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Magnonics

Magnonics is the scientific and technological field focused on the study, excitation, propagation, detection, and manipulation of spin waves—collective magnetic excitations known as magnons—in ordered magnetic materials, enabling charge-free information transport, processing, and storage at micro- and nanoscales. These quasiparticles arise from the of spins in materials like (YIG), offering advantages such as low energy dissipation and compatibility with to frequencies. The principles of stem from the dynamics of magnetic order, where spin waves are influenced by , dipole-dipole, and interactions, as well as external fields or spin torques. Coherent magnons, in particular, allow for , nonlinear driving, confinement in waveguides, and , paving the way for devices that mimic electronic circuits but without . Materials such as low-damping insulators (e.g., YIG films) and synthetic antiferromagnets are central, supporting magnon wavelengths down to 50 nm at GHz frequencies. Historically, magnonics builds on foundational studies of ferromagnetic in the mid-20th century, with significant advancements emerging in the through micron-scale experiments and accelerating in the via nanoscale fabrication and hybrid systems. milestones include the demonstration of room-temperature magnon –Einstein condensates and coherent magnon-photon in YIG. Today, the field addresses challenges like material damping and transduction efficiency while advancing toward practical applications. Notable applications encompass wave-based computing for logic gates and , neuromorphic systems for , and quantum technologies through hybrid magnonics interfacing magnons with photons, phonons, or defects like nitrogen-vacancy centers. These promise significant reductions in compared to conventional , particularly for high-frequency on-chip circuits and in-memory . Future directions include architectures, ultrafast THz magnonics via lasers, and topological magnonic phases for robust signal propagation.

Introduction

Definition and Principles

Magnonics is the scientific discipline focused on the generation, propagation, detection, and manipulation of magnons—quasiparticles that represent the quantized excitations of waves—in magnetic materials, primarily for applications in information processing and transmission. Unlike charge-based carriers in conventional , magnons enable the transport of information without associated electric currents, thereby minimizing energy dissipation through . This field draws analogies to , where photons carry light signals, and phononics, with phonons mediating acoustic waves, but leverages the unique properties of collective dynamics in ordered magnetic systems. Magnons arise from the collective precession of in a magnetic and can be categorized based on the underlying magnetic order. In ferromagnetic materials, magnons correspond to low-energy excitations where align parallel, resulting in a net and typically longer coherence lengths. Antiferromagnetic magnons, by contrast, occur in systems with antiparallel spin alignments that cancel the net , offering advantages such as higher frequencies and reduced stray fields due to the absence of interactions. Synthetic magnons emerge in engineered structures, such as synthetic antiferromagnets composed of coupled ferromagnetic layers separated by non-magnetic spacers, which mimic antiferromagnetic behavior while allowing tunable interactions via interlayer coupling. The operational scales of magnons are well-suited for nanoscale devices, with wavelengths spanning from tens of nanometers to hundreds of micrometers, enabling compatibility with modern lithographic fabrication techniques. Their frequencies generally fall in the gigahertz (GHz) range, from approximately 1 to 15 GHz for common ferromagnetic systems, facilitating with technologies for excitation and readout. These characteristics position magnonics as a promising low-power complement to paradigms.

Significance in Modern Technology

Magnonics offers significant advantages over conventional charge-based , primarily through its ultra-low . Unlike electrical currents, which generate due to resistive losses, magnons propagate as neutral excitations in magnetic materials, enabling information transport without charge motion and thus minimizing . This property allows for highly efficient on-chip at ultrahigh frequencies, potentially reducing in systems significantly, by up to an compared to traditional technology. Additionally, magnons support high-speed propagation with group velocities that enable rapid signal transmission, while their nanoscale wavelengths facilitate integration with existing architectures for hybrid devices. Recent milestones, including the 2024 Magnonics Roadmap and the 2025 realization of inverse-design magnonic logic gates, underscore ongoing progress toward energy-efficient computing devices. As traditional electronics approach the physical limits imposed by Moore's Law, magnonics emerges as a promising wave-based computing paradigm to sustain performance scaling. By leveraging interference and superposition of spin waves, magnonic systems can perform parallel computations with reduced interconnect delays and power overheads, addressing the bottlenecks of transistor miniaturization and heat management in integrated circuits. This shift toward wave interference-based logic could enable more scalable architectures for beyond-Moore computing, where energy efficiency becomes paramount for exascale and quantum-hybrid systems. Magnonics also intersects with broader fields such as , forming hybrid magnon-spintronics systems that combine spin-wave propagation with charge-spin conversion for enhanced device functionality. These hybrids exploit magnon interactions with electrons or other quasiparticles to enable coherent across domains, potentially integrating magnonic logic with spintronic elements like magnetic tunnel junctions. Such synergies promise versatile platforms for low-power and sensing applications. Key metrics underscore ' practical viability: magnon coherence lengths can extend up to several microns in optimized materials, allowing reliable propagation over distances comparable to interconnect scales in modern chips. Attenuation rates for magnons are substantially lower than those of electrical signals in terms of energy loss per distance, as the absence of ohmic dissipation preserves over these lengths, with reported decay lengths exceeding 100 μm in low-damping ferromagnets. These characteristics position as a complementary for energy-constrained environments.

