The antennas are electrically isolated from the waveguides by a layer of Al 2O 3 that is 100 nm thick. The centre-to-centre separation between the two antennas is of the order of 20 μm. Each antenna consists of two parallel branches or arms with width of 4 μm and edge-to-edge separation of 4 μm. The measurements are carried out with a vector network analyser (VNA). Thus, even though the spin waves do not actually interfere themselves, we use the term spin-wave interference in the following to remind us that the properties of spin waves are controlled for the realisation of interference. In the following, we show that the measured interference signal entirely depends on the amplitudes of and relative phase between the spin waves. The electrical signal produced inductively by FM1 interferes with that produced by FM2 within antenna 2, where the total interference signal is measured. Direct current ( I dc) can also be applied through FM2 to change the propagation properties of the spin wave propagating through it. Spin waves propagate through the two spin-wave waveguides FM1 and FM2. The resonance condition depends on H, f and the wave vector ( k). This rf magnetic field generates spin waves at the same frequency f in two waveguides (FM1 and FM2) of Co 20Fe 60B 20 above a normal metal, especially under the resonance condition. In the present work, under a fixed applied magnetic field (biased field) ( H), a continuous radio-frequency (rf) current ( I rf) is passed through antenna 1 at frequency ( f) to generate an rf magnetic field. Figure 1 is a sketch of the device layout along with the operating principle. We measure interference signals on various devices. In the case of our interferometer, the spin wave propagating through one branch has a shifted dispersion curve compared with the spin wave in the other branch, resulting in a phase difference between them. Like other published results on spin-wave propagation and spin-wave logic gates 12, 14, 17, it is a step towards spin-wave-based logics on micrometre and nanometre scales. Herein we demonstrate the manipulation of spin-wave interference using a Mach–Zehnder-type interferometer on a micrometre scale. However, there have been very few reports on Mach–Zehnder-type spin-wave interferometers on millimetre scale with yttrium iron garnet as a magnetic medium 14, 23. Spin-wave interferences have been reported experimentally in micro stripes using rising and falling edges of electrical pulses 20, 21 and oppositely propagating spin waves 22 that do not allow free manipulation of the interference. However, spin-wave-based logics are mainly proposed theoretically down to nanometre scale 6, 19. The basic building block of spin-wave logics is the spin-wave interferometer where the interference of two or more spin waves can be manipulated. The first important step in the development of spin-wave-based devices would be the realization of spin-wave logics. Recent reports have shown the possibility of switching the propagation direction at will 17, 18. Spin waves can be generated in various ways 3, 14, 15 and amplified 16. Spin waves can thus be applied to long-range propagation of information, as the loss of information per unit propagation length is smaller than that of diffusive spin currents at room temperature. Indeed the propagation length of such waves is notably longer than the electron spin diffusion length in semiconductors or metals. Because they are waves, one can use the phase to convey information. These propagating spin waves carry angular momentum like diffusive spin currents in spintronics. Interestingly, one can excite spin waves locally and detect them after propagation 3, 10, 11, 12, 13. Spin waves can be regarded as the collective spin resonance of electrons in a magnetic material. Many new concepts of information transport using spin waves have been proposed in recent years 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
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