Collective Spin Wave Research Articles

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.

Detecting fractionalization in critical spin liquids using color centers

Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024

Brillouin Light Scattering from Magnetic Excitations.

Brillouin light scattering (BLS) has been established as a standard technique to study thermally excited sound waves with frequencies up to ~100 GHz in transparent materials. In BLS experiments, one usually uses a Fabry-Pérot interferometer (FPI) as a spectrometer. The drastic improvement of the FPI contrast factor over 1010 by the development of the multipass type and the tandem multipass type FPIs opened a gateway to investigate low energy excitations (ħω ≤ 1 meV) in various research fields of condensed matter physics, including surface acoustic waves and spin waves from opaque surfaces. Over the last four decades, the BLS technique has been successfully applied to study collective spin waves (SWs) in various types of magnetic structures including thin films, ultrathin films, multilayers, superlattices, and artificially arranged dots and wires using high-contrast FPIs. Now, the BLS technique has been fully established as a unique and powerful technique not only for determination of the basic magnetic constants, including the gyromagnetic ratio, the magnetic anisotropy constants, the magnetization, the SW stiffness constant, and other features of various magnetic materials and structures, but also for investigations into coupling phenomena and surface and interface phenomena in artificial magnetic structures. BLS investigations on the Fe/Cr multilayers, which exhibit ferromagnetic-antiferromagnetic arrangements of the adjacent Fe layer's magnetizations depending on the Cr layer's thickness, played an important role to open the new field known as "spintronics" through the discovery of the giant magnetoresistance (GMR) effect. In this review, I briefly surveyed the historical development of SW studies using the BLS technique and theoretical background, and I concentrated our BLS SW studies performed at Tohoku University and Ishinomaki Senshu University over the last thirty five years. In addition to the ferromagnetic SW studies, the BLS technique can be also applied to investigations of high-frequency magnetization dynamics in superparamagnetic (SPM) nanogranular films in the frequency domain above 10 GHz. One can excite dipole-coupled SPM excitations under external magnetic fields and observe them via the BLS technique. The external field strength determines the SPM excitations' frequencies. By performing a numerical analysis of the BLS spectrum as a function of the external magnetic field and temperature, one can investigate the high-frequency magnetization dynamics in the SPM state and determine the magnetization relaxation parameters.

Nonreciprocal collective magnetostatic wave modes in geometrically asymmetric bilayer structure with nonmagnetic spacer.

Nonreciprocity, i.e. inequivalence in amplitudes and frequencies of spin waves propagating in opposite directions, is a key property underlying functionality in prospective magnonic devices. Here we demonstrate experimentally and theoretically a simple approach to induce frequency nonreciprocity in a magnetostatically coupled ferromagnetic bilayer structure with a nonmagnetic spacer by its geometrical asymmetry. Using Brillouin light scattering, we show the formation of two collective spin wave modes in Fe81Ga19/Cu/Fe81Ga19 structure with different thicknesses of ferromagnetic layers. Experimental reconstruction and theoretical modeling of the dispersions of acoustic and optical collective spin wave modes reveal that both possess nonreciprocity reaching several percent at the wavenumber of 22 × 104 rad cm-1. The analysis demonstrates that the shift of the amplitudes of counter-propagating coupled modes towards either of the layers is responsible for the nonreciprocity because of the pronounced dependence of spin wave frequency on the layers' thickness. The proposed approach enables the design of multilayered ferromagnetic structures with a given spin wave dispersion for magnonic logic gates.

Almost indistinguishable single photons via multiplexing cascaded biphotons with cavity modulation and phase compensation

The cascade-emitted biphotons generated from alkali metal atomic ensembles are an excellent entanglement resource which enables long-distance quantum communication. The communication of quantum information between distant locations can be realized by utilizing the low-loss telecom bandwidth in the upper transition of the cascaded photons in a fiber-based quantum network. Meanwhile, the infrared photon from the lower transition of this highly directional and frequency-correlated biphoton can be created using the four-wave mixing process and can be stored locally as a collective spin wave. Here, we theoretically investigate the frequency entanglement of this biphoton and propose two approaches to remove the two photons' mutual correlations in frequency spaces. The first approach applies an optical cavity which modulates the biphoton spectrum into a more symmetric and narrow spectral function by multiplexing multiple atomic ensembles with phase compensation. The purity of the single photons reaches up to 0.999, and the entanglement entropy $S$ of the biphoton is reduced to 0.006, which is 200 times smaller than the one without multiplexing. The other approach employs a symmetric pumping of the laser fields in two atomic ensembles, which leads to a moderate reduction of $S\ensuremath{\sim}0.3$ when nondiscrimination detection devices are used for both photons. An extremely low frequency entanglement implies an almost indistinguishable single-photon source, which offers a potential resource for photonic quantum emulation and computation.

High-dimensional entanglement between a photon and a multiplexed atomic quantum memory

Multiplexed quantum memories and high-dimensional entanglement can improve the performance of quantum repeaters by promoting the entanglement generation rate and the quantum communication channel capacity. Here, we experimentally generate a high-dimensional entangled state between a photon and a collective spin wave excitation stored in the multiplexed atomic quantum memory. We verify the entanglement dimension by the quantum witness and the entanglement of formation. Then we use the high-dimensional entangled state to test the violation of the Bell-type inequality. Our work provides an effective method to generate multidimensional entanglement between the flying photonic pulses and the atomic quantum interface.

