Propagating Spin Waves Research Articles

Injection locking in DC-driven spintronic vortex oscillators via surface acoustic wave modulation

Control of the microwave signal generated by spin-transfer torque oscillators (STOs) is crucial for their applications in spin wave generation and neuromorphic computing. This study investigates injection locking of a DC-driven vortex STO using surface acoustic waves (SAWs) to enhance the STO’s signal and allow for its synchronization with external inputs. We employ a simplified model based on Thiele’s formalism and highlight the role of vortex deformations in achieving injection locking. Micromagnetic simulations are conducted to validate our theoretical predictions, revealing how the locking bandwidth depends on SAW amplitude, as well as on the amplitude and direction of an applied external field. Our findings are pivotal for advancing experimental research and developing efficient low-power synchronization methods for large-scale STO networks.

Reconfigurable magnonic crystals: Spin wave propagation in Pt/Co multilayer in saturated and stripe domain phase

To control the spin wave (SW) propagation, external energy sources such as magnetic fields, electric currents, or complex nanopatterning are used, which can be challenging at the deep nanoscale level. In this work, we overcome such limitations by demonstrating SW propagation in Pt/Co multilayers at a remanent state controlled by stripe domain patterns, using Brillouin light scattering and micromagnetic simulations. We show that parallel stripes with a periodicity around 100 nm exhibit reconfigurability, as the stripes can be rotated by applying the in-plane field without damaging their shape. This allows us to study SW propagation perpendicular and parallel to the stripes. We observe multimodal SW spectra—three bands in perpendicular and five in parallel geometry. Numerical results allow us to identify all observed modes and to explain the differences between two configurations by the unequal contribution of all three magnetization components in the SW dynamics. We find that the experimentally measured non-reciprocal dispersion (for the wavevector perpendicular to the stripes) is not the breaking of time-symmetry but the asymmetry in intensity of the measured signals of two different low-frequency modes, which is due to the inhomogeneous SW amplitude distribution over the multilayer thickness and the limited light penetration depth. Our results pave the way for easy reprogrammability and high energy efficiency in nanomagnonics.

Spatially extended nonlinear generation of short-wavelength spin waves in yttrium iron garnet nanowaveguides

Spatially extended nonlinear generation of short-wavelength spin waves in yttrium iron garnet nanowaveguides

Influence of local Dzyaloshinskii–Moriya interaction on spin waves in symmetrical heavy metal/ferromagnet/heavy metal multilayer

Abstract In a heavy metal/ferromagnet/heavy metal multilayer with inversion symmetry, the total interlayer Dzyaloshinskii–Moriya interaction (iDMI) is expected to be absent while the local iDMI constants for the top and bottom FM atomic layers can still be nonzero. This study investigates the influence of local iDMI on spin waves in this structure, in which the FM medium consists of two atomic layers with opposite local iDMI at the bottom HM/FM interface and the top FM/HM interface. Theoretical analysis and simulations are conducted to examine the spin-wave dynamics and propagation in the symmetrical sandwich structure. The results show that the local iDMI decreases the characteristic frequency of spin waves, indicating a regulation of spin wave propagation by iDMI and shows the asymmetry of spin-wave propagation between the two FM atomic layers due to iDMI. This work paves the way for deep exploration of spin waves in such structures and offers valuable insights for subtle magnetic interactions in other symmetrical multilayers.

Steerable current-driven emission of spin waves in magnetic vortex pairs.

The efficient excitation of spin waves is a key challenge in the realization of magnonic devices. We demonstrate current-driven generation of spin waves in antiferromagnetically coupled magnetic vortices. We use time-resolved x-ray microscopy to directly image the emission of spin waves upon the application of alternating currents flowing directly through the magnetic stack. Micromagnetic simulations allow us to identify the current-driven Oersted field as the main origin of excitation, in contrast to spin-transfer torques. In our case, these internal Oersted fields have an orders of magnitude higher spin-wave excitation efficiency than commonly used stripline antennas. For magnetostrictive materials, we furthermore demonstrate that the direction of magnon propagation can be steered by increasing the excitation amplitude, which modifies the underlying magnetization profile through an additional anisotropy. The demonstrated methods allow for the efficient and tunable excitation of spin waves, marking a substantial advance concerning the design of magnonic devices.

