Spin wavepackets in the Kagome ferromagnet Fe3Sn2: Propagation and precursors.

The propagation of spin waves in magnetically ordered systems has emerged as a potential means to shuttle quantum information over large distances. Conventionally, the arrival time of a spin wavepacket at a distance, d, is assumed to be determined by its group velocity, vg. Here, we report time-resolved optical measurements of wavepacket propagation in the Kagome ferromagnet Fe3Sn2 that demonstrate the arrival of spin information at times significantly less than d/vg. We show that this spin wave "precursor" originates from the interaction of light with the unusual spectrum of magnetostatic modes in Fe3Sn2. Related effects may have far-reaching consequences toward realizing long-range, ultrafast spin wave transport in both ferromagnetic and antiferromagnetic systems.

Asymmetric Magnon Frequency Comb.

We theoretically show the asymmetric spin wave transmission in a coupled waveguide-skyrmion structure, where the skyrmion acts as an effective nanocavity allowing the whispering gallery modes for magnons. The asymmetry originates from the chiral spin wave mode localized in the circular skyrmion wall. By inputting two-tone excitations and mixing them in the skyrmion wall, we observe a unidirectional output magnon frequency comb propagating in the waveguide with a record number of teeth (>50). This coupled waveguide-cavity structure turns out to be a universal paradigm for generating asymmetric magnon frequency combs, where the cavity can be generalized to other magnetic structures that support the whispering gallery mode of magnons. Our results advance the understanding of the nonlinear interaction between magnons and magnetic textures and open a new pathway to exploring the asymmetric spin wave transmission and to steering the magnon frequency comb.

Zero-Field Spin Waves in YIG Nanowaveguides.

Spin-wave-based transmission and processing of information is a promising emerging nanotechnology that can help overcome limitations of traditional electronics based on the transfer of electrical charge. Among the most important challenges for this technology is the implementation of spin-wave devices that can operate without the need for an external bias magnetic field. Here we experimentally demonstrate that this can be achieved using submicrometer wide spin-wave waveguides fabricated from ultrathin films of a low-loss magnetic insulator, yttrium iron garnet (YIG). We show that these waveguides exhibit a highly stable single-domain static magnetic configuration at zero field and support long-range propagation of spin waves with gigahertz frequencies. The experimental results are supported by micromagnetic simulations, which additionally provide information for the optimization of zero-field guiding structures. Our findings create the basis for the development of energy-efficient zero-field spin-wave devices and circuits.

Magnon-Optic Effects with Spin-Wave Leaky Modes: Tunable Goos-Hänchen Shift and Wood's Anomaly.

We demonstrate numerically how a spin wave (SW) beam obliquely incident on the edge of a thin film placed below a ferromagnetic stripe can excite leaky SWs guided along the stripe. During propagation, leaky waves emit energy back into the layer in the form of plane waves and several laterally shifted parallel SW beams. This resonance excitation, combined with interference effects of the reflected and re-emitted waves, results in the magnonic Wood's anomaly and a significant increase of the Goos-Hänchen shift magnitude. This yields a unique platform to control SW reflection and transdimensional magnonic router that can transfer SWs from a 2D platform into a 1D guided mode.

Magnon Confinement in an All-on-Chip YIG Cavity Resonator Using Hybrid YIG/Py Magnon Barriers.

Confining magnons in cavities can introduce new functionalities to magnonic devices, enabling future magnonic structures to emulate the established photonic and electronic components. As a proof-of-concept, we report magnon confinement in a lithographically defined all-on-chip YIG cavity created between two YIG/Permalloy bilayers. We take advantage of the modified magnetic properties of the covered/uncovered YIG film to define on-chip distinct regions with boundaries capable of confining magnons. We confirm this by measuring multiple spin-pumping voltage peaks in a 400 nm wide platinum strip placed along the center of the cavity. These peaks coincide with multiple spin-wave resonance modes calculated for a YIG slab with the corresponding geometry. The fabrication of micrometer-sized YIG cavities following this technique represents a new approach to control coherent magnons, while the spin-pumping voltage in a nanometer-sized Pt strip demonstrates to be a noninvasive local detector of the magnon resonance intensity.

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.

Wilberforce-like Larmor Magnetic Moment and Spin Precession.

In a Wilberforce pendulum, two mechanical oscillators are coupled: one pertains to the longitudinal (tension) motion and the other to the rotational (twisting) motion. It is shown that the longitudinal magnetic moment of circular currents, and similarly the magnetic moment of a spin-chain, can exhibit a Wilberforce-like vibration. The longitudinal oscillation is related to the Langevin diamagnetism, while the twisting motion is superimposed on the magnetic moment and spin precession. The calculations show that the coupling term is nonlinear in this (longitudinal) vibrating and (magnetic moment) precession system. By increasing the strength of the coupling we arrive at a spectrum, where further vibrational modes can be associated with the rotation of the precession. This means that the extent of the change in coherence can be demonstrated. Since the coupling strength can be different due to local effects, this can be an important factor from the point of view of signal propagation and in preserving signal shapes. The amount specifying the dissipation is introduced to express the degree of deviation. A relationship exists between the parameter characteristic of the coupling strength and how its quantity influences decoherence and dissipation.