Historical Development

Early Theoretical Foundations

The theoretical foundations of magnonics trace back to the early , when physicists began modeling the collective behavior of spins in magnetic materials. In 1930, introduced the concept of spin waves as low-energy collective excitations in ferromagnets, describing them as quantized deviations from the aligned spin state that propagate through the lattice like waves. This idea provided a quantum mechanical explanation for the temperature dependence of in ferromagnets, predicting that thermal excitations of these spin waves lead to a reduction in net magnetization proportional to T^{3/2} at low temperatures. Building on Bloch's work, and developed a phenomenological equation in 1935 to describe the precessional dynamics of in ferromagnetic materials. The Landau-Lifshitz equation captures the torque exerted by an effective on the vector, incorporating both conservative and a dissipative term that causes the to relax toward . This model laid the groundwork for understanding time-dependent phenomena without delving into microscopic quantum details. In the 1950s, Yigael Yafet extended these ideas by investigating interactions between magnons and conduction electrons in metallic ferromagnets. His theoretical analysis showed that spin-orbit coupling mixes spin states during , leading to spin-flip processes mediated by emission or absorption, which contribute to spin relaxation rates in metals. This work highlighted the role of magnon-electron interactions in damping spin excitations and influencing properties in conducting magnets. Experimental confirmation of as quanta came through early neutron scattering studies in the 1950s and 1960s. Pioneering inelastic neutron scattering experiments on ferromagnetic materials like iron and revealed dispersion relations matching theoretical predictions for , with energy gaps and stiffness constants aligning with Bloch's model. These observations, conducted at facilities such as , provided direct evidence of magnon excitations and validated the wave-like nature of deviations in ordered magnets.

Modern Emergence and Milestones

The field of magnonics began to emerge as a distinct in the early , driven by advances in nanofabrication and interest in spin wave-based alternatives to charge-based electronics. Building on 20th-century theories of spin dynamics, researchers started investigating periodic magnetic structures for controlling magnon propagation, analogous to photonic crystals. The term "magnonic crystal" was introduced in 2001 by Yu. V. Gulyaev and Sergei A. Nikitov to describe artificially structured magnetic media with engineered spin wave bandgaps. Independently in the same year, Henryk Puszkarski and Maciej Krawczyk proposed the concept, emphasizing its potential for tunable dispersion relations in ferromagnetic materials. These foundational ideas laid the groundwork for magnonics, though the broader term "magnonics" gained traction around 2005–2008 through reviews and proposals linking spin waves to . A pivotal moment came in 2005 with the proposal of spin-wave logic gates by Mikhail P. Kostylev and colleagues, demonstrating how of propagating s could perform operations with low energy dissipation. This was followed in 2006 by the experimental observation of Bose-Einstein condensation of s at in films by Sergei O. Demokritov et al., achieving coherent populations exceeding 10^14 cm^{-3} under parametric pumping. These achievements highlighted magnonics' promise for coherent manipulation and stimulated device-oriented research. The formal establishment of the field occurred with the First on Magnonics, held in , , from August 2–7, 2009, organized by the Institute for the Physics of Complex Systems. Titled "Magnonics: From Fundamentals to Applications," the event drew over 100 participants and featured talks on generation, propagation, and logic, solidifying magnonics as an interdisciplinary area at the intersection of and physics. The 2010s saw rapid progress through experimental milestones that validated magnonic concepts for practical use. In 2010, Z. K. Wang et al. demonstrated nanostructured bicomponent /permalloy magnonic crystals with size-tunable bandgaps up to 1 GHz, enabling reconfigurable wave filtering at frequencies. In 2012, V. Chumak et al. proposed an all-spin logic device utilizing intrinsic nonlinearity from spin-wave , foundational for all-magnonic circuits. By 2013, room-temperature magnonic crystals were realized in -based periodic arrays, exhibiting stable bandgap formation and submicron-scale propagation lengths greater than 10 wavelengths, as reported by groups exploring Damon-Eshbach modes. These developments, compiled in the seminal book Magnonics: From Fundamentals to Applications edited by Sergei O. Demokritov and Alexander N. Slavin, underscored the shift toward device integration. Recent advances through 2025 have expanded into hybrid and exotic systems, enhancing scalability and functionality. In 2022, Antonio et al. reported strongly coupled magnon-plasmon in graphene-two-dimensional ferromagnetic insulator heterostructures, achieving hybridization at with Rabi splitting up to ~100 GHz and separation distances up to 0.5 μm, opening pathways for opto-magnonic interfaces. By 2025, further integrations, such as 3D-printed magnonic waveguides and topological magnon insulators, have been reported, with symposia continuing to drive the field toward beyond-Moore paradigms. These milestones reflect ' evolution from theoretical curiosity to a viable platform.