Coherent spin wave excitation with radio-frequency spin–orbit torque

Spin waves, collective perturbations of magnetic moments, are both fundamental probes for magnetic physics and promising candidates for energy-efficient signal processing and computation. Traditionally, coherent propagating spin waves have been generated by radio frequency (RF) inductive Oersted fields from current-carrying electrodes. An alternative mechanism, spin–orbit torque (SOT), offers more localized excitation through interfacial spin accumulation but has been mostly limited to DC to kHz frequencies. SOT driven by RF currents, with potentially enhanced pumping efficiency and unique spin dynamics, remains largely unexplored, especially in magnetic insulators. Here, we conduct a comprehensive theoretical and computational investigation into the generation of coherent spin waves via RF-SOT in the prototypical yttrium iron garnet. We characterize the excitation of forward volume, backward volume, and surface modes in both linear and nonlinear regimes, employing single and interdigitated electrode configurations. We reveal and explain several unique and surprising features of RF-SOT compared to inductive excitation, including higher efficiency, distinct mode selectivity, and directional symmetry, a ∼3π/4 phase offset, reduced anharmonic distortion in the nonlinear regime, and the absence of second harmonic generation. These insights position RF-SOT as a promising new mechanism for future magnonic and spintronic applications.

Investigation of Mode-Induced Spin Wave Transmission Blockage by In Situ Nanoscale Grooves.

In the pursuit of advancing spin-wave optics, the propagation of magnetostatic surface spin-waves is investigated in a uniform permalloy waveguide with in-situ nanopatterned grooves created through Atomic Force Microscopy nanolithography and Focused Ion Beam etching. The study unveils that the introduction of narrow constrictions and grooves leads to a non-monotonic reduction of the transmitted spin-wave signal intensity as the spin-wave pathway is shrinked. The remarkable feature that a stronger signal extinction is obtained for a narrow groove compared to a spin-waveguide interrupted by a full gap, where only inefficient transport through dipolar coupling is allowed, is highlighted. Combining experimental and numerical analyses, the intricate interplay between spin-wave diffraction and reflection at the waveguide edges is unraveled, being at the origin of a transverse-mode variation responsible for the signal extinction when detected using coplanar antennas. The findings offer insights into the controllable manipulation of detected spin-wave intensity, thereby opening promising avenues for the improvement of spin-wave switches and interferometers, and for the nanopatterning of graded indexmagnonics.

Spin-wave emission using a V-shaped antenna

We investigated the dynamics of spin waves in micro-patterned Permalloy thin films using time-resolved magneto-optic Kerr effect microscopy (TR-MOKE). By applying an external magnetic field, we observe the field dependence of spin wave signals with picosecond resolution. Fourier transform analysis of the signals confirms their agreement with the dispersion relation, demonstrating the successful detection of propagating spin waves using the MOKE technique. Furthermore, we perform dynamic measurements of interfering spin waves generated by a V-shaped antenna. The experimental results reveal differences in spin wave amplitude at each detection point. In combination with simulation analysis based on wave propagation from the V-shaped antenna, we reproduced the experimental results and revealed the existence of a protective zone.

Generating grating in cavity magnomechanics

Abstract We investigate the phenomenon of magnomechanically induced grating (MMIG) within a cavity magnomechanical system, comprising magnons (spins in a ferromagnet, such as yttrium iron garnet), cavity microwave photons, and phonons (Li et al 2018 Phys. Rev. Lett. 121 203601). By applying an external standing wave control, we observe modifications in the transmission profile of a probe light beam, signifying the presence of MMIG. Through numerical analysis, we explore the diffraction intensities of the probe field, examining the impact of interactions between cavity magnons, magnon-phonon interactions, standing wave field strength, and interaction length. MMIG systems leverage the unique properties of magnons, and collective spin excitations with attributes like long coherence times and spin-wave propagation. These distinctive features can be harnessed in MMIG systems for innovative applications in information storage, retrieval, and quantum memories, offering various orders of diffraction grating.

Designed Spin-Texture-Lattice to Control Anisotropic Magnon Transport in Antiferromagnets.

Spin waves in magnetic materials are promising information carriers for future computing technologies due to their ultra-low energy dissipation and long coherence length. Antiferromagnets are strong candidate materials due, in part, to their stability to external fields and larger group velocities. Multiferroic antiferromagnets, such as BiFeO3 (BFO), have an additional degree of freedom stemming from magnetoelectric coupling, allowing for control of the magnetic structure, and thus spin waves, with the electric field. Unfortunately, spin-wave propagation in BFO is not well understood due to the complexity of the magnetic structure. In this work, long-range spin transport is explored within an epitaxially engineered, electrically tunable, 1D magnonic crystal. A striking anisotropy is discovered in the spin transport parallel and perpendicular to the 1D crystal axis. Multiscale theory and simulation suggest that this preferential magnon conduction emerges from a combination of a population imbalance in its dispersion, as well as anisotropic structural scattering. This work provides a pathway to electrically reconfigurable magnonic crystals inantiferromagnets.

