Magnetic field-controlled nanoscale spin-wave vertical directional coupler

The directional coupler is a fundamental element of wave-based circuits. The state of the art for the spin-wave directional couplers consists mostly of macroscopic waveguides or two-dimensional planar systems. In this Letter, we present the design of the nanoscale spin-wave vertical directional coupler with a very high efficiency exceeding 99.5%. We demonstrate that the operation of the coupler can be controlled by the magnitude of the external magnetic field. Moreover, it can perform multiplexing and demultiplexing of the spin-wave signal. Such a device ought to become an essential element of the three-dimensional magnonic circuits.