in Europe Conference & Exhibition (DATE): Proceedings, pp. 642-645, 2020
[4] Q. Wang, P. Pirro, R. Verba, A. Slavin, B. Hillebrands, and A. V. Chumak, “Reconfigurable nanoscale spin-wave directional coupler”, Sci. Adv., vol. 4, p. e1701517, 2018.
[5] Q. Wang, M. Kewenig, M. Schneider, R. Verba, F. Kohl, B. Heinz, et al., “A magnonic directional coupler for integrated magnonic half-adders”, Nature Electronics, vol. 3, p. 765, 2020.