All-magnonic repeater based on bistability

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

Magnetic field induced spin wave reflection by a domain wall in synthetic antiferromagnets

Micromagnetic simulations are used to investigate the effect of an external magnetic field on the interaction between domain walls and linearly polarized propagating spin waves in synthetic antiferromagnets. Two regimes with a sharp transition between them are found. At large fields, spin waves are strongly reflected by the domain wall and, consequently, the latter is propelled forward. At low fields, however, there is no reflection and yet the domain wall undergoes a small forward displacement, which is attributed to the change in linear momentum of the magnons as they pass through the domain wall and to the imbalance in the population of the two oscillation modes present in the linearly polarized excitation. The transition between the two regimes occurs at the field value for which the excitation frequency falls below the threshold of the high-frequency mode.

Spin waves in ferrimagnets near the angular magnetization compensation temperature: A micromagnetic study

Spin wave propagation along a ferrimagnetic strip with out-of-plane magnetization is studied by means of micromagnetic simulations. The ferrimagnetic material is considered to be formed by two antiferromagnetically coupled sub-lattices. Two critical temperatures can be defined for such systems: that of magnetization compensation and that of angular momentum compensation, both different due to distinct Landé factors for each sub-lattice. Spin waves in the strip are excited by a spin current injected at one of its edges. The obtained dispersion diagrams show exchange-dominated forward volume spin waves. For a given excitation frequency, the Néel vector describes highly eccentric orbits, the eccentricity depending on temperature, whose semi-major axis is oriented differently at distinct locations on the FiM strip.

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.

Magnonics: Materials, physics, and devices

Magnon, the quanta of spin waves, can serve as an efficient spin information carrier for memory and logic applications, with the advantages of the Joule-heating free induced low power-dissipation property and the phase-coherent induced quantum phenomena. In analogy to spintronics, magnonics focuses on the excitation, detection, and manipulation of magnons (spin waves). In recent years, with the development of nanotechnology, abundant magnonic phenomena emerge in the nanoscale, such as the spin Seebeck effect, magnon-mediated electric current drag effect, magnon valve effect, magnon junction effect, magnon resonant transimission, magnon transfer torque, spin wave propagation, subterahertz spin wave excitation, magnon Bose–Einstein condensation, and so on. Here, we review the recent progresses in magnonics from physics, materials to devices, shedding light on the future directions for magnonics.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

Formation of chirality in propagating spin waves

A general approach to quantify chirality, or absence of parity symmetry, of spin waves has been developed and applied to spin waves propagating in obliquely magnetized ferromagnetic films. Using theoretical arguments and numerical calculations, it is shown that, upon increasing spin wave wavevector, initially achiral spin waves develop chiral properties through the “parity exchange” mechanism, which implies, in particular, that chiral spin waves appear in pairs. The most striking example of the parity exchange mechanism is the simultaneous formation of two chiral waves: the magnetostatic surface wave and the recently discovered heterosymmetric spin wave, which were previously considered independent of each other. Another manifestation of the parity exchange is the formation of strongly chiral waves near the anti-crossings of spin wave branches of unequal symmetry. These findings illustrate viable paths to engineering spin wave systems with prescribed chiral spectra that had not previously been considered.

Collective spin waves in RKKY interlayer-coupled Ni80Fe20/Ru/Ni80Fe20 nanowire arrays

We report on a comprehensive investigation of collective spin waves in Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer-coupled Ni80Fe20 (10 nm)/Ru(1.0 nm)/ Ni80Fe20 (10 nm) nanowire (NW) arrays. We employed Brillouin light scattering to probe the field- and wavevector-dependences of the spin-wave frequency spectra. The acquired data were subsequently analyzed and interpreted within the framework of a microscopic Hamiltonian-based method, enabling a detailed understanding of the observed spin-wave behavior. We observed the propagation of Bloch-type collective spin waves within the arrays, characterized by distinct magnonic bandwidths that stem from the combined influence of RKKY interlayer and inter-NW dynamical dipolar interactions.

Micromagnetic simulations for local phase control of propagating spin waves through voltage-controlled magnetic anisotropy

Spin waves, known for their ability to propagate without the involvement of moving charges, hold immense promise for on-chip information transfer and processing, offering a path toward post-CMOS computing technologies. This study investigates the potential synergy between propagating Damon–Eshbach spin waves and voltage-controlled magnetization in the pursuit of environmentally sustainable computing solutions. Employing micromagnetic simulations, we assess the feasibility of utilizing spin waves in DE mode in conjunction with localized voltage-induced alterations in surface anisotropy to enable low-energy logic operations. Our findings underscore the critical importance of selecting an optimal excitation frequency and gate width, which significantly influence the efficiency of the phase shift induced in propagating spin waves. Notably, we demonstrate that a realistic phase shift of 2.5 [π mrad] can be achieved at a Co(5 nm)/MgO material system via the voltage-controlled magnetic anisotropy effect. Moreover, by tuning the excitation frequency, Co layer thickness, gate width, and carefully selecting the dielectric layer, we extrapolate the potential to enhance the phase shift by a factor of 200 when compared to MgO dielectrics. This research contributes valuable insights toward developing next-generation computing technologies with reduced energy consumption.