Reconfigurable Spin-Wave Interferometer at the Nanoscale.

Spin waves can transfer information free of electron transport and are promising for wave-based computing technologies with low-power consumption as a solution to severe energy losses in modern electronics. Logic circuits based on the spin-wave interference have been proposed for more than a decade, while it has yet been realized at the nanoscale. Here, we demonstrate the interference of spin waves with wavelengths down to 50 nm in a low-damping magnetic insulator. The constructive and destructive interference of spin waves is detected in the frequency domain using propagating spin-wave spectroscopy, which is further confirmed by the Brillouin light scattering. The interference pattern is found to be highly sensitive to the distance between two magnetic nanowires acting as spin-wave emitters. By controlling the magnetic configurations, one can switch the spin-wave interferometer on and off. Our demonstrations are thus key to the realization of spin-wave computing system based on nonvolatile nanomagnets.

Spin-Wave Emission from Vortex Cores under Static Magnetic Bias Fields.

We studied the influence of a static in-plane magnetic field on the alternating-field-driven emission of nanoscale spin waves from magnetic vortex cores. Time-resolved scanning transmission X-ray microscopy was used to image spin waves in disk structures of synthetic ferrimagnets and single ferromagnetic layers. For both systems, it was found that an increasing magnetic bias field continuously displaces the wave-emitting vortex core from the center of the disk toward its edge without noticeably altering the spin-wave dispersion relation. In the case of the single-layer disk, an anisotropic lateral expansion of the core occurs at higher magnetic fields, which leads to a directional rather than radial-isotropic emission and propagation of waves. Micromagnetic simulations confirm these findings and further show that focusing effects occur in such systems, depending on the shape of the core and controlled by the static magnetic bias field.

Directional Excitation of a High-Density Magnon Gas Using Coherently Driven Spin Waves.

Controlling magnon densities in magnetic materials enables driving spin transport in magnonic devices. We demonstrate the creation of large, out-of-equilibrium magnon densities in a thin-film magnetic insulator via microwave excitation of coherent spin waves and subsequent multimagnon scattering. We image both the coherent spin waves and the resulting incoherent magnon gas using scanning-probe magnetometry based on electron spins in diamond. We find that the gas extends unidirectionally over hundreds of micrometers from the excitation stripline. Surprisingly, the gas density far exceeds that expected for a boson system following a Bose-Einstein distribution with a maximum value of the chemical potential. We characterize the momentum distribution of the gas by measuring the nanoscale spatial decay of the magnetic stray fields. Our results show that driving coherent spin waves leads to a strong out-of-equilibrium occupation of the spin-wave band, opening new possibilities for controlling spin transport and magnetic dynamics in target directions.

The Interaction between Surface Acoustic Waves and Spin Waves: The Role of Anisotropy and Spatial Profiles of the Modes.

The interaction between different types of wave excitation in hybrid systems is usually anisotropic. Magnetoelastic coupling between surface acoustic waves and spin waves strongly depends on the direction of the external magnetic field. However, in the present study we observe that even if the orientation of the field is supportive for the coupling, the magnetoelastic interaction can be significantly reduced for surface acoustic waves with a particular profile in the direction normal to the surface at distances much smaller than the wavelength. We use Brillouin light scattering for the investigation of thermally excited phonons and magnons in a magnetostrictive CoFeB/Au multilayer deposited on a Si substrate. The experimental data are interpreted on the basis of a linearized model of interaction between surface acoustic waves and spin waves.

Observation of Coherent Spin Waves in a Three-Dimensional Artificial Spin Ice Structure.

Harnessing high-frequency spin dynamics in three-dimensional (3D) nanostructures may lead to paradigm-shifting, next-generation devices including high density spintronics and neuromorphic systems. Despite remarkable progress in fabrication, the measurement and interpretation of spin dynamics in complex 3D structures remain exceptionally challenging. Here, we take a first step and measure coherent spin waves within a 3D artificial spin ice (ASI) structure using Brillouin light scattering. The 3D-ASI was fabricated by using a combination of two-photon lithography and thermal evaporation. Two spin-wave modes were observed in the experiment whose frequencies showed nearly monotonic variation with the applied field strength. Numerical simulations qualitatively reproduced the observed modes. The simulated mode profiles revealed the collective nature of the modes extending throughout the complex network of nanowires while showing spatial quantization with varying mode quantization numbers. The study shows a well-defined means to explore high-frequency spin dynamics in complex 3D spintronic and magnonic structures.

