Propagating Spin Waves Research Articles

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.

Application of the quantum model of the rotating wave approximation to the generation of spin waves in nanowires

The paper simulates systems in which two types of spin waves can occur, propagating in opposite directions. To achieve this, the quantum slow-wave approximation is employed, allowing for the determination of the probability distribution of occupied states in a quantum two-particle system subjected to perturbations, commonly referred to as Rabi oscillations. This model is specifically applied to a configuration of parallel nanowires exposed to an external electromagnetic wave within the microwave range. The study explores a potential application of the investigated nanostructures in the development of a device for detecting electromagnetic fields.

Emission of fast-propagating spin waves by an antiferromagnetic domain wall driven by spin current

Antiferromagnets (AFMs) have great benefits for spintronic applications such as high frequencies (up to THz), high speeds (up to tens of km/s) of magnetic excitations, and field-free operation. Advanced devices will require high-speed propagating spin waves (SWs) as signal carriers, i.e., SWs with high k vectors, the excitation of which remains challenging. We show that a domain wall (DW) in anisotropic AFM driven by the spin current can be a source of such propagating SWs with high frequencies and group velocities. In the proposed generator, the spin current, with polarization directed along the easy anisotropy axis, excites the precession of the Néel vector within the DW. The threshold current is defined by the value of the anisotropy in the hard plane, and the frequency of the DW precession is tunable by the strength of the spin current. We show that the above precession of spins inside the DW leads to robust emission of high-frequency propagating SWs into the AFM strip with very short wavelengths comparable to the exchange length, which is hard to achieve by any other method. Published by the American Physical Society 2024

Strain-induced multi-band spin-wave logic gate based on alligator-type magnonic crystal/PZT structure

Here, we report the results of strain-controlled spin-wave propagation regimes in a double-period multiferroic structure. It consists of an alligator-type magnonic crystal with a period of 250 μm and a piezoelectric layer, featuring a periodic counter-pin-type electrode system with a period of 125 μm. Employing microwave measurements, we acquired the transmission and dispersion of spin waves under various external electric field configurations applied to the piezoelectric layer. The formation of bandgaps in the magnon spectrum and the variation of the spin-wave transmission when altering the configurations of the external electric field are demonstrated. A finite element method reveals that the combination of the non-uniformity in the initial internal magnetic field of the magnonic crystal, which is caused by the presence of periodic alligator-type regions, together with elastic deformations, heightens the amplitude of the modulation of the internal magnetic field. Micromagnetic modeling has demonstrated that this modulation enhancement results in the variation of the spin-wave transmission at the frequency of the magnonic bandgap center of the magnonic crystal. The proposed design of the reconfigurable magnonic crystal creates a condition for the nucleation of the spin-wave bandgap, with further enhancement of the spin-wave reflection from the periodic grating induced by strain. We demonstrate the potential use of the proposed device as a multi-band NAND/NXOR spin-wave based logic gate.

Excitation of exchange spin waves in a magnetic insulator thin film at cryogenic temperatures

Spin waves and their quanta, magnons, are promising candidates for next-generation electronic devices, due to their low-power consumption and compatibility with radio-frequency-based electronic devices. For achieving magnon-based hybrid quantum systems for quantum memory and computation, the investigation of spin-wave propagation at cryogenic temperatures is highly required. In this article, we report the excitation and detection of exchange spin waves with wavelengths of tens of nanometers in an yttrium iron garnet (YIG) thin film at cryogenic temperatures. We find that the exchange spin waves are unidirectional in all temperature ranges, owing to the chiral dynamical dipolar coupling between the spin-wave mode in the YIG and the ferromagnetic resonance mode in the cobalt nanowire. Notably, a high exchange spin-wave group velocity of 2 km s−1 at 10 K is observed. Our results are promising for the development of high-speed and energy-efficient quantum magnonic devices operating at cryogenic temperatures.