Fundamental Concepts

Spin Waves and Magnons

Spin waves represent collective excitations in magnetically ordered materials, characterized by the precessional motion of spins around their positions within a . This coherent deviation from the alignment propagates as a wave-like disturbance, maintaining the overall direction while reducing its magnitude locally. In the quantum mechanical description, spin waves are quantized into discrete units known as magnons, which behave as bosonic quasiparticles. Magnons follow Bose-Einstein statistics, enabling their occupation numbers to increase significantly at low temperatures, which leads to thermal excitation and a corresponding reduction in net . This thermal depopulation of magnon states accounts for the observed temperature dependence of , following a T^{3/2} law at low temperatures. Different geometries and magnetization configurations give rise to distinct types of spin waves, such as backward volume modes and Damon-Eshbach surface modes in thin films. Backward volume modes occur when the wave vector is parallel to the , exhibiting a negative relative to the . Damon-Eshbach modes, in contrast, are localized at the surface of thin ferromagnetic films with in-plane perpendicular to the direction, displaying nonreciprocal characteristics. The energy of magnons arises from multiple interactions, including the Zeeman energy due to external , exchange energy from nearest-neighbor couplings, and dipolar energy from long-range magnetostatic interactions. These contributions determine the , with dominating at short wavelengths and dipolar effects becoming prominent at longer scales.

Wave Propagation in Magnetic Materials

Wave propagation of s in magnetic materials is characterized by distinct behaviors depending on the magnetic ordering, with ferromagnetic () and antiferromagnetic (AFM) systems exhibiting different and group velocities. In materials, such as (YIG) films, group velocities typically range from 1 to 2.5 km/s for magnetostatic surface waves in nanosized waveguides, decreasing with narrower conduit widths due to confinement effects. velocities in these systems can reach tens of km/s, but the lower group velocity limits practical propagation distances to micrometers without . In contrast, AFM materials like (α-Fe₂O₃) support much higher group velocities, up to 20 km/s for bulk modes and 6 km/s for surface modes, enabling faster signal transport over distances exceeding 10 μm with coherent propagation. This difference arises from the negligible dipolar fields in AFMs compared to the strong magnetization-driven dipolar contributions in FMs, which result in steeper relations and higher velocities in the former. Material parameters significantly influence magnon propagation dynamics. Gilbert damping (α) introduces intrinsic losses that attenuate wave amplitude exponentially with distance, with lower values—such as α ≈ 1.75 × 10⁻⁴ in high-quality YIG—enabling propagation lengths up to centimeters in thin films. Higher damping, around 10⁻³ in metallic FMs like Co₂₅Fe₇₅ (similar to ), restricts lengths to ~20 μm. Magnetic anisotropy modulates the dispersion curve, enhancing and reducing attenuation in cubic anisotropic materials by up to twofold compared to isotropic ones, as it alters the effective field and wave confinement. Exchange stiffness (A), quantifying spin-spin interactions, determines the short-wavelength and overall dispersion steepness; for instance, A ≈ 20 pJ/m in Co₂₅Fe₇₅ supports exchange-dominated propagation in nanoscale structures, while values around 12 pJ/m in ferrimagnetic spinels like NiZn ferrite promote coherence in insulator-based systems. In practical waveguides, magnon propagation is tailored by geometry and material choice. (Ni₈₀Fe₂₀) stripes, typically 20-50 nm thick, guide Damon-Eshbach surface waves with group velocities increasing fourfold (from ~1 km/s to 4 km/s) as thickness rises from 10 to 40 nm, due to reduced boundary scattering. YIG films, prized for their ultralow (α ≈ 6.7 × 10⁻⁵), achieve propagation over millimeters in sub-micron-wide conduits, with decay lengths of 1.8-12 μm depending on width, making them ideal for low-loss interconnects. Attenuation in these systems arises from multiple mechanisms beyond intrinsic . Two-magnon , an extrinsic where a propagating scatters into lower-energy modes via defects or , dominates in thin FM films like and Co₂₅Fe₇₅, broadening ferromagnetic resonance linewidths and limiting propagation to tens of micrometers; it is suppressed in out-of-plane magnetized configurations. Radiative losses occur when spin waves leak energy to the surrounding medium, particularly at edges in YIG structures, becoming significant for narrow pumping sources and contributing to thresholds by increasing effective . In AFMs, such losses are less pronounced due to higher velocities, but surface imperfections still induce over 3-4 μm lengths.