Applications of nanomagnets as dynamical systems: II.

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

Propagation of Spin-Wave Packets in Individual Nanosized Yttrium Iron Garnet Magnonic Conduits.

Modern-day CMOS-based computation technology is reaching its fundamental limitations. The emerging field of magnonics, which utilizes spin waves for data transport and processing, proposes a promising path to overcome these limitations. Different devices have been demonstrated recently on the macro- and microscale, but the feasibility of the magnonics approach essentially relies on the scalability of the structure feature size down to the extent of a few 10 nm, which are typical sizes for the established CMOS technology. Here, we present a study of propagating spin-wave packets in individual yttrium iron garnet (YIG) conduits with lateral dimensions down to 50 nm. Space and time-resolved microfocused Brillouin-light-scattering (BLS) spectroscopy is used to characterize the YIG nanostructures and measure the spin-wave decay length and group velocity directly. The revealed magnon transport at the scale comparable to the scale of CMOS proves the general feasibility of magnon-based data processing.

Nanoscale Detection of Magnon Excitations with Variable Wavevectors Through a Quantum Spin Sensor.

We report the optical detection of magnons with a broad range of wavevectors in magnetic insulator Y3Fe5O12 thin films by proximate nitrogen-vacancy (NV) single-spin sensors. Through multimagnon scattering processes, the excited magnons generate fluctuating magnetic fields at the NV electron spin resonance frequencies, which accelerate the relaxation of NV spins. By measuring the variation of the emitted spin-dependent photoluminescence of the NV centers, magnons with variable wavevectors up to ∼5 × 107 m-1 can be optically accessed, providing an alternative perspective to reveal the underlying spin behaviors in magnetic systems. Our results highlight the significant opportunities offered by NV single-spin quantum sensors in exploring nanoscale spin dynamics of emergent spintronic materials.

All-Dielectric Nanophotonics Enables Tunable Excitation of the Exchange Spin Waves.

Launching and controlling magnons with laser pulses opens up new routes for applications including optomagnetic switching and all-optical spin wave emission and enables new approaches for information processing with ultralow energy dissipation. However, subwavelength light localization within the magnetic structures leading to efficient magnon excitation that does not inherently absorb light has still been missing. Here, we propose to marriage the laser-induced ultrafast magnetism and nanophotonics to efficiently excite and control spin dynamics in magnetic dielectric structures. We demonstrate that nanopatterning by a 1D grating of trenches allows localization of light in spots with sizes of tens of nanometers and thus launch the exchange standing spin waves of different orders. The relative amplitude of the exchange and magnetostatic spin waves can be adjusted on demand by modifying laser pulse polarization, incidence angle, and wavelength. Nanostructuring of the magnetic media provides a unique possibility for the selective spin manipulation, a key issue for further progress of magnonics, spintronics, and quantum technologies.

Nanoimaging of Ultrashort Magnon Emission by Ferromagnetic Grating Couplers at GHz Frequencies.

On-chip signal processing at microwave frequencies is key for modern mobile communication. When one aims at small footprints, low power consumption, reprogrammable filters, and delay lines, magnons in low-damping ferrimagnets offer great promise. Ferromagnetic grating couplers have been reported to be specifically useful as microwave-to-magnon transducers. However, their interconversion efficiency is unknown and real-space measurements of the emitted magnon wavelengths have not yet been accomplished. Here, we image with subwavelength spatial resolution the magnon emission process into ferrimagnetic yttrium iron garnet (YIG) at frequencies up to 8 GHz. We evidence propagating magnons of a wavelength of 98.7 nm underneath the gratings, which enter the YIG without a phase jump. Counterintuitively, the magnons exhibit an even increased amplitude in YIG, which is unexpected and due to a further wavelength conversion process. Our results are of key importance for magnonic components, which efficiently control microwave signals on the nanoscale.

Spin Wave Radiation by a Topological Charge Dipole.

The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a significant challenge. Here, we propose that skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.

Spin Wave Injection and Propagation in a Magnetic Nanochannel from a Vortex Core.

Spin waves can be used as information carriers with low energy dissipation. The excitation and propagation of spin waves along reconfigurable magnonic circuits is the subject of much interest in the field of magnonic applications. Here we experimentally demonstrate an effective excitation of spin waves in reconfigurable magnetic textures at frequencies as high as 15 GHz and wavelengths as short as 80 nm from Ni80Fe20 (Py) nanodisk-film hybrid structures. Most importantly, we demonstrate these spin wave modes, which were previously confined within a nanodisk, can now couple to and propagate along a nanochannel formed by magnetic domain walls at zero magnetic bias field. The tunable high-frequency, short-wavelength, and propagating spin waves may play a vital role in energy efficient and programmable magnonic devices at the nanoscale.