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

High data rate spin-wave transmitter

Spin-wave devices have recently become a strong competitor in computing and information processing owing to their excellent energy efficiency. Researchers have explored magnons, the quanta of spin-waves, as an information carrier and significant progress has occurred in both excitation and computation. However, most transmission designs remain immature in terms of data rate and information complexity as they only utilize simple spin-wave pulses and suffer from signal distortion. In this work, using micromagnetic simulations, we demonstrate a spin-wave transmitter that operates reliably at a data rate of 4 Gbps over significant (multi-micron) distances with error rates as low as 10-14. Spin-wave amplitude is used to encode information. Carrier frequency and data rate are carefully chosen to restrict dispersion spreading, which is the main reason for signal distortion. We show that this device can be integrated into either pure-magnonic circuits or modern electronic networks. Our study reveals the potential for achieving an even higher data rate of 10 Gbps and also offers a comprehensive and logical methodology for performance tuning.

Magnetic anisotropy and phononic properties of two-dimensional ferromagnetic Fe3GeS2 monolayer

In 2023, Fe3GeS2 monolayer with Curie temperature of 630 K is predicted, which is promising to be used in next-generation spintronic devices. However, its magnetic anisotropy and phononic properties are still unclear. In this paper, we implemented the first-principles calculations on Fe3GeS2 monolayer, and found its ferromagnetic ground state with robustness to the -1.5%-1.3% biaxial strain. Meanwhile, the out-of-plane magnetic anisotropy dominated by dipolar interaction is found in Fe3GeS2 monolayer. Finally, we studied the phononic properties to identify the dynamical stability of Fe3GeS2 monolayer and highlight the contribution from the anharmonic interaction of optical phonons to the thermal expansion coefficient. We also find two single-phonon modes can be used to design quantum mechanical resonators with a wide cool-temperature range. These results can provide a comprehensive understanding of the magnetism and phonon properties of two-dimensional (2D) Fe3GeS2, beneficial for the application of 2D Fe3GeS2 in spintronics.

All-magnonic repeater based on bistability

Bistability, a universal phenomenon found in diverse fields such as biology, chemistry, and physics, describes a scenario in which a system has two stable equilibrium states and resets to one of the two states. The ability to switch between these two states is the basis for a wide range of applications, particularly in memory and logic operations. Here, we present a universal approach to achieve bistable switching in magnonics, the field processing data using spin waves. A pronounced bistable window is observed in a 1 μm wide magnonic conduit under an external rf drive. The system is characterized by two magnonic stable states defined as low and high spin-wave amplitude states. The switching between these two states is realized by another propagating spin wave sent into the rf driven region. This magnonic bistable switching is used to design a magnonic repeater, which receives the original decayed and distorted spin wave and regenerates a new spin wave with amplified amplitude and normalized phase. Our magnonic repeater can be installed at the inputs of each magnonic logic gate to overcome the spin-wave amplitude degradation and phase distortion during previous propagation and achieve integrated magnonic circuits or magnonic neuromorphic networks.

Stimulated Amplification of Propagating Spin Waves

Spin-wave amplification techniques are key to the realization of magnon-based computing concepts. We introduce a novel mechanism to amplify spin waves in magnonic nanostructures. Using the technique of rapid cooling, we create a nonequilibrium state in excess of high-energy magnons and demonstrate the stimulated amplification of an externally seeded, propagating spin wave. Using an extended kinetic model, we qualitatively show that the amplification is mediated by an effective energy flux of high energy magnons into the low energy propagating mode, driven by a nonequilibrium magnon distribution.

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-phonon coupling: from fundamental physics to applications

In recent decades, there are immense applications for bulk and few-layer magnetic insulators in biomedicine, data storage, and signal transfer. In these applications, the interaction between spin and lattice vibration has significant impacts on the device performance. In this article, we systematically review the fundamental physical aspects of magnon-phonon coupling in magnetic insulators. We first introduce the fundamental physics of magnons and magnon-phonon coupling in magnetic insulators and then discuss the influence of magnon-phonon coupling on the properties of magnons and phonons. Finally, a summary is presented, and we also discuss the possible open problems in this field. This article presents the advanced understanding of magnon-phonon coupling in magnetic insulators, which provides new opportunities for improving various possible applications.