Theoretical Framework

Landau-Lifshitz-Gilbert Equation

The Landau-Lifshitz-Gilbert (LLG) equation serves as the foundational dynamical equation governing the of in ferromagnetic materials, essential for describing propagation in . Originally formulated by Landau and Lifshitz in 1935 to model the dispersion of magnetic permeability in ferromagnets, it captures the precessional motion of under an effective magnetic field. In 1955, introduced a revised term, reformulating the equation to better align with experimental observations of relaxation, particularly in ferromagnetic experiments. The LLG equation is expressed as \frac{d\mathbf{M}}{dt} = -\gamma \mathbf{M} \times \mathbf{H}_\mathrm{eff} + \frac{\alpha}{M_s} \mathbf{M} \times \frac{d\mathbf{M}}{dt}, where \mathbf{M} is the vector, \gamma is the , \mathbf{H}_\mathrm{eff} is the effective , \alpha is the dimensionless Gilbert parameter (typically \alpha \ll 1), and M_s = |\mathbf{M}| is the . The first term on the right-hand side describes the precessional , causing \mathbf{M} to rotate around \mathbf{H}_\mathrm{eff} at the Larmor , analogous to on a classical in a field. The second term represents Gilbert , which drives \mathbf{M} toward alignment with \mathbf{H}_\mathrm{eff} by dissipating energy, ensuring conservation of the magnitude M_s while allowing rotational relaxation. This form is equivalent to the original Landau-Lifshitz equation but offers advantages in and physical interpretation for low-damping regimes common in magnonic materials like (YIG). The effective field \mathbf{H}_\mathrm{eff} aggregates contributions from various physical interactions within the material. The exchange field arises from quantum mechanical spin alignments between neighboring atoms, typically modeled as \mathbf{H}_\mathrm{ex} = \frac{2A}{M_s^2} \nabla^2 \mathbf{M}, where A is the exchange stiffness constant promoting spatial coherence in spin waves. The demagnetizing field accounts for long-range dipolar interactions influenced by sample geometry and magnetization distribution. For uniform magnetization, \mathbf{H}_\mathrm{demag} = -\mathbf{N} \cdot \mathbf{M}, where \mathbf{N} is the demagnetization tensor. In non-uniform cases, such as spin waves, it is obtained by solving the magnetostatic problem numerically, which influences wave confinement in magnonic structures. The Zeeman field, \mathbf{H}_\mathrm{Z} = \mathbf{H}_\mathrm{ext} + \mathbf{H}_\mathrm{ani}, includes the applied external field \mathbf{H}_\mathrm{ext} and anisotropy field \mathbf{H}_\mathrm{ani} from crystal or shape symmetries, tuning the equilibrium magnetization direction critical for magnon excitation. For small-amplitude excitations, such as those generating spin waves (as briefly referenced in the fundamental concepts section), the LLG equation can be linearized around the equilibrium magnetization direction, typically along the z-axis with \mathbf{M} \approx M_s \hat{z} + \mathbf{m}_\perp where |\mathbf{m}_\perp| \ll M_s. This approximation yields coupled linear differential equations for the transverse components m_x and m_y, facilitating analytical solutions for plane-wave magnons with relations that depend on wavevector and material parameters, while retaining effects proportional to \alpha. Such is pivotal in magnonics for predicting low-energy spin-wave modes in waveguides and crystals without resorting to full nonlinear simulations.

Dispersion Relations and Simulations

Dispersion relations describe the relationship between the frequency \omega and wavevector \mathbf{k} of magnons, essential for understanding their propagation characteristics in magnetic media. These relations emerge from solving the linearized Landau-Lifshitz-Gilbert equation under appropriate boundary conditions, incorporating Zeeman, exchange, and dipolar interactions. In ferromagnetic thin films, for spin waves propagating perpendicular to the equilibrium magnetization direction (e.g., Damon–Eshbach geometry), the dipolar-exchange dispersion relation approximates magnon frequencies as \omega(k) \approx \gamma \sqrt{(H + D k^2)(H + M_s + D k^2)}, where \gamma is the gyromagnetic ratio, H the applied magnetic field, M_s the saturation magnetization, D the spin-wave stiffness constant, and k the magnitude of the wavevector (in cgs units, M_s often incorporates the $4\pi factor). This expression captures the interplay between demagnetizing field effects, which dominate at low k, and exchange contributions that prevail at higher k. Note that for backward volume geometry in thin films, a more complete magnetostatic treatment accounting for film thickness is required to capture the characteristic backward dispersion (initial decrease in frequency with k). The zero-wavevector limit (k = 0) yields the Kittel mode, corresponding to uniform of the across the sample, with \omega = \gamma \sqrt{H(H + M_s)}. This mode sets the baseline for ferromagnetic in perpendicularly magnetized thin films, where shape anisotropy enhances the effective field. In confined geometries like ferromagnetic spheres, the spectrum includes higher-order nonuniform known as Walker modes, which satisfy magnetostatic boundary conditions and exhibit quantized above the Kittel mode. These modes feature azimuthal or polar nodal structures, enabling selective excitation for magnonic applications in finite samples. Micromagnetic simulations numerically solve the Landau-Lifshitz-Gilbert equation to predict dispersion relations in complex structures beyond analytical tractability. The Object Oriented Micromagnetic Framework (OOMMF), a finite-difference code developed by NIST, facilitates time- and frequency-domain analyses of spin-wave dynamics in patterned films and nanostructures. MuMax3, a GPU-accelerated finite-difference solver, extends these capabilities to larger scales and three-dimensional geometries, efficiently computing spectra in devices with sub-micrometer features. For systems with spatial inhomogeneities, such as graded or compositions, finite methods offer adaptive meshing and precise handling of irregular boundaries, yielding accurate dispersions through variational formulations of the micromagnetic .

