Nanoscale magnonic Fabry-Pérot resonator for low-loss spin-wave manipulation

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.

Reversing the magnetization of 50-nm-wide ferromagnets by ultrashort magnons in thin-film yttrium iron garnet

Spin waves (magnons) can enable neuromorphic computing by which one aims at overcoming limitations inherent to conventional electronics and the von Neumann architecture. Encoding magnon signal by reversing magnetization of a nanomagnetic memory bit is pivotal to realize such novel computing schemes efficiently. A magnonic neural network was recently proposed consisting of differently configured nanomagnets that control nonlinear magnon interference in an underlying yttrium iron garnet (YIG) film [Papp et al., Nat. Commun., 2021, 12, 6422]. In this study, we explore the nonvolatile encoding of magnon signals by switching the magnetization of periodic and aperiodic arrays (gratings) of Ni81Fe19 (Py) nanostripes with widths w between 50 nm and 200 nm. Integrating 50-nm-wide nanostripes with a coplanar waveguide, we excited magnons having a wavelength λ of ≈100 nm. At a small spin-precessional power of 11 nW, these ultrashort magnons switch the magnetization of 50-nm-wide Py nanostripes after they have propagated over 25 μm in YIG in an applied field. We also demonstrate the magnetization reversal of nanostripes patterned in an aperiodic sequence. We thereby show that the magnon-induced reversal happens regardless of the width and periodicity of the nanostripe gratings. Our study enlarges substantially the parameter regime for magnon-induced nanomagnet reversal on YIG and is important for realizing in-memory computing paradigms making use of magnons with ultrashort wavelengths at low power consumption.

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.

True amplification of spin waves in magnonic nano-waveguides

Magnonic nano-devices exploit magnons - quanta of spin waves - to transmit and process information within a single integrated platform that has the potential to outperform traditional semiconductor-based electronics. The main missing cornerstone of this information nanotechnology is an efficient scheme for the amplification of propagating spin waves. The recent discovery of spin-orbit torque provided an elegant mechanism for propagation losses compensation. While partial compensation of the spin-wave losses has been achieved, true amplification - the exponential increase in the spin-wave intensity during propagation - has so far remained elusive. Here we evidence the operating conditions to achieve unambiguous amplification using clocked nanoseconds-long spin-orbit torque pulses in magnonic nano-waveguides, where the effective magnetization has been engineered to be close to zero to suppress the detrimental magnon scattering. We achieve an exponential increase in the intensity of propagating spin waves up to 500% at a propagation distance of several micrometers.

Probing spin waves in Co3O4 nanoparticles for magnonics applications

The magnetic properties of spinel nanoparticles can be controlled by synthesizing particles of a specific shape and size. The synthesized nanorods, nanodots and cubic nanoparticles have different crystal planes selectively exposed on the surface. The surface effects on the static magnetic properties are well documented, while their influence on spin waves dispersion is still being debated. Our ability to manipulate spin waves using surface and defect engineering in magnetic nanoparticles is the key to designing magnonic devices. We synthesized cubic and spherical nanoparticles of a classical antiferromagnetic material Co3O4 to study the shape and size effects on their static and dynamic magnetic proprieties. Using a combination of experimental methods, we probed the magnetic and crystal structures of our samples and directly measured spin wave dispersions using inelastic neutron scattering. We found a weak, but unquestionable, increase in exchange interactions for the cubic nanoparticles as compared to spherical nanoparticle and bulk powder reference samples. Interestingly, the exchange interactions in spherical nanoparticles have bulk-like properties, despite a ferromagnetic contribution from canted surface spins.

