Spin-wave Devices Research Articles

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.

Acoustically driven ferromagnetic resonance in YIG thin films

Acoustically driven ferromagnetic resonance (ADFMR) is a platform that enables efficient generation and detection of spin waves via magnetoelastic coupling with surface acoustic waves (SAWs). While previous studies successfully achieved ADFMR in ferromagnetic metals, there are only few reports on ADFMR in magnetic insulators such as yttrium iron garnet (Y3Fe5O12, YIG) despite more favorable spin wave properties, including low damping and long coherence length. The growth of high-quality YIG films for ADFMR devices is a major challenge due to poor lattice-matching and thermal degradation of the piezoelectric substrates during film crystallization. In this work, we demonstrate ADFMR of YIG thin films on LiNbO3 (LNO) substrates. We employed a SiOx buffer layer and rapid thermal annealing for crystallization of YIG films with minimal thermal degradation of LNO substrates. Optimized ADFMR device designs and time-gating measurements were used to enhance the ADFMR signal and overcome the intrinsically low magnetoelastic coupling of YIG. YIG films have a polycrystalline structure with an in-plane easy direction due to biaxial stresses induced during cooling after crystallization. The YIG device shows clear ADFMR patterns with maximum absorption for H ≈ 160 mT parallel to SAW propagation, which is consistent with our simulation results based on existing theoretical models. These results expand possibilities for developing efficient spin wave devices with magnetic insulators.

High‐Speed and Long‐Distance Spin‐Wave Propagation in Spinel γ‐Fe2O3 Epitaxial Thin Films

AbstractIn spin wave (SW) devices, the modulation of SWs for computational units is necessary, imposing extremely high demands on material systems. In this study, high‐quality epitaxial‐grown spinel γ‐Fe2O3 thin films on conductive Nb‐doped SrTiO3 substrates, achieving fast‐speed, high‐frequency, and long‐distance SW propagation in this ferrimagnetic material, are developed. A novel two‐step film growth technique using pulsed laser deposition is proposed and optimized, and the damping constant, exchange stiffness, and anisotropies of γ‐Fe2O3 are determined. Compared to reported semiconductor magnetic materials, these epitaxial‐grown γ‐Fe2O3 thin films exhibit a significantly lower damping constant of 10−2, representing a substantial advancement. Using finite‐difference calculations, SW propagation is simulated, and vital information on transmission distance and dispersion curves is obtained. Experimental results show excellent agreement with these simulations. By applying a voltage to both sides of the conducting substrate, current across the film and SW device, resulting in the frequency shift of the SWs, is generated. These results demonstrate that high‐quality γ‐Fe2O3 films developed through the two‐step growth method can efficiently propagate SWs, offering possibilities for various modulation methods in SW‐based computing devices. This study positions spinel γ‐Fe2O3 as a promising ferrimagnetic candidate for future applications in efficient SW modulation within computational systems.

Dirac points and flat bands in two-dimensional magnonic crystals with honeycomb–kagome structure

Based on the model of magnonic crystals (MCs) with honeycomb structure, we propose another model of two-dimensional MCs with honeycomb–kagome structure that is a periodic magnetic composite system composed of Fe, Co, or Py ferromagnetic cylindrical scatterers arranged in the EuO matrix as the honeycomb–kagome structure. The band structures of magnons in these systems are studied numerically by using the plane-wave expansion method. The results show that the Dirac points of magnons will be generated at the Brillouin region points if the scatterers are close-packed, that is to say, the edges of cylindrical scatterers are in contact with each other. The frequency of Dirac points can be indirectly adjusted by changing the radius ratio of close-packed cylinders. In addition, in the case of a large difference in the radius between the close-packed cylindrical scatterers, there will be a magnonic flat band in the band structure, which is a phenomenon of so-called compact localized states different from the impurity state in the crystal, and it is formed by the highly interference superposition of spin waves in the honeycomb–kagome structure. The research on the generation and modulation of magnonic Dirac points and flat bands not only expands the research content of condensed matter topological physics but also provides a promising platform for the application of artificial MCs in the fabrication of spin-wave topological devices.

Numerical simulations of a magnonic reservoir computer

A numerical model for a spin wave delay-line active ring resonator is presented. Spin wave dynamics along a one-dimensional strip of magnetic material are modeled using the nonlinear Schrödinger equation. The equation is solved numerically in Fourier space using the fourth-order Runge–Kutta method and yields qualitative agreement with experimental measurements of spin wave dynamics in two different regimes. The model provides a useful tool for performing experiments based on neuromorphic computing and logic gates in traveling spin wave devices.