Experimental Techniques

Generation of Magnons

Magnons, the quanta of s, can be generated through various physical mechanisms that couple external stimuli to the spin system in magnetic materials. These methods enable the excitation of coherent modes, which are essential for magnonic devices. The choice of technique depends on the desired frequency range, spatial localization, and , with frequencies typically spanning gigahertz to regimes. One of the most common approaches involves excitation, where radiofrequency currents in conductive structures produce oscillating that drive . In particular, striplines—narrow metallic conductors patterned on or near the magnetic sample—generate localized fields from the , inducing uniform or propagating spin waves across the sample. This method achieves efficient excitation at frequencies (1–100 GHz) by matching the applied field to the material's ferromagnetic resonance, allowing for nanoscale spatial control in thin films like (YIG). Spin-transfer torque (STT) provides an alternative, current-driven mechanism particularly suited to metallic ferromagnets such as . Here, spin-polarized electrons from an adjacent heavy-metal layer, like , inject into the magnetic layer via spin-orbit interactions or direct transfer, exciting magnons through on the local magnetization. This all-electrical approach enables efficient generation of short-wavelength magnons (down to nanometers) and has been demonstrated to sustain auto-oscillations in spin-torque nano-oscillators, with power outputs reaching microwatts. For ultrafast dynamics, laser-induced heating using pulses offers picosecond-scale magnon generation. Intense near-infrared pulses rapidly heat the electron system, leading to demagnetization and subsequent relaxation that populates modes via electron- scattering. In materials like or YIG, this non-equilibrium process excites broadband magnons up to frequencies, with pulse durations as short as 100 enabling time-resolved studies of propagation. Thermal generation exploits temperature gradients to drive magnon currents through the magnon Seebeck effect, where a thermal imbalance across a magnetic like YIG creates a non-equilibrium magnon population via interfacial magnon-phonon drag or bulk thermoelectric processes. This method produces pure spin currents without charge flow, with observed voltage signals up to microvolts in Pt/YIG bilayers under gradients of 1–10 K/μm, facilitating low-power, dissipation-free excitation at . The excitation efficiency is tuned by aligning the gradient with the magnon for optimal mode matching.

Detection and Measurement Methods

Detection and measurement of in magnetic materials rely on techniques that probe the dynamic associated with spin waves, enabling characterization of their , wavevector, and amplitude. These methods are essential for understanding magnon propagation and interactions, providing insights into material properties and device performance. Non-optical approaches complement optical ones by offering electrical readout suitable for integration in spintronic systems. Brillouin light scattering (BLS) is a non-contact optical spectroscopy technique widely used for wavevector-resolved detection of magnons, where of by spin waves shifts the 's according to the magnon . In BLS, a probing beam interacts with the sample, and the scattered is analyzed with a tandem Fabry-Pérot interferometer to resolve shifts on the order of GHz, allowing measurement of magnon wavelengths from micrometers to sub-micrometers. This method excels in studying propagating spin waves in ferromagnetic films and nanostructures, with sensitivity enhanced by micro-focusing for nanoscale resolution. For instance, BLS has revealed high-wavevector magnons in (YIG) films, confirming theoretical dispersion curves with wavevectors up to 10^6 rad/m. Ferromagnetic resonance (FMR) detects uniform precession modes (k=0 magnons) through microwave absorption, where an external magnetic field tunes the resonance frequency, and the absorption signal indicates magnon excitation. Broadband FMR setups using vector network analyzers measure the susceptibility by sweeping microwave frequencies from 1 to 40 GHz, quantifying parameters like Gilbert damping and anisotropy fields in thin films. This technique is particularly effective for bulk or uniform samples, such as permalloy or YIG, where linewidth analysis reveals relaxation mechanisms. FMR has been instrumental in verifying zero-wavevector magnon modes in ferromagnets, with resonance frequencies following the Kittel formula f = \frac{\gamma}{2\pi} \sqrt{(H + H_k)(H + H_k + 4\pi M_s)}, where \gamma is the gyromagnetic ratio, H the applied field, H_k the anisotropy field, and M_s the saturation magnetization. Electrical detection of magnons often employs the inverse spin Hall effect (ISHE) in adjacent layers, converting spin current from magnon into a measurable voltage via spin-orbit coupling. In a typical setup, s in a ferromagnet like YIG propagate to a detector, where the spin accumulation generates a transverse charge current proportional to the spin Hall angle, typically yielding voltages in the nV to μV range for GHz excitations. This method enables all-electrical readout of propagating magnons over micrometer distances, with spin diffusion lengths up to 10 μm in YIG at . Seminal experiments demonstrated ISHE detection of pure spin currents from magnons, confirming spin-to-charge efficiencies of about 0.01 in Pt/YIG bilayers. Time-resolved Kerr microscopy provides spatial and temporal mapping of magnon dynamics using the magneto-optical , where polarized laser pulses probe local changes with resolution. In this pump-probe configuration, a short laser pulse excites or modulates the , and subsequent probe pulses measure the Kerr rotation or ellipticity across the sample surface, resolving propagation speeds on the order of 10^3 m/s in metallic ferromagnets. The technique achieves sub-micron via focused beams, ideal for visualizing wavefronts in waveguides or antidot lattices. For example, vectorial Kerr has captured non-collinear textures in propagating waves, revealing phase accumulation over 100 μm propagation lengths in stripes.