Designing a Periodic Structure with a Composition Gradient Stack Unit to Realize a Good Comprehensive Dielectric Property of Yttrium Iron Garnet Multilayer Film

Y3Fe5O12 (YIG) thin films are highly needed in microwave devices, but the low saturation magnetization and low dielectric constant greatly limit the application of YIG thin films. It was reported that the ion substitution, for example, Pr3+, could increase the dielectric constant of Y3-xPrxFe5O12 (YPrxIG). Unfortunately, the dielectric loss would also be significantly increased. In this work, [YPr0.20IG/YPr0.15IG/YPr0.10IG]N multilayer films were fabricated via the chemical solution deposition method, by designing a periodic structure with the [YPr0.20IG/YPr0.15IG/YPr0.10IG] composition gradient stack. In comparison to the average composition of YPr0.15IG, high saturation magnetization, high dielectric constant, and low loss were successfully simultaneously achieved in the multilayer structure. The N = 6 film exhibited a higher saturation magnetization of 252.8 emu/cm3 than the value (213.1) of the YPr0.15IG (average composition) film. The dielectric constant of the N = 6 film reached 25.6 in contrast to the value of 18.3 for the YPr0.15IG film at 12.4 GHz, which was the contribution of the rapid flip of the electric dipole of a single-unit dielectric material and the accumulation of interface charge. Furthermore, the dielectric loss of the film with N = 6 decreased to 0.0036 compared with the value (0.0102) of the average composition film. This work demonstrated a strategy of designing a periodic structure with a composition gradient stack unit to realize a good comprehensive dielectric property through taking advantage of the multiple effects of "coherent growth, component matching, and interface accumulation".

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.

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.

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.

Spin-Wave Optics in YIG Realized by Ion-Beam Irradiation

Direct focused-ion-beam writing is presented as an enabling technology for realizing functional spin-wave devices of high complexity, and demonstrate its potential by optically-inspired designs. It is shown that ion-beam irradiation changes the characteristics of yttrium iron garnet films on a submicron scale in a highly controlled way, allowing one to engineer the magnonic index of refraction adapted to desired applications. This technique does not physically remove material, and allows rapid fabrication of high-quality architectures of modified magnetization in magnonic media with minimal edge damage (compared to more common removal techniques such as etching or milling). By experimentally showing magnonic versions of a number of optical devices (lenses, gratings, Fourier-domain processors) this technology is envisioned as the gateway to building magnonic computing devices that rival their optical counterparts in their complexity and computational power.

Reversal of nanomagnets by propagating magnons in ferrimagnetic yttrium iron garnet enabling nonvolatile magnon memory

Despite the unprecedented downscaling of CMOS integrated circuits, memory-intensive machine learning and artificial intelligence applications are limited by data conversion between memory and processor. There is a challenging quest for novel approaches to overcome this so-called von Neumann bottleneck. Magnons are the quanta of spin waves. Their angular momentum enables power-efficient computation without charge flow. The conversion problem would be solved if spin wave amplitudes could be stored directly in a magnetic memory. Here, we report the reversal of ferromagnetic nanostripes by spin waves which propagate in an underlying spin-wave bus. Thereby, the charge-free angular momentum flow is stored after transmission over a macroscopic distance. We show that the spin waves can reverse large arrays of ferromagnetic stripes at a strikingly small power level. Combined with the already existing wave logic, our discovery is path-breaking for the new era of magnonics-based in-memory computation and beyond von Neumann computer architectures.

Imaging and phase-locking of non-linear spin waves

Non-linear processes are a key feature in the emerging field of spin-wave based information processing and allow to convert uniform spin-wave excitations into propagating modes at different frequencies. Recently, the existence of non-linear magnons at half-integer multiples of the driving frequency has been predicted for Ni80Fe20 at low bias fields. However, it is an open question under which conditions such non-linear spin waves emerge coherently and how they may be used in device structures. Usually non-linear processes are explored in the small modulation regime and result in the well known three and four magnon scattering processes. Here we demonstrate and image a class of spin waves oscillating at half-integer harmonics that have only recently been proposed for the strong modulation regime. The direct imaging of these parametrically generated magnons in Ni80Fe20 elements allows to visualize their wave vectors. In addition, we demonstrate the presence of two degenerate phase states that may be selected by external phase-locking. These results open new possibilities for applications such as spin-wave sources, amplifiers and phase-encoded information processing with magnons.

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.