Left-handed polarized spin waves induced by spin polarized electric currents in ferromagnetic domain walls

Polarization refers to the orientation of the wave oscillation which is a fundamental property of wave. It has been used widely to encode information in photonics and phononics. In magnonics, spin wave also has been used for transmitting and processing information. However, exploiting the spin wave polarization to design devices has not been achieved yet in ferromagnets as only the right-handed polarized spin waves can be accommodated in ferromagnets. Our eariler study suggests that the left-handed polarized spin waves can be introduced into ferromagnets by appling a spin-polarized electric current, thus making it possible to design spin wave devices with polarization encoding. But the critical current needed to induce left-handed polarized spin wave in a uniformly magnetized ferromagnet is too high to be realized experimentally. Magnetic domain wall can serve as spin wave guide, and the cutoff frequency of spin wave in a domain wall approaches zero. In this work, the dispersion relationship and propagation characteristics of spin wave in a Bloch domain wall are studied based on the Landau-Lifshitz equation in the presence of a spin-polarized electrical current. It is found that the stable left-handed spin wave can be generated in the domain wall with only a small current density. Micromagnetic simulations confirm the theoretical analysis results. In addition, due to the different excitation efficiencies and spin transfer torque induced propagating nonreciprocity of left- and right-handed polarized spin wave, it is possible to excite selectively the left- and right-handed polarized spin wave, as well as nearly linearly polarized spin waves. This study provides a practical and feasible solution for designing spin wave devices based on the polarization coding technique.

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.

Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile, while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Coherent magnon-induced domain-wall motion in a magnetic insulator channel.

Advancing the development of spin-wave devices requires high-quality low-damping magnetic materials where magnon spin currents can efficiently propagate and effectively interact with local magnetic textures. Here we show that magnetic domain walls can modulate spin-wave transport in perpendicularly magnetized channels of Bi-doped yttrium iron garnet. Conversely, we demonstrate that the magnon spin current can drive domain-wall motion in the Bi-doped yttrium iron garnet channel device by means of magnon spin-transfer torque. The domain wall can be reliably moved over 15-20 µm distances at zero applied magnetic field by a magnon spin current excited by a radio-frequency pulse as short as 1 ns. The required energy for driving the domain-wall motion is orders of magnitude smaller than those reported for metallic systems. These results facilitate low-switching-energy magnonic devices and circuits where magnetic domains can be efficiently reconfigured by magnon spin currents flowing within magnetic channels.

Performance Enhancement of a Spin-Wave-Based Reservoir Computing System Utilizing Different Physical Conditions

We numerically study how to enhance reservoir computing performance by thoroughly extracting the spin-wave device potential for higher-dimensional information generation. The reservoir device has a 1-input exciter and 120-output detectors on the top of a continuous magnetic garnet film for spin-wave transmission. For various nonlinear and fading-memory dynamic phenomena distributing in the film space, small in-plane magnetic fields are used to prepare stripe domain structures and various damping constants at the film sides and bottom are explored. The ferromagnetic resonant frequency and relaxation time of spin precession clearly characterizes the change in spin dynamics with the magnetic field and damping constant. The common input signal for reservoir computing is a 1-GHz cosine wave with random 6-valued amplitude modulation. A basic 120-dimensional reservoir output vector is obtained from time-series signals at the 120-output detectors under each of three magnetic field conditions. Then, 240- and 360-dimensional reservoir output vectors are also constructed by concatenating two and three basic ones, respectively. In nonlinear autoregressive moving average (NARMA) prediction tasks, the computational performance is enhanced as the dimension of the reservoir output vector becomes higher and a significantly low prediction error is achieved for the tenth-order NARMA task using the 360-dimensional vector and optimum damping constant. The results are clear evidence that the collection of diverse output signals efficiently increases the dimensionality of the integrated reservoir state vector (i.e. reservoir-state richness) and thereby contributes to high computational performance. This paper demonstrates that performance enhancement through various configuration settings is a practical approach for on-chip reservoir computing devices with small numbers of real output nodes.

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.

Magnon flatband effect in antiferromagnetically coupled magnonic crystals

The dispersion relationships in antiferromagnetically coupled magnonic crystals (MCs) were investigated using micromagnetic simulations. In contrast to traditional MCs, antiferromagnetically coupled MCs have two oppositely polarized modes, enabling the realization of synthetic ferrimagnetic and synthetic antiferromagnetic MCs. The magnon flatband effect was discovered, and a large bandgap of the dispersion relation was also realized in this structure. We found that the center frequency and width of the dispersion bands with a specific polarization were influenced by the thickness and thickness ratio of the spin-up and spin-down magnetic sublattices. Based on these results, spin-wave filtering devices were proposed. Our study uncovered the magnon dispersion relations of a type of MC, which provides fresh insights into the development of ultra-efficient magnonic devices.