Study on microscopic origin of spin excitation in TmFeO3 by time-resolved multicolor optical pump-probe spectroscopy

Spin dynamics of TmFeO3, mainly induced by two different mechanisms, were investigated by time-resolved multicolor pump-probe spectroscopy using femtosecond laser pulses. The spin dynamics, caused either by spin-reorientation phase transition or optical polarization-dependent effect, were distinguished by investigating their dependencies on external magnetic field and optical polarization. Spectral-dependent magneto-optic studies of the spin phase transition-induced spin dynamics revealed that laser-induced nonthermal exchange interaction between the electron states of iron (Fe3+) and thulium (Tm3+) ions is crucial for subsequent spin dynamics. This exchange interaction is influenced by the population change of the 4f electron states of Tm3+ ions, making the spin wave generation highly dependent on crystal temperature. However, spectroscopic studies of the polarization-dependent spin dynamics show that they are only related to the 3d electrons of Fe3+ ions, therefore, the spin dynamics appear to be a universal effect over a wide temperature range. Our observation can be further applied to study extended orthoferrite systems with other rare earth atoms.

Spatial control of hybridization-induced spin-wave transmission stop band

Spin-wave (SW) propagation close to the hybridization-induced transmission stop band is investigated within a trapezoid-shaped 200 nm thick yttrium iron garnet film using time-resolved magneto-optic Kerr effect microscopy and broadband spin-wave spectroscopy, supported by micromagnetic simulations. The gradual reduction of the effective field within the structure leads to local variations of the SW dispersion relation and results in a SW hybridization at a fixed position in the trapezoid where the propagation vanishes, since the SW group velocity approaches zero. By tuning external field or frequency, spatial control of the spatial stop band position and spin-wave propagation is demonstrated and utilized to gain transmission control over several microstrip lines.

Universal scaling between wave speed and size enables nanoscale high-performance reservoir computing based on propagating spin-waves

Physical implementation of neuromorphic computing using spintronics technology has attracted recent attention for the future energy-efficient AI at nanoscales. Reservoir computing (RC) is promising for realizing the neuromorphic computing device. By memorizing past input information and its nonlinear transformation, RC can handle sequential data and perform time-series forecasting and speech recognition. However, the current performance of spintronics RC is poor due to the lack of understanding of its mechanism. Here we demonstrate that nanoscale physical RC using propagating spin waves can achieve high computational power comparable with other state-of-art systems. We develop the theory with response functions to understand the mechanism of high performance. The theory clarifies that wave-based RC generates Volterra series of the input through delayed and nonlinear responses. The delay originates from wave propagation. We find that the scaling of system sizes with the propagation speed of spin waves plays a crucial role in achieving high performance.

Resonant generation of propagating second-harmonic spin waves in nano-waveguides

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

Nonlinear magnonic coupler using backpropagating surface spin waves

We investigated a spin-wave propagation in a magnon-crystal structure formed from two lateral microwaveguides separated by a one-dimensional antidot array. The mechanisms of control of the backpropagating regime of the surface spin waves both with geometry tuning and with power level variation in the case of in-plane magnetization are investigated by the method of micro-magnetic modeling and the experimental method of Brillouin light scattering spectroscopy. It was shown that for the case of spin-waves propagation through the isolated channels the shape anisotropy in the coupling region can be tuned effectively by a variation of the distance between the channels. The regime of nonlinear switching of the signal and backward propagation was observed in microwave and Brillouin spectroscopy measurements. The proposed effect of the signal separation manifests itself in the spatially and frequency-selective regimes of spin-wave propagation. Proposed spin-wave coupler opens an alternative way for the design of the functional interconnections of spin-wave based units in the planar magnonic networks.

