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

No abstract

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 ...

Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of current challenges and the outlook of further development for each research direction.

A nano-scale reconfigurable magnonic crystal is designed using voltage-controlled perpendicular magnetic anisotropy (PMA) in ferromagnetic-dielectric hetero-structures. A periodic array of gate metallic stripes is placed on top of a MgO/Co structure in order to apply a periodic electric field and to modify the PMA in Co. It is numerically demonstrated that the application of the voltage to the gate stripes modifies the spin-wave propagation and leads to the formation of band gaps in the spin-wave spectrum. The band gaps are dynamically controllable, i.e. it is possible to switch band gaps on and off within a few nanoseconds. The width and the center frequency of the band gaps is defined by the applied voltage. At last, it is shown that the application of the voltage to selected, rather than to all gate stripes allows for a pre-defined modification of the band gap spectra. The proposed voltage-controlled reconfigurable magnonic crystal opens a new way to low power consumption magnonic applications.

The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mechanism of external injection of bosons by irradiation is required. Here, we present a novel and universal approach to enable BEC of quasi-particles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose-Einstein condensation.Bosons are particles of integer spin that allow for the fundamental quantum effect of Bose-Einstein Condensation (BEC), which manifests itself in the formation of a macroscopic coherent state in an otherwise incoherent, thermalized many-particle system. The phenomenon of BEC was originally predicted for an ideal gas by Albert Einstein in 1924 based on the theory developed by Satyendra Nath Bose. Nowadays, Bose-Einstein condensates are investigated experimentally in a variety of different systems which includes real particles such as ultra-cold gases (1, 2) as well as quasi-particles with the likes of exciton-polaritons (3, 4), photons (5, 6) or magnons (7-9). The phenomenon can be reached by a major decrease in the system temperature or by an increase in the particle density. In order to condensate atomic gases, extremely low temperatures on the order of mK are required since the density of such gases must be very low to prevent their cohesion. In contrast, the quasi-stationary cooling of a quasi-particle system is accompanied by a decrease in its population and prevents BEC. Thus, an artificial injection of bosons is required to reach the threshold for BEC. Since quasi-particle systems allow for high

The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nano-scale thickness. Our results reveal that chiral Magneto Static Surface Waves (cMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects. cMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of cMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long-(dipole dominated) and short-wavelength (exchange dominated) spin waves. Micromagnetic simulations confirm the robust character of the cMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing cMSSWs in nano-scale thin films.