Deeply nonlinear excitation of self-normalized short spin waves

Spin waves are ideal candidates for wave-based computing, but the construction of magnetic circuits is blocked by a lack of an efficient mechanism to excite long-running exchange spin waves with normalized amplitudes. Here, we solve the challenge by exploiting a deeply nonlinear phenomenon for forward volume spin waves in 200-nm-wide nanoscale waveguides and validate our concept using microfocused Brillouin light scattering spectroscopy. An unprecedented nonlinear frequency shift of more than 2 GHz is achieved, corresponding to a magnetization precession angle of 55° and enabling the excitation of spin waves with wavelengths down to 200 nm. The amplitude of the excited spin waves is constant and independent of the input microwave power due to the self-locking nonlinear shift, enabling robust adjustment of the spin-wave amplitudes in future on-chip magnonic integrated circuits.

3D Magnonic Conduits by Direct Write Nanofabrication

Magnonics is a rapidly developing domain of nanomagnetism, with application potential in information processing systems. Realisation of this potential and miniaturisation of magnonic circuits requires their extension into the third dimension. However, so far, magnonic conduits are largely limited to thin films and 2D structures. Here, we introduce 3D magnonic nanoconduits fabricated by the direct write technique of focused-electron-beam induced deposition (FEBID). We use Brillouin light scattering (BLS) spectroscopy to demonstrate significant qualitative differences in spatially resolved spin-wave resonances of 2D and 3D nanostructures, which originates from the geometrically induced non-uniformity of the internal magnetic field. This work demonstrates the capability of FEBID as an additive manufacturing technique to produce magnetic 3D nanoarchitectures and presents the first report of BLS spectroscopy characterisation of FEBID conduits.

Enhancing the Curie Temperature in Cr2Ge2Te6 via Charge Doping: A First-Principles Study

In this work, we explore the impacts of charge doping on the magnetism of a Cr₂Ge₂Te₆ monolayer using first-principles calculations. Our results reveal that doping with 0.3 electrons per unit cell can enhance the ferromagnetic exchange constant in a Cr₂Ge₂Te₆ monolayer from 6.874 meV to 10.202 meV, which is accompanied by an increase in the Curie temperature from ~85 K to ~123 K. The enhanced ratio of the Curie temperature is up to 44.96%, even higher than that caused by surface functionalization on monolayer Cr₂Ge₂Te₆, manifesting the effectiveness of charge doping by improving the magnetic stability of 2D magnets. This remarkable enhancement in the ferromagnetic exchange constant and Curie temperature can be attributed to the increase in the magnetic moment on the Te atom, enlarged Cr-Te-Cr bond angle, reduced Cr-Te distance, and the significant increase in super-exchange coupling between Cr and Te atoms. These results demonstrate that charge doping is a promising route to improve the magnetic stability of 2D magnets, which is beneficial to overcome the obstacles in the application of 2D magnets in spintronics.

Tailoring crosstalk between localized 1D spin-wave nanochannels using focused ion beams

1D spin-wave conduits are envisioned as nanoscale components of magnonics-based logic and computing schemes for future generation electronics. À-la-carte methods of versatile control of the local magnetization dynamics in such nanochannels are highly desired for efficient steering of the spin waves in magnonic devices. Here, we present a study of localized dynamical modes in 1-[Formula: see text]m-wide permalloy conduits probed by microresonator ferromagnetic resonance technique. We clearly observe the lowest-energy edge mode in the microstrip after its edges were finely trimmed by means of focused Ne[Formula: see text] ion irradiation. Furthermore, after milling the microstrip along its long axis by focused ion beams, creating consecutively [Formula: see text]50 and [Formula: see text]100 nm gaps, additional resonances emerge and are attributed to modes localized at the inner edges of the separated strips. To visualize the mode distribution, spatially resolved Brillouin light scattering microscopy was used showing an excellent agreement with the ferromagnetic resonance data and confirming the mode localization at the outer/inner edges of the strips depending on the magnitude of the applied magnetic field. Micromagnetic simulations confirm that the lowest-energy modes are localized within [Formula: see text]15-nm-wide regions at the edges of the strips and their frequencies can be tuned in a wide range (up to 5 GHz) by changing the magnetostatic coupling (i.e., spatial separation) between the microstrips.

Reconfigurable Magnonic Crystals Based on Imprinted Magnetization Textures in Hard and Soft Dipolar-Coupled Bilayers

Reconfigurable magnetization textures offer control of spin waves with promising properties for future low-power beyond-CMOS systems. However, materials with perpendicular magnetic anisotropy (PMA) suitable for stable magnetization-texture formation are characterized by high damping, which limits their applicability in magnonic devices. Here, we propose to overcome this limitation by using hybrid structures, i.e., a PMA layer magnetostatically coupled to a low-damping soft ferromagnetic film. We experimentally show that a periodic stripe-domain texture from a PMA layer is imprinted upon the soft layer and induces a nonreciprocal dispersion relation of the spin waves confined to the low-damping film. Moreover, an asymmetric bandgap features the spin-wave band diagram, which is a clear demonstration of collective spin-wave dynamics, a property characteristic for magnonic crystals with broken time-reversal symmetry. The composite character of the hybrid structure allows for stabilization of two magnetic states at remanence, with parallel and antiparallel orientation of net magnetization in hard and soft layers. The states can be switched using a low external magnetic field; therefore, the proposed system obtains an additional functionality of state reconfigurability. This study offers a link between reconfigurable magnetization textures and low-damping spin-wave dynamics, providing an opportunity to create miniaturized, programmable, and energy-efficient signal processing devices operating at high frequencies.