Applications and Devices

Logic and Computing Elements

In magnonics, logic and computing elements leverage the interference and superposition of spin waves to perform operations, offering potential advantages in and parallelism over traditional charge-based . A key primitive is the majority gate, which determines the dominant input state among three signals. This is achieved through the interference of spin waves propagating in a (YIG) , where logical states '0' and '1' are encoded as phases of 0 and π radians, respectively. When the majority of inputs share the same phase, constructive interference produces a strong output signal at that phase; otherwise, destructive interference suppresses it, yielding the minority phase. An experimental prototype demonstrated this functionality with a switching time of approximately 10 ns, using a YIG film patterned into a three-input structure under a magnetic of 1160 . Reconfigurability in magnonic is enabled by external magnetic biasing fields, which tune the and of spin waves to alter behavior without physical reconfiguration. By applying localized or global bias fields, the relative shifts in waveguides can be controlled, switching between functions such as , or in a single device. For instance, in cross-junction geometries, the bias field adjusts the wavevector matching at intersections, directing superposition outcomes to enable reversible operations. This approach allows dynamic reprogramming, with simulations showing near-100% transmission or efficiency depending on field orientation. Basic arithmetic operations like and XOR are realized through superposition in multi-waveguide setups. In a two-input , inputs encoded as packets interfere at a junction: same- inputs (00 or 11) result in constructive superposition and transmission to one output, while opposite phases (01 or 10) cause destructive and to the other, effectively computing the XOR. follows similarly, with the sum represented by the total accumulation across paths. These wave-based primitives exploit the linearity of spin-wave propagation, enabling of multiple frequencies. In , inverse-design approaches enabled reconfigurable magnonic logic gates using arrays of current loops for operations. Magnonic logic elements exhibit high , with operations consuming on the order of 10 fJ per , significantly lower than the ~1 pJ typical for 45 nm inverters due to the absence of charge motion and . This stems from the minimal energy required to excite and interfere spin waves, primarily limited by input transducers, and positions magnonics as a candidate for low-power beyond architectures.

Data Storage and Interconnects

Magnonics offers promising approaches for non-volatile data storage by leveraging the coherent propagation and long relaxation times of magnons in magnetic materials. One key concept involves magnon-based random access memory (RAM) utilizing coherent state storage in yttrium iron garnet (YIG) spheres coupled to microwave cavities. In this scheme, multiple YIG spheres enable the formation of magnon dark modes, which are subradiant states decoupled from the cavity environment, achieving storage lifetimes exceeding 100 ns with efficiencies up to 30% for microwave pulses. These dark modes, induced by a magnetic field gradient across the spheres, support broadband operation over 80 MHz and multimode storage without requiring rapid field switching, making them suitable for gradient memory architectures that preserve quantum coherence for potential quantum information applications. Spin-wave buses serve as low-loss interconnects in chip-scale magnonic networks, facilitating efficient signal without charge currents and thus minimizing . These buses consist of ferromagnetic waveguides, such as those made from or YIG films, where spin waves propagate with encoding (0 for "1" and π for "0") over distances of several micrometers at GHz frequencies. A clocked scheme incorporates magneto-electric cells and spin-wave to enable non-volatile , , and non-reciprocal , with power consumption below 1 μW per interconnect in simulated pipelines. This approach reduces circuit area and energy compared to traditional interconnects, supporting scalable networks for beyond-CMOS computing. Hybrid magnonic-CMOS interfaces enable read and write operations by integrating spin-wave transducers, such as antennas or magneto-electric converters, directly with silicon-based electronics. These interfaces convert electrical signals from circuits into spin waves for writing via inductive or piezoelectric excitation in YIG or waveguides, achieving switching times around 5 ns with energies as low as 1 nW over 15 μm propagation distances. For reading, inverse transducers detect magnon-induced voltage or current modulations, allowing seamless data retrieval with compatibility to standard fabrication processes. Such hybrids leverage the low of YIG for reliable operations while addressing integration challenges through on-chip geometries. A significant advantage in magnonic interconnects and storage arises from parallel , enabling multi-bit within a single . By exciting spin waves at distinct frequencies (e.g., spaced by 10-50 MHz), multiple independent data streams can propagate simultaneously without interference, as each frequency acts as a separate logical encoded by or . This supports high throughput in YIG-based structures, facilitating dense, low-power multi-bit transmission in chip-scale networks.