Midpoint geometric integrators for inertial magnetization dynamics

We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines a higher-order nonlinear dynamical system with very different nature compared to the classical LLG equation, requiring twice as many degrees of freedom for space-time discretization. It exhibits essential conservation properties, namely magnetization amplitude preservation, magnetization projection conservation, and a balance equation for generalized free energy, leading to a Lyapunov structure (i.e. the free energy is a decreasing function of time) when the external magnetic field is constant in time. We propose two second-order numerical schemes for integrating the iLLG dynamics over time, both based on implicit midpoint rule. The first scheme unconditionally preserves all the conservation properties, making it the preferred choice for simulating inertial magnetization dynamics. However, it implies doubling the number of unknowns, necessitating significant changes in numerical micromagnetic codes and increasing computational costs especially for spatially inhomogeneous dynamics simulations. To address this issue, we present a second time-stepping method that retains the same computational cost as the implicit midpoint rule for classical LLG dynamics while unconditionally preserving magnetization amplitude and projection. Special quasi-Newton techniques are developed for solving the nonlinear system of equations required at each time step due to the implicit nature of both time-steppings. The numerical schemes are validated on analytical solution for macrospin terahertz frequency response and the effectiveness of the second scheme is demonstrated with full micromagnetic simulation of inertial spin waves propagation in a magnetic thin-film.

True amplification of spin waves in magnonic nano-waveguides

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

Magnonic combinatorial memory

In this work, we consider a type of magnetic memory where information is encoded into the mutual arrangement of magnets. The device is an active ring circuit comprising magnetic and electric parts connected in series. The electric part includes a broadband amplifier, phase shifters, and attenuators. The magnetic part is a mesh of magnonic waveguides with magnets placed on the waveguide junctions. There are amplitude and phase conditions for auto-oscillations to occur in the active ring circuit. The frequency(s) of the auto-oscillation and spin wave propagation path(s) in the magnetic part depends on the mutual arrangement of magnets in the mesh. The propagation path is detected with a set of power sensors. The correlation between circuit parameters and spin wave path is the basis of memory operation. The combination of input/output switches connecting electric and magnetic parts and electric phase shifters constitute the memory address. The output of the power sensors is the memory state. We present experimental data on the proof-of-the-concept experiments on the prototype with three magnets placed on top of a single-crystal yttrium iron garnet Y3Fe2(FeO4)3 (YIG) film. There are three selected places for the magnets to be placed. There is a variety of spin wave propagation paths for each configuration of magnets. The results demonstrate a robust operation with an On/Off ratio for path detection exceeding 35 dB at room temperature. The number of possible magnet arrangements scales factorially with the size of the magnetic part. The number of possible paths per one configuration scales factorial as well. It makes it possible to drastically increase the data storage density compared to conventional memory devices. Magnonic combinatorial memory with an array of 100 × 100 magnets can store all information generated by humankind. Physical limits and constraints are also discussed.

Frequency-selective coherent propagating spin waves induced by localized perpendicular magnetic anisotropy nanofilm stack

Magnonics has long been hailed as a promising technology poised to overcome the heat dissipation challenges in traditional electronic devices. With the escalating integration level of magnon devices, the demand arises for lower external field excitation conditions, coupled with enhanced coherence and frequency-selective excitation characteristics. In this proposal, we suggest introducing a localized perpendicular magnetic anisotropy nanofilm stack into the spin-wave transmission channel to finely regulate the propagation characteristics of spin waves. This adjustment can be achieved by altering the width and period of the stack in both horizontal and vertical dimensions. Additionally, the optimal transmission characteristics of spin waves are achieved at low frequencies (1–1.67 GHz) and in the presence of small magnetic fields (0–20 mT). Frequency-selective spin waves with triggering stability can effectively prevent signal folding resulting from changes in microwave power within the range of −30 to 0 dBm. At 1.08 GHz, the group velocity of frequency-selective spin waves can be increased by up to 2.86 times. This innovative method of regulating spin waves presents a potential alternative pathway for the development of future magnonic circuits.

A current-controlled magnonic reservoir for physical reservoir computing

Physical reservoir computers based on principles of magnonics promise energy efficient data processing and a reduction in the size and weight of the neuromorphic computing devices. The present work is a major step toward all-magnonic implementation of the recently proposed concept of a physical reservoir based on the spin wave active ring. The main component of the ring is a spin wave delay line employing a thin film of yttrium iron garnet (YIG) as the spin wave guiding medium. We propose controlling spin wave propagation in the YIG film electronically to enter input data into the reservoir. To this end, we exploit a physical effect of scattering of backward volume spin waves from a highly localized Oersted field of a dc current flowing through a metallic strip sitting on top of the YIG film. We find experimentally that a very small current (on the order of several milliamps) through the strip is able to control the amplitude of auto-oscillations in the ring. The use of the current control of spin wave propagation as a means to enter input data into the reservoir reduces the number of non-magnetic components of the reservoir to just one (a microwave amplifier). In addition, the proposed current-controlled magnonic reservoir demonstrates a record-high short-term memory capacity of 5.53, as our experiments show. Our findings open up an avenue for reduction of energy consumption by magnonic active-ring-based physical reservoirs, their micro-miniaturization, and all-magnonic implementation.