Sensitivity enhancement in magnetic sensor using CoFeB/Y3Fe5O12 resonator

Magnonics, an emerging research field that uses the quanta of spin waves as data carriers, has a potential to dominate the post-CMOS era owing to its intrinsic property of ultra-low power operation. Spin waves can be manipulated by a wide range of parameters; thus, they are suitable for sensing applications in a wide range of physical fields. In this study, we designed a highly sensitive, simple structure, and ultra-low power magnetic sensor using a simple CoFeB/Y₃Fe₅O₁₂ bilayer structure. We demonstrated that the CoFeB/Y₃Fe₅O₁₂ bilayer structure can create a sharp rejection band in its spin-wave transmission spectra. The lowest point of this strong rejection band allows the detection of a small frequency shift owing to the external magnetic field variation. Experimental observations revealed that such a bilayer magnetic sensor exhibits 20 MHz frequency shifts upon the application of an external magnetic field of 0.5 mT. Considering the lowest full width half maximum, which is about 2 MHz, a sensitivity of 10^–2 mT order can be experimentally achieved. Furthermore, the higher sensitivity in the order of 10^–6 T (µT) has been demonstrated using the sharp edge of the rejection band of the CoFeB/Y₃Fe₅O₁₂ bilayer device. A Y-shaped spin waves interference device with two input arms consisting of CoFeB/Y₃Fe₅O₁₂ and Y₃Fe₅O₁₂ has been theoretically investigated. We proposed that such a structure can demonstrate a magnetic sensitivity in the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-9}$$\end{document}10-9 T (nT) at room temperature. The sensitivity of the sensor can be further enhanced by tuning the width of the CoFeB metal stripe.

Tuning of Magnetic Damping in Y3Fe5O12/Metal Bilayers for Spin-Wave Conduit Termination

In this work, we investigate the structural and dynamic magnetic properties of yttrium iron garnet (YIG) films grown onto gadolinium gallium garnet (GGG) substrates with thin platinum, iridium, and gold spacer layers. Separation of the YIG film from the GGG substrate by a metal film strongly affects the crystalline structure of YIG and its magnetic damping. Despite the presence of structural defects, however, the YIG films exhibit a clear ferromagnetic resonance response. The ability to tune the magnetic damping without substantial changes to magnetization offers attractive prospects for the design of complex spin-wave conduits. We show that the insertion of a 1-nm-thick metal layer between YIG and GGG already increases the effective damping parameter enough to efficiently absorb spin waves. This bilayer structure can therefore be utilized for magnonic waveguide termination. Investigating the dispersionless propagation of spin-wave packets, we demonstrate that a damping unit consisting of the YIG/metal bilayers can dissipate incident spin-wave signals with reflection coefficient R < 0.1 at a distance comparable to the spatial width of the wave packet.

Frequency multiplication by collective nanoscale spin-wave dynamics

Frequency multiplication is a process in modern electronics in which harmonics of the input frequency are generated in nonlinear electronic circuits. Devices based on the propagation and interaction of spin waves are a promising alternative to conventional electronics. The characteristic frequency of these excitations is in the gigahertz (GHz) range and devices are not readily interfaced with conventional electronics. Here, we locally probe the magnetic excitations in a soft magnetic material by optical methods and show that megahertz-range excitation frequencies cause switching effects on the micrometer scale, leading to phase-locked spin-wave emission in the GHz range. Indeed, the frequency multiplication process inside the magnetic medium covers six octaves and opens exciting perspectives for spintronic applications, such as all-magnetic mixers or on-chip GHz sources.

Minimum Entropy Production Effect on a Quantum Scale

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

Spin wave localization and guiding by magnon band structure engineering in yttrium iron garnet

In spintronics the propagation of spin-wave excitations in magnetically ordered materials can also be used to transport and process information. One of the most popular materials in this regard is the ferrimagnetic insulator yttrium-iron-garnet due its exceptionally small spin-wave damping parameter. While the small relaxation rate allows for large propagation length of magnetic excitations, it also leads to non-locality of the magnetic properties. By imaging spin waves their band structure is mapped. In doing so wave vector selection is shown to suppress dispersion effects to a large extent allowing for local measurements of spin relaxation. Moreover we demonstrate even higher control of magnon propagation by employing the wave vector selectivity near an avoided crossing of different spin-wave modes where the group velocity approaches zero. Here local engineering of the dispersion allows constructing magnonic waveguides and at the same time reveals the local relaxation properties.