Magnetic Anisotropy of Yttrium Iron Garnet from Density Functional Theory

For applications in magnetic memory and spintronic devices, ferrimagnetic insulators (FMIs) with perpendicular magnetic anisotropy (PMA) are of special interest. Because of its low magnetic losses, yttrium iron garnet (Y3Fe5O12, also known as YIG) is frequently regarded as the most promising FMI film. However, YIG films typically have an in-plane easy axis, which limits their potential applications. In YIG films, several strategies are suggested to obtain PMA. In YIG and doped YIG films, the epitaxial strain brought on by lattice mismatch has proven to be a successful method for achieving PMA. The investigation on the theoretical mechanism of PMA induction has not yet been reported, even though PMA has been successfully induced in YIG and other FMIs films. In this study, density functional theory has been used to systematically examine the effects of mechanical strain, including in-plane biaxial strain and out-of-plane strain, on magnetic anisotropy energy (MAE) in YIG and bismuth-doped YIG (BiYIG). The findings demonstrate that unstrained YIG has no magnetic anisotropy. Additionally, it has been found that the easy axis of the YIG may be changed from being in-plane to being out-of-plane by an out-of-plane compressive strain or a modest tensile in-plane biaxial strain. From the examination of the electronic structure, it has been observed that the local density of states close to the Fermi energy is mostly responsible for the shift in MAE. It is anticipated that the modulation of PMA in YIG and the design of spin wave devices based on YIG will both benefit from these results.

Simulation on spin wave transmission and domain wall dynamics in a permalloy nanostrip

Spin waves (SWs), the magnons, can potentially be used for fast and energy efficient information processing and the interaction of SWs with a magnetic domain wall (DW), which is quite complex, can play a key role in the development of magnonic devices. Manipulation of SW amplitude and phase is the key step in realization of spin wave devices. The SW transmission through DW is strongly dependent on the magnetization angle inside the DW and spatial movement of DW is coupled to this interaction. Magnonic spin transfer torque and linear momentum transfer of SW, collectively, control the motion of the DW and the rotation of magnetization inside the DW. In the present work, micromagnetic simulations were performed considering a ferromagnetic permalloy nanostrip with perpendicular magnetic anisotropy (PMA) using mumax3 platform to study SW transmission through DW. The correlation between rotation in magnetization tilt angle (δϕ) inside an initially Néel-type DW and SW-transmission ratio (TD) was investigated at different SW-frequencies ranging from 18 GHz to 28 GHz. Applied SW amplitude at each frequency was sufficiently large for transverse DW to show oscillatory motion along the length of the strip. The results showed that the dependence of TD on rotation in magnetization angle (δϕ) decreases as the frequency of SW is increased and it approaches a nearly isotropic behavior at higher frequencies.

Design of Reconfigurable Spin-Wave Nanochannels Based on Strain-Mediated Multiferroic Heterostructures and Logic Device Applications

A method based on the magnetoelectric effect present in multiferroic heterostructures was used to design a reconfigurable waveguide (WG) channel for spin wave (SW) transmission. The multiferroic heterostructures consisted of a piezoelectric (PZT) layer and an adjacent ferromagnetic (CoFeB) layer within the WG region. By applying voltage to the PZT layer, a piezostrain would be generated and transferred to the ferromagnetic layer, leading to a magnetoelastic field in the latter, which could modulate SW dispersion, including propagation frequency and SW vector. Two applications based on these piezostrain-modulated SW dispersion parameters were explored. A piezostrain-modulated, multiple-shaped WG channel was first proposed to allow specific-frequency SW propagation via control of the applied strain. Then, piezostrain was used to perform a phase shift modulation in the multiferroic SW channel. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\pi }$ </tex-math></inline-formula> -phase shift in the propagation of SW was obtained by customizing the length of strain operation for a given frequency. A phase shifter was designed to build an interferometer to fulfill the destruct and construct logic functions based on strain-controlled SWs. These simulation results highlight the considerable potential of strain engineering to control logical and computational reconfigurable SW devices.

Dirac cones and valley topological states of classical spin waves in artificial magnonic crystals with two-dimensional honeycomb lattice

A model of artificial magnonic crystals (AMCs) with a two-dimensional honeycomb lattice of cylindrical ferromagnetic rods embedded in another ferromagnetic material is proposed. Topological properties including Dirac cones, Dirac-like point and valley states of classical spin waves in the above AMCs are theoretically investigated by numerically solving the Landau-Lifshitz equation. It is shown that Dirac cones and valley states at the boundary of the first Brillouin zone can be generated in the dispersion relation. Furthermore, Dirac-like point can also be obtained at the center of the first Brillouin zone due to the accidental degeneracy of the magnonic bands. These discoveries of Dirac cones, Dirac-like point and valley topological states in artificial magnonic crystals not only open a new field in topological condensed matter, but also provide a novel platform for fabricating topological classical spin-wave devices.