Advanced and Emerging Topics

Nanoscale and 2D Magnonics

In nanoscale magnonic structures, such as nanowires and dots with dimensions below 100 , spin waves exhibit quantization due to spatial confinement, resulting in discrete modes with wavelengths as short as 10-100 . These quantized arise from the boundary conditions imposed by the finite size, leading to patterns analogous to quantum mechanical particle-in-a-box states, where the mode frequencies are determined by the structure's geometry and material parameters. For instance, in nanowires approximately 100 wide, parametric excitation techniques have enabled the generation and propagation of these short-wavelength , with experimental verification through Brillouin light scattering spectroscopy showing mode confinement and reduced group velocities compared to bulk materials. Edge modes represent a key phenomenon in these sub-100 nm structures, where magnons localize at the boundaries due to inhomogeneous demagnetization fields, enhancing selectivity and enabling unidirectional propagation. In magnonic crystals composed of nanoscale stripes, topological can stabilize these edge modes against backscattering, allowing nonreciprocal spin-wave with propagation lengths exceeding several micrometers even at GHz frequencies. Such edge-localized magnons have been observed in (YIG) Fabry-Pérot resonators patterned at the nanoscale, where dipolar coupling at the interfaces creates robust, low-loss channels for . The integration of magnonics with two-dimensional (2D) van der Waals ferromagnets has opened new avenues for atomically thin magnonic systems, particularly in materials like chromium triiodide (CrI₃), where intrinsic ferromagnetism persists down to the monolayer limit with Curie temperatures around 45 K. Post-2020 advances have revealed exotic magnon dispersions in CrI₃, including massless Dirac-like magnons in its honeycomb lattice, which emerge from the interplay of nearest-neighbor exchange and spin-orbit coupling, enabling topological band structures with potential for valley-dependent transport. Experimental magneto-Raman spectroscopy has directly observed these 2D magnons in few-layer CrI₃ flakes, confirming their quadratic dispersion at low energies and hybridization with phonons, which could facilitate tunable magnonic devices through strain or gating. These developments highlight CrI₃'s suitability for integrating magnonics with 2D electronics, leveraging its van der Waals stacking for heterostructure-based edge mode engineering without lattice mismatch issues. At the nanoscale, thermal magnons—those excited by ambient temperature fluctuations—become dominant due to the increased and reduced energy barriers for excitation in confined geometries, often outnumbering coherently driven magnons and introducing inherent stochasticity. This thermal dominance enhances the potential for paradigms in magnonics, where random magnon fluctuations can serve as a resource for probabilistic operations, such as in magnon-based paramétrons that exhibit bistable switching influenced by for energy-efficient logic. For example, in nanoscale elements, nonlinear interactions among thermal magnons amplify telegraph in , enabling hardware acceleration of simulations with switching rates tunable via external fields. A primary challenge in nanoscale and magnonics is the increased observed in nanostructures, which arises from surface scattering, interfacial dead layers, and enhanced spin-pumping effects, often elevating the parameter by factors of 2-10 compared to bulk values. In patterned YIG nanowires below 100 nm, this manifests as shorter lengths (typically <1 μm at room temperature) and mode-dependent losses, where higher-order quantized modes experience greater attenuation due to boundary-induced two-magnon scattering. For materials like CrI₃, extrinsic from substrate interactions further complicates low-loss operation, necessitating encapsulation strategies to mitigate phonon-magnon coupling and preserve coherence times. These issues limit device scalability, though recent epitaxial growth techniques on gadolinium gallium garnet substrates have reduced effective in YIG nanostructures to near-bulk levels of α ≈ 10⁻⁴. The 2024 Magnonics Roadmap summarizes recent progress in nanoscale magnonics, including magnon wavelengths down to 50 nm at microwave frequencies in YIG films and voltage-controlled excitation of spin waves using magnetic anisotropy. Advances in 2D van der Waals magnets, such as synthetic antiferromagnets, enable non-reciprocal spin waves for enhanced nanoscale devices.

Hybrid Magnonic Systems

Hybrid magnonic systems integrate magnonic elements with other physical platforms, such as , electronics, and superconductivity, to leverage the unique properties of spin waves for enhanced functionality in information processing and quantum technologies. These hybrids enable coherent interactions between magnons and excitations in complementary systems, facilitating efficient and reduced dissipation. Magnon- coupling in cavity optomagnonics arises from magneto-optical effects like Faraday rotation in magnetized materials, such as yttrium iron garnet (YIG), placed within optical or cavities, allowing reversible energy exchange between magnons and . The coupling strength, often reaching hundreds of MHz in regimes, enters the strong coupling limit when it exceeds the decay rates of both quasiparticles, quantified by cooperativity C = 4 G^2 / (\kappa \Gamma) > 1, where G is the vacuum coupling rate, \kappa the decay, and \Gamma the magnon damping. This regime enables applications as quantum interfaces, such as bidirectional between and optical domains for quantum networks, and the generation of entangled magnon- states for processing. In electronic-magnonic hybrids, the in heavy metal/ferromagnet bilayers, such as Pt/YIG, generates s by converting charge currents into pure currents that inject into the magnetic layer via interfacial exchange. Experiments on Pt/YIG/Pt(Ta) trilayers demonstrate this through nonlocal voltage measurements, revealing magnon-mediated current drag with voltages scaling linearly with injected current and showing angular dependence aligned with magnetization, confirming efficient excitation at . This mechanism supports spintronic devices by enabling electrical control and detection of waves with minimal . Recent developments in antiferromagnetic magnonics hybrids have advanced -frequency operations through structures like canted antiferromagnets interfaced with for spin Hall detection. In α-Fe₂O₃/ hybrids, nonreciprocal -wave is observed with separations exceeding 1 GHz and group velocities up to 20 km/s, allowing sub-terahertz magnon modes (around 17 GHz experimentally, with potential extension to THz via material tuning) to be electrically excited and detected with 40% asymmetry due to magnon-enhanced spin Hall effects. These 2023 findings enable compact, low-dissipation devices for ultrafast at terahertz scales. Superconducting-magnonic devices combine ferromagnetic films like YIG/ with superconducting resonators, such as NbN, to achieve low-loss magnon transport by minimizing dissipation in the hybrid structure. In such systems, -polaritons form via coherent with strengths of about 105 MHz, detected through spin pumping into the layer, enabling efficient, cryogenic operation with high cooperativity for quantum applications. The superconducting elements provide nearly lossless mediation, supporting long-distance spin-wave propagation with reduced thermal noise. The 2024 Magnonics Roadmap highlights advances in hybrid quantum magnonics, including coherent magnon-photon coupling in YIG resonators and deterministic generation of quantum magnon Fock states using superconducting qubits as of 2023. In 2025, single-shot magnon was demonstrated in a -superconducting with remotely coupled YIG spheres, enabling coherent transfer of multiple magnon pulses.

