We propose a nanoscale spin-wave directional coupler that allows the realization of magnonic integrated circuits.

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Spin waves are investigated in Yttrium Iron Garnet (YIG) waveguides with a thickness of 39 nm and widths ranging down to 50 nm, i.e., with aspect ratios thickness over width approaching unity, using Brillouin Light Scattering spectroscopy. The experimental results are verified by a semi-analytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semi-analytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nano-structures.Spin waves and their quanta, magnons, typically feature frequencies in the GHz to THz range and wavelengths in the micrometer to nanometer range. They are envisioned for the design of faster and smaller next generational information processing devices where information is carried by magnons instead of electrons [1][2][3][4][5][6][7][8][9]. In the past, spin-wave modes in thin films or rather planar waveguides with thickness-towidth aspect ratios ar = h/w << 1 have been studied. Such thin waveguides demonstrate the effect of "dipolar pinning" at the lateral edges, and for its theoretical description the thin strip approximation was developed, in which only pinning of the much-larger-in-amplitude dynamic in-plane magnetization component is taken into account [10][11][12][13][14][15]. The recent progress in fabrication technology leads to the development of nanoscopic magnetic devices in which the width w and the thickness h become comparable [16][17][18][19][20][21][22][23]. The description of such waveguides is beyond the thin strip model of effective pinning, because the scale of nonuniformity of the dynamic dipolar fields, which is described as "effective dipolar boundary conditions", becomes comparable to the waveguide width. Additionally, both, in-plane and out-of-plane dynamic magnetization components, become involved in the effective dipolar pinning, as they become of comparable amplitude.Thus, a more general model should be developed and verified experimentally. In addition, such nanoscopic feature sizes imply that the spin-wave modes bear a strong exchange character, since the widths of the structures are now comparable to the exchange length [24]. A proper description of the spin-wave eigenmodes in nanoscopic strips which considers the influence of the exchange interaction, as well as the shape of the structure, is fundamental for the field of magnonics.In this Letter, we discuss the evolution of the frequencies and profiles of the spin-wave modes in nanoscopic waveguides where the aspect ratio ar evolves from the thin film case ar → 0 to a rectangular bar with ar → 1. Yttrium Iron Garnet (YIG) waveguides with a thickness of 39 nm and widths ranging down to 50 nm are fabricated and the quasi-ferromagnetic resonance (quasi-FMR) frequencies within them are measured using microfocused Brillouin Ligh...

Modern-days CMOS-based computation technology is reaching fundamental limitations which restrain further progress towards faster and more energy efficient devices [1]. A promising path to overcome these limitations is the emerging field of magnonics which utilizes spin waves for data transport and computation operations [2-5]. Many different devices have already been demonstrated on the macro-and microscale [2,4-12]. However, the feasibility of this technology essentially relies on the scalability to the nanoscale and a proof that coherent spin waves can propagate in these structures.Here, we present a study of the spin-wave dynamics in individual yttrium iron garnet (YIG) magnonic conduits with lateral dimensions down to 50 nm. Space and time resolved micro-focused Brillouin-Light-Scattering (BLS) spectroscopy is used to extract the exchange constant and directly measure the spin-wave decay length and group velocity. Thereby, the first experimental proof of propagating spin waves in individual nano-sized YIG conduits and the fundamental feasibility of a nano-scaled magnonics are demonstrated.State of the art investigations are typically performed in micron-sized structures [13][14][15] lacking the final push to the nanoscale and are often based on the so-called Damon-Eshbach (DE) geometry, since this geometry provides a high spin-wave group velocity [16]. However, large bias magnetic fields are required to achieve the corresponding magnetization state in nano-sized conduits. Therefore, using the Backward-Volume (BV) geometry is a necessity regarding any application of spin waves for data processing, since it corresponds to the natural self-magnetized state of such a conduit. Besides the propagation geometry, the choice of material is crucial as well. Being the material providing the lowest known spin-wave damping, yttrium iron garnet (YIG) is the naturally preferred material for magnonics. However, this comes at the cost of a complex crystallographic structure [17] featuring a unit cell size of 1.2376 nm [18], which opens up the question whether the material can be scaled down to the nanoscale while preserving its unique properties during this process.Here, a thin (111) YIG film with a thickness of = 44 nm is used, which is grown on top of a 500 µm thick (111) Gadolinium Gallium Garnet (GGG) substrate by Liquid Phase Epitaxy (LPE) [19]. A preliminary characterization by stripline Vector-Network-Analyzer ferromagnetic resonance (VNA-FMR) spectroscopy [20,21] is performed to obtain the fundamental magnetic properties. The measurement, shown in Supplementary Fig. S1, yields a saturation magnetization of s = (140.7 ± 2.8) kA m and a Gilbert damping parameter of = (1.75 ± 0.08) × 10 −4 . These values are common for high-quality YIG thin films [19]. Thereafter, the nanostructuring process is carried out by Figure 2| Measurement of the thermal spin-wave population and determined exchange constant. (a) Exemplary thermal BLS spectra in the absence of any microwave excitation for a = 1000 YIG waveguide. A field dependent ...