Tunable spin-wave nonreciprocity in synthetic antiferromagnetic domain walls

Nonreciprocal propagation of spin waves provides the possibility to design novel functional magnonic devices. In the present paper, based on micromagnetic simulation, we investigate the properties of the spin waves propagating within magnetic domain walls in a synthetic antiferromagnetic bilayer structure and demonstrate a giant frequency nonreciprocity, of which not only the magnitude but also the sign can be efficiently controlled by an external magnetic field. This results from the field-induced modification of the hybridization between the domain-wall spin wave channels from different magnetic layers. The unidirectional excitation of the gigahertz hybridized domain-wall spin waves by a nanostripline antenna is also demonstrated. Our finding suggests the nanoscale antiferromagnetic domain walls should be a promising platform for programmable nonreciprocal spin-wave devices.

Interplay Between Nonlinear Spectral Shift and Nonlinear Damping of Spin Waves in Ultrathin Yttrium Iron Garnet Waveguides

We use the phase-resolved imaging to directly study the nonlinear modification of the wavelength of spin waves propagating in 100-nm thick, in-plane magnetized YIG waveguides. We show that, by using moderate microwave powers, one can realize spin waves with large amplitudes corresponding to precession angles in excess of 10 degrees and nonlinear wavelength variation of up to 18 percent in this system. We also find that, at large precession angles, the propagation of spin waves is strongly affected by the onset of nonlinear damping, which results in a strong spatial dependence of the wavelength. This effect leads to a spatially dependent controllability of the wavelength by the microwave power. Furthermore, it leads to the saturation of nonlinear spectral shift's effects several micrometers away from the excitation point. These findings are important for the development of nonlinear, integrated spin-wave signal processing devices and can be used to optimize their characteristics.

Experimental Demonstration of a Spin-Wave Lens Designed With Machine Learning

We present the design and experimental realization of a device that acts like a spin-wave lens i.e., it focuses spin waves to a specified location. The structure of the lens does not resemble any conventional lens design, it is a nonintuitive pattern produced by a machine learning algorithm. As a spin-wave design tool, we used our custom micromagnetic solver "SpinTorch" that has built-in automatic gradient calculation and can perform backpropagation through time for spin-wave propagation. The training itself is performed with the saturation magnetization of a YIG film as a variable parameter, with the goal to guide spin waves to a predefined location. We verified the operation of the device in the widely used mumax3 micromagnetic solver, and by experimental realization. For the experimental implementation, we developed a technique to create effective saturation-magnetization landscapes in YIG by direct focused-ion-beam irradiation. This allows us to rapidly transfer the nanoscale design patterns to the YIG medium, without patterning the material by etching. We measured the effective saturation magnetization corresponding to the FIB dose levels in advance and used this mapping to translate the designed scatterer to the required dose levels. Our demonstration serves as a proof of concept for a workflow that can be used to realize more sophisticated spin-wave devices with complex functionality, e.g., spin-wave signal processors, or neuromorphic devices.

Ultrafast spin wave propagation in thick magnetic insulator films with perpendicular magnetic anisotropy

Magnetostatic forward volume spin-waves (MFVSWs) are magnetic moments propagated perpendicular to the film plane and offer reciprocity configurations, which is suitable for spin-wave logic devices with low power consumption. However, owing to the strong shape anisotropy field, magnetic films are easily magnetized in the film plane. Fabrication of thick magnetic films with low Gilbert damping and large perpendicular magnetization anisotropy was an unsolved problem. The promising materials with low damping and easy to modify properties are ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$-based single-crystal films. High quality $({\mathrm{Y}}_{1.26}{\mathrm{Bi}}_{0.18}{\mathrm{Lu}}_{0.96}{\mathrm{Ca}}_{0.6})({\mathrm{Fe}}_{4.4}{\mathrm{Ge}}_{0.6}){\mathrm{O}}_{12}$ micrometer-thick films with strong anisotropy field up to 1862 Oe, narrow out-of-plane ferromagnetic resonance linewidth as low as 2 Oe, and low Gilbert damping approximately $(7.06\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ grow on the gadolinium gallium garnet substrate successfully. The garnet film shows a MFVSW group velocity of 2.25 km/s, relaxation time 50 ns, and decay length up to $115\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$, paving the road towards ultralow power dissipation magnonic devices (microwave devices) based on magnetic insulators.