Low-Loss Nanoscopic Spin-Wave Guiding in Continuous Yttrium Iron Garnet Films

Long-distance transport and control of spin waves through nanochannels is essential for integrated magnonic technology. Current strategies relying on the patterning of single-layer nano-waveguides suffer from a decline of the spin-wave decay length upon downscaling or require large magnetic bias field. Here, we introduce a new waveguiding structure based on low-damping continuous yttrium iron garnet (YIG) films. Rather than patterning the YIG film, we define nanoscopic spin-wave transporting channels within YIG by dipolar coupling to ferromagnetic metal nanostripes. The hybrid material structure offers long-distance transport of spin waves with a decay length of ∼20 μm in 160 nm wide waveguides over a broad frequency range at small bias field. We further evidence that spin waves can be redirected easily by stray-field-induced bends in continuous YIG films. The combination of low-loss spin-wave guiding and straightforward nanofabrication highlights a new approach toward the implementation of magnonic integrated circuits for spin-wave computing.

Giant nonlinear self-phase modulation of large-amplitude spin waves in microscopic YIG waveguides

Nonlinear self-phase modulation is a universal phenomenon responsible, for example, for the formation of propagating dynamic solitons. It has been reported for waves of different physical nature. However its direct experimental observation for spin waves has been challenging. Here we show that exceptionally strong phase modulation can be achieved for spin waves in microscopic waveguides fabricated from nanometer-thick films of magnetic insulator, which support propagation of spin waves with large amplitudes corresponding to angles of magnetization precession exceeding 10°. At these amplitudes, the nonstationary nonlinear dynamic response of the spin system causes an extreme broadening of the spectrum of spin-wave pulses resulting in a strong spatial variation of the spin-wave wavelength and a temporal variation of the spin-wave phase across the pulse. Our findings demonstrate great complexity of nonlinear wave processes in microscopic magnetic structures and importance of their understanding for technical applications of spin waves in integrated devices.

Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y_{3}Fe_{5}O_{12} (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Probing Magnetic Defects in Ultra-Scaled Nanowires with Optically Detected Spin Resonance in Nitrogen-Vacancy Center in Diamond

Magnetic nanowires (NWs) are essential building blocks of spintronics devices as they offer tunable magnetic properties and anisotropy through their geometry. While the synthesis and compositional control of NWs have seen major improvements, considerable challenges remain for the characterization of local magnetic features at the nanoscale. Here, we demonstrate nonperturbative field distribution mapping in ultrascaled magnetic nanowires with diameters down to 6 nm by scanning nitrogen-vacancy magnetometry. This enables localized, minimally invasive magnetic imaging with sensitivity down to 3 μT Hz^-1/2. The imaging reveals the presence of weak magnetic inhomogeneities inside in-plane magnetized nanowires that are largely undetectable with standard metrology and can be related to local fluctuations of the NWs' saturation magnetization. In addition, the strong magnetic field confinement in the nanowires allows for the study of the interaction between the stray magnetic field and the nitrogen-vacancy sensor, thus clarifying the contrasting formation mechanisms for technologically relevant magnetic nanostructures.

Control of the Bose-Einstein Condensation of Magnons by the Spin Hall Effect

Previously, it has been shown that rapid cooling of yttrium-iron-garnet-platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of -8% and +6% was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

The 2021 Magnonics Roadmap

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

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.

Propagation of Spin Waves in a 2D Vortex Network

Efficient propagation of spin waves in a magnetically coupled vortex is crucial to the development of future magnonic devices. Thus far, only a double vortex can serve as spin-wave emitter or oscillator; the propagation of spin waves in the higher-order vortex is still lacking. Here, we experimentally realize a higher-order vortex (2D vortex network) by a designed nanostructure, containing four cross-type chiral substructures. We employ this vortex network as a waveguide to propagate short-wavelength spin waves (∼100 nm) and demonstrate the possibility of guiding spin waves from one vortex to the network. It is observed that the spin waves can propagate into the network through the nanochannels formed by the Bloch-Néel-type domain walls, with a propagation decay length of several micrometers. This technique paves the way for the development of low-energy, reprogrammable, and miniaturized magnonic devices.