Challenges and Future Directions

Technical Limitations

One of the primary technical limitations in magnonics arises from the high magnetic damping inherent in metallic ferromagnets, such as or CoFeB, which significantly restricts -wave propagation distances. In these materials, damping parameters typically range from 0.005 to 0.02, leading to attenuating over lengths of only a few micrometers—often less than ten times the wavelength—due to magnon-electron and magnon-phonon scattering mechanisms. This damping not only reduces in potential devices but also limits the of magnonic interconnects and logic elements, as longer propagation is essential for practical circuit integration. While insulating ferrimagnets like (YIG) exhibit much lower damping (α ≈ 10^{-4}), their use is often constrained by other factors, leaving metallic systems dominant for CMOS-compatible applications yet hampered by this inefficiency. Magnonic systems also suffer from pronounced temperature sensitivity, where thermal fluctuations alter key parameters like saturation magnetization, exchange stiffness, and damping, thereby degrading performance. At elevated temperatures, reduced magnetization lowers spin-wave frequencies and increases damping via thermally activated defects, while room-temperature Johnson-Nyquist noise further limits detection sensitivity and data rates in readout processes. In advanced applications, such as certain coherent quantum effects in quantum magnonics, cryogenic operation below 100 mK is often required to suppress thermal magnons, though magnon Bose-Einstein condensation can be achieved at room temperature under parametric pumping. Even in hybrid setups, temperature variations can destabilize magnon-phonon or magnon-photon couplings, necessitating precise thermal control that complicates practical implementation. Fabrication of periodic magnonic crystals presents substantial challenges, particularly in achieving high-quality nanostructures with uniform periodicity and smooth interfaces over large areas. Techniques like or focused ion-beam milling enable nanoscale patterning but struggle with reproducibility, edge roughness, and maintaining spin-orbit interactions, often resulting in inconsistent bandgaps and increased scattering losses. For metallic films, integrating periodic modulations of thickness or composition exacerbates damping issues, while growing ultrathin insulating layers (e.g., YIG < 100 nm) demands epitaxial methods like , which are costly and incompatible with . These fabrication hurdles limit the realization of tunable band structures essential for waveguiding and filtering in magnonic devices. Interfacing magnonic structures with silicon-based electronics remains a critical bottleneck, primarily due to mismatches in material properties and inefficient energy transduction between spin and charge domains. Exciting and detecting sub-100 nm wavelength magnons requires high-efficiency transducers, such as antennas or spin-Hall nano-oscillators, but current methods suffer from low conversion efficiencies (often <1%) and impedance mismatches with CMOS circuitry. Direct integration of magnetic films on silicon substrates is hindered by lattice mismatches and poor epitaxial growth—e.g., YIG on Si yields high defect densities—while metallic ferromagnets introduce eddy current losses that degrade electronic performance. These difficulties impede hybrid spintronic-CMOS systems, where seamless signal exchange is vital for practical computing architectures.

Research Trends and Prospects

Recent research in is shifting toward room-temperature antiferromagnetic systems, driven by the discovery of layered altermagnets that generate non-collinear currents at ambient conditions, enabling efficient spintronic functionalities without cryogenic cooling. Synthetic antiferromagnets, composed of tunable ferromagnetic layers with antiferromagnetic , further this trend by allowing precise control of propagation through adjustments in layer thickness and composition, facilitating room-temperature magnonic crystals and waveguides. These advancements, highlighted in the 2024 Magnonics Roadmap, promise enhanced nonreciprocal dynamics and integration into practical devices by leveraging materials like (YIG) multilayers. In , magnon reservoirs have emerged as a focal point, with 2024-2025 studies demonstrating their use in energy-efficient physical via nonlinear interactions. For instance, time-multiplexed systems employing photon-magnon coupling achieve high-accuracy temporal data processing, mimicking dynamics without traditional architectures. Current-controlled magnonic reservoirs in nanoscale YIG structures further enable tunable, low-power , reducing energy consumption by orders of magnitude compared to CMOS-based alternatives. The 2025 Roadmap on Nanomagnetism emphasizes magnonic networks for synaptic emulation, projecting scalable neuromorphic hardware with deep-subwavelength precision by the late 2020s. Quantum is advancing through entanglement generation via magnon pairs, as shown in driven synthetic antiferromagnets where spin-orbit torques spontaneously produce paired magnons for preparation. Recent investigations have explored magnon pairing, revealing potential for bipartite entanglement in quantum interconnects. These developments, including enhanced remote - entanglement via squeezed fields, position as a for quantum technologies, with strong optomagnonic in YIG structures enabling microwave-to-optical . Emerging 2025 research on topological further promises robust signal propagation against damping and disorder. Looking to market impacts, magnonics is poised to contribute to beyond-CMOS technologies, with markets—including magnonic components—forecast to exceed $4 billion by 2030 through applications in low-energy and . Roadmaps project widespread adoption in the 2030s, featuring charge-free architectures that bridge high-speed and SSD gaps while slashing power dissipation in and .