Nanoscopic spin-wave channeling along programmable magnetic domain walls in a CoFeB/BaTiO3 multiferroic heterostructure

We report a micromagnetic study on spin-wave propagation along magnetic domain walls in a ferromagnetic/ferroelectric bilayer. In our system, strain coupling between the two ferroic materials and inverse magnetostriction produce a fully correlated domain pattern wherein straight and narrow ferroelectric domain walls pin the magnetic domain walls. Consequently, an external magnetic field does tailor the spin structure of the magnetic domain walls instead of moving them. We use experimental parameters from a previously studied CoFeB/BaTiO3 material system to investigate the potential of artificial multiferroics for programmable nanoscopic spin-wave channeling. We show that spin waves are transported along the pinned magnetic domain walls at zero magnetic field and low frequency due to a local demagnetizing field. Further, switching of the domain wall spin structure from a head-to-tail to a head-to-head configuration abruptly changes the propagating spin-wave mode. We study the effect of magnetic field strength on the localized modes and discuss reversible control of spin-wave channeling via electric-field-driven magnetic domain wall motion. Nanoscopic guiding of propagating spin waves by an electric field, in combination with positional robustness to and mode programming by an external magnetic field, offers prospects for low-power and reconfigurable domain-wall-based magnonic devices.

Realizing polarization-dependent unidirectional magnon channel in antiferromagnetic domain wall

Achieving unidirectional spin wave (or magnon) transport in domain wall (DW) represents the key step for designing functional magnonic devices. Here, we theoretically investigate the propagation behavior of spin waves (SWs) in antiferromagnetic DW when the Dzyaloshinskii–Moriya interaction (DMI) and/or spin transfer torque (STT) are considered. On the one hand, we find that the DMI lifts the degeneracy of magnon bands, from which one can obtain pure right- or left-handed polarized SWs. On the other hand, the nonreciprocal attenuation of magnons induced by STT is identified. Interestingly, we realize the polarization-dependent unidirectional propagation of SWs when the nonadiabatic coefficient β exceeds a critical value. Moreover, the micromagnetic simulations verify the theoretical predictions with good agreement. Our work provides a simple method for achieving unidirectional magnons with desired polarity in antiferromagnetic DW, which is indispensable for future magnonic computing and communication.

A spin wave driven skyrmion-based diode on a T-shaped nanotrack.

The propagation of spin waves is one of the promising ways to design nanoscale spintronic devices. The spin waves can interact with the magnetic skyrmion, a particle-like object that is topologically stabilized by Dzyaloshinskii-Moriya interaction (DMI) in thin film heterostructures. In this work, a spin wave-driven skyrmion-based diode is proposed by employing a T-shaped ferromagnetic nanotrack. The one-way motion of the skyrmion is achieved by exploiting the mid-arm at the center of the nanotrack. This prevents the reverse motion of the skyrmion owing to the skyrmion Hall effect (SkHE) and the absence of a repulsive force from the far edge in the mid-arm region. In order to facilitate the diode functionality of the spin wave-driven skyrmion, the amplitude and frequency of the excitation field should be considered in the ranges 0.07 T ≤ H0 ≤ 0.4 T and 60 GHz ≤ f ≤ 80 GHz, respectively. The micromagnetic interaction energy between the edges and the spin wave-driven skyrmion creates a potential gradient that induces the force which is responsible for the longitudinal motion of the skyrmion. The suggested spin wave driven diode exhibits a processing speed on the order of 100 m s-1 at 60 GHz frequency and 0.4 T amplitude. Hence, this device paves the way for the development of complete non-charge based magnetic devices for various spintronic applications.