Inverse-design magnonic devices

The field of magnonics offers a new type of low-power information processing, in which magnons, the quanta of spin waves, carry and process data instead of electrons. Many magnonic devices were demonstrated recently, but the development of each of them requires specialized investigations and, usually, one device design is suitable for one function only. Here, we introduce the method of inverse-design magnonics, in which any functionality can be specified first, and a feedback-based computational algorithm is used to obtain the device design. We validate this method using the means of micromagnetic simulations. Our proof-of-concept prototype is based on a rectangular ferromagnetic area that can be patterned using square-shaped voids. To demonstrate the universality of this approach, we explore linear, nonlinear and nonreciprocal magnonic functionalities and use the same algorithm to create a magnonic (de-)multiplexer, a nonlinear switch and a circulator. Thus, inverse-design magnonics can be used to develop highly efficient rf applications as well as Boolean and neuromorphic computing building blocks.

Dynamic control of spin-wave propagation

In this work we present a method to dynamically control the propagation of spin-wave packets. By altering an external magnetic field the refraction of the spin wave at a temporal inhomogeneity is enabled. Since the inhomogeneity is spatially invariant, the spin-wave impulse remains conserved while the frequency is shifted. We demonstrate the stopping and rebound of a traveling Backward-Volume type spin-wave packet.

Controlling the Nonlinear Relaxation of Quantized Propagating Magnons in Nanodevices

Relaxation of linear magnetization dynamics is well described by the viscous Gilbert damping processes. However, for strong excitations, nonlinear damping processes such as the decay via magnon-magnon interactions emerge and trigger additional relaxation channels. Here, we use space- and time-resolved microfocused Brillouin light scattering spectroscopy and micromagnetic simulations to investigate the nonlinear relaxation of strongly driven propagating spin waves in yttrium iron garnet nanoconduits. We show that the nonlinear magnon relaxation in this highly quantized system possesses intermodal features, i.e., magnons scatter to higher-order quantized modes through a cascade of scattering events. We further show how to control such intermodal dissipation processes by quantization of the magnon band in single-mode devices, where this phenomenon approaches its fundamental limit. Our study extends the knowledge about nonlinear propagating spin waves in nanostructures which is essential for the construction of advanced spin-wave elements as well as the realization of Bose-Einstein condensates in scaled systems.

Magnon-phonon interaction in antiferromagnetic two-dimensional MXenes

Antiferromagnetic material possesses excellent robustness to an external magnetic field perturbation, which makes it promising in application of spintronic devices. The magnon-phonon interaction plays a vital role in spintronic devices. In this work, we performed first-principles calculation to study the effect of magnon-phonon interaction on magnon spectra of the antiferromagnetic MXenes Cr₂TiC₂FCl, and calculated the phonon dominated magnon relaxation time based on the magnon spectra broadening. Due to the large exchange constants across Cr-Cr pairs, high magnon energy is found in Cr₂TiC₂FCl. We find that compared with the acoustic magnons, the optical magnons have stronger interaction with phonon modes. Moreover, relaxation time of optical magnons and acoustic magnons have quite different wavevector dependence. Our results about spin coupling to specific phonon polarizations can shed light on the understanding of magnon damping and energy dissipation in two-dimensional antiferromagnetic materials.

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.

Effects of molecular adsorption on the spin-wave spectrum and magnon relaxation in two-dimensional Cr2Ge2Te6

In this work, we performed detailed first-principles calculation and theoretical analysis to investigate the effect of molecular adsorption on the spin-wave spectrum and magnon relaxation in a Cr2Ge2Te6 (CGT) monolayer. It is found that NH3, NO, and NO2 adsorption can enhance the exchange constant of CGT, which can result in a blue-shift in the spin-wave spectrum. At 30 K, by means of a thorough investigation of many possible lattice configurations excited by thermal fluctuation, we identify the magnon scattering rate from the intrinsic lattice vibrational modes, and find that the relaxation of optical and acoustic magnons exhibits a completely different wave vector dependence. Moreover, although the adsorption of NO2 and NH3 molecules has a negligible influence on the magnon-phonon interaction, the adsorption of NO molecules results in a significant increase in magnon scattering strength. In the long-wavelength limit, the interlayer vibrational modes induced by NO adsorption increase the magnon-phonon scattering strength by ∼12.7%. The remarkable interlayer magnon-phonon interaction is ascribed to the strong CGT-NO coupling and large molecular vibration amplitude. Considering the importance of magnon relaxation time in the application of spin devices, we suggest that both the impacts on the exchange interaction and scattering rate must be considered when manipulating two-dimensional magnets by surface functionalization.