Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths.

Nonreciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic, and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles have so far yielded moderate nonreciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly nonreciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 µm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed nonreciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory, and their peculiarities are further discussed in terms of caustic spin-wave focusing.

Direct Observation of Propagating Spin Waves in the 2D van der Waals Ferromagnet Fe5GeTe2.

Magnetism in reduced dimensionalities is of great fundamental interest while also providing perspectives for applications of materials with novel functionalities. In particular, spin dynamics in two dimensions (2D) have become a focus of recent research. Here, we report the observation of coherent propagating spin-wave dynamics in a ∼30 nm thick flake of 2D van der Waals ferromagnet Fe5GeTe2 using X-ray microscopy. Both phase and amplitude information were obtained by direct imaging below TC for frequencies from 2.77 to 3.84 GHz, and the corresponding spin-wave wavelengths were measured to be between 1.5 and 0.5 µm. Thus, parts of the magnonic dispersion relation were determined despite a relatively high magnetic damping of the material. Numerically solving an analytic multilayer model allowed us to corroborate the experimental dispersion relation and predict the influence of changes in the saturation magnetization or interlayer coupling, which could be exploited in future applications by temperature control or stacking of 2D-heterostructures.

Experimental Observation of Flat Bands in One-Dimensional Chiral Magnonic Crystals.

Spin waves represent the collective excitations of the magnetization field within a magnetic material, providing dispersion curves that can be manipulated by material design and external stimuli. Bulk and surface spin waves can be excited in a thin film with positive or negative group velocities and, by incorporating a symmetry-breaking mechanism, magnetochiral features arise. Here we study the band diagram of a chiral magnonic crystal consisting of a ferromagnetic film incorporating a periodic Dzyaloshinskii-Moriya coupling via interfacial contact with an array of heavy-metal nanowires. We provide experimental evidence for a strong asymmetry of the spin wave amplitude induced by the modulated interfacial Dzyaloshinskii-Moriya interaction, which generates a nonreciprocal propagation. Moreover, we observe the formation of flat spin-wave bands at low frequencies in the band diagram. Calculations reveal that depending on the perpendicular anisotropy, the spin-wave localization associated with the flat modes occurs in the zones with or without Dzyaloshinskii-Moriya interaction.

Spin-Wave Channeling in Magnetization-Graded Nanostrips.

Magnetization-graded ferromagnetic nanostrips are proposed as potential prospects to channel spin waves. Here, a controlled reduction of the saturation magnetization enables the localization of the propagating magnetic excitations in the same way that light is controlled in an optical fiber with a varying refraction index. The theoretical approach is based on the dynamic matrix method, where the magnetic nanostrip is divided into small sub-strips. The dipolar and exchange interactions between sub-strips have been considered to reproduce the spin-wave dynamics of the magnonic fiber. The transition from one strip to an infinite thin film is presented for the Damon-Eshbach geometry, where the nature of the spin-wave modes is discussed. An in-depth analysis of the spin-wave transport as a function of the saturation magnetization profile is provided. It is predicted that it is feasible to induce a remarkable channeling of the spin waves along the zones with a reduced saturation magnetization, even when such a reduction is tiny. The results are compared with micromagnetic simulations, where a good agreement is observed between both methods. The findings have relevance for envisioned future spin-wave-based magnonic devices operating at the nanometer scale.

Emission and propagation of 1D and 2D spin waves with nanoscale wavelengths in anisotropic spin textures.

Spin waves offer intriguing perspectives for computing and signal processing, because their damping can be lower than the ohmic losses in conventional complementary metal-oxide-semiconductor (CMOS) circuits. Magnetic domain walls show considerable potential as magnonic waveguides for on-chip control of the spatial extent and propagation of spin waves. However, low-loss guidance of spin waves with nanoscale wavelengths and around angled tracks remains to be shown. Here, we demonstrate spin wave control using natural anisotropic features of magnetic order in an interlayer exchange-coupled ferromagnetic bilayer. We employ scanning transmission X-ray microscopy to image the generation of spin waves and their propagation across distances exceeding multiples of the wavelength. Spin waves propagate in extended planar geometries as well as along straight or curved one-dimensional domain walls. We observe wavelengths between 1 µm and 150 nm, with excitation frequencies ranging from 250 MHz to 3 GHz. Our results show routes towards the practical implementation of magnonic waveguides in the form of domain walls in future spin wave logic and computational circuits.