Study of High-Frequency Magneto-Elastic Waves Using a Low-Frequency Alternating Magnetic Field

Magnetically ordered materials belong to systems with broad spectra of collective magnetic oscillations, spin waves, and systems with the highest degree of nonlinearity. We consider the possibility of studying spin waves using high-frequency harmonics, the possibility of parametric excitation of high-frequency collective magnetic oscillations using alternating magnetic fields of the lower frequency. As a model system allowing us to show proof of the principle, we use a system of magnetoelastic waves (MEWs) of high-temperature antiferromagnet with easy-plane anisotropy. The modulation method is used when an additional RF magnetic field was applied to the sample, which yielded satellites at the multiple of the pump field frequency microwave signal that passed the sample in a helix resonator when the parametric pump threshold was exceeded. We observed the process of parametric excitation of MEWs up to 64 harmonics of the pump field at a pump power up to 30 dBm. Our research is of interest for magnetic materials of nano sizes.

Collective spin waves in arrays of asymmetric and symmetric width nanowires: effect of the film layering sequence

We have studied, experimentally and theoretically, the effect of a layering sequence on the magnonic band structure in dense arrays of both asymmetric- and symmetric cross-section tri-layered Py/Cu/Fe and Fe/Cu/Py nanowires. The spin-wave dispersion for these artificial crystals has been measured with Brillouin light scattering (BLS) spectroscopy. We also carried out numerical simulations of the dispersion using an original model employing a 2D Green’s function description of the dynamic dipole field of the precessing magnetization. The presence of the Cu spacer exchange-decouples the two magnetic layers, which stabilizes two equilibrium states of static magnetization. These are the parallel and antiparallel states, for which the static magnetization vectors for the layers are either co-aligned or anti-aligned to each other, respectively. These states are stable in a range of applied fields that depend on the layer width and their ordering in the stack. The magnetization configurations and layers sequence, as well as the presence of acoustic (in-phase) and optic (out-of-phase) spin-wave modes, have a significant impact on the magnonic band structure both in terms of the frequency positions of the dispersive and stationary modes and on their spatial profiles.

Collective spinon spin wave in a magnetized U(1) spin liquid

We study the transverse dynamical spin susceptibility of the two dimensional U(1) spinon Fermi surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed non-interacting spinon approximation. Short-range interaction leads to a new collective mode: a "spinon spin wave" which splits off from the two-spinon continuum at small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing non-zero power law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as $B^{2/3}$ with magnetic field $B$ at low temperature. Our results form the basis for a theory of inelastic neutrons scattering, ESR, and resonant inelastic x-ray scattering (RIXS) studies of this quantum spin liquid state.

Band structure of a one-dimensional bilayer magnonic crystal

The band structure of two coupled one-dimensional (1D) bicomponent magnonic crystals is constructed from theory. The model takes into account both the exchange interaction and the long-range dipolar interaction between the magnonic crystals, for which different coupling configurations are analyzed systematically. In comparison with a monolayer 1D bicomponent magnonic crystal, the band structure of the bilayer magnonic crystal is significantly modified and depends on the geometric positioning between the layers. The widths of the band gaps may be altered considerably to induce a flattening of the high-frequency modes or nonreciprocity in frequency of two counterpropagating collective spin waves. In the latter case, the nonreciprocity is mainly observed in modes with frequencies above the first band gap, whereas the low-frequency modes remain almost reciprocal. These theoretical results show that two coupled magnonic crystals are excellent candidates to assist in controlling the collective spin waves, thereby permitting great versatility in designing reconfigurable spin-based devices.

Collective modes of three-dimensional magnetic structures: A study of target skyrmions

• We explored the three-dimensional (3D) collective modes of target skyrmion under different external magnetic fields. • The three regimes captured by the spectrum calculations directly reflect the ground states of the target skyrmion. • All the collective modes were spatially resolved. • 3D analysis is necessary to understand the collective modes of 3D magnetic structures. Three-dimensional magnetic textures present their richness not only in variety of ground state structures, but also in their dazzling collective modes. As an example, the target skyrmion, a topological spin texture with a central skyrmion and an extra concentric helical ring, has been enabled by confining a chiral magnet in a nanodisk geometry. In this work we investigate the collective spin wave modes of the target skyrmion in the external field region of −400 mT to 400 mT. Through micromagnetic simulations we reproduced three major phases of the target skyrmion, and derived resonance modes at varying external magnetic field by the power spectral density study. All typical modes were resolved in terms of their dynamical snapshots in temporal domain and the corresponding spatial Fourier transformations. Some modes are shown to behave similarly in-plane but differently out-of-plane, and vice versa. This suggests, on a broader scope, that both responses will be necessary to fully characterize collective modes of three-dimensional spin textures.

Reprogrammability and Scalability of Magnonic Fibonacci Quasicrystals

Magnonic quasicrystals can be used to manipulate spin waves, offering possibilities beyond those of periodic magnonic crystals. The authors investigate one-dimensional magnonic Fibonacci quasicrystals and demonstrate the existence of collective spin waves over a broad range of wave vectors. The spin-wave spectra here are tunable by changing magnetic field amplitude (for continuous band-structure adjustment), magnetization configuration (for reprogrammability), or the dimensions of the elements (for scalability). Beyond being fundamentally interesting, these properties show that magnonic quasicrystals are promising for tomorrow's spintronic, microwave, and magnonic technologies.

Magnetic-field-controlled magnon chaos in an active cavity-magnon system

The quantized collective spin waves in a ferrimagnet coupled to an optical cavity have recently proven to be an excellent platform for researching unconventional light–matter interaction. Here, we propose an active cavity-magnon system to study the chaotic dynamics of magnon induced by the intrinsic magnon Kerr nonlinearity. With the experimental attainable parameters, it is clearly shown that our regime enables switching from regular to chaotic motion and vice versa as well as regulating the lifetime of transient chaos just by tuning the external magnetic field, which is ascribed to magnetic-field-controlled magnonical nonlinearity. This investigation offers insight into the underlying physical process of nonlinear magnonic dynamics. In particular, our results pave the way towards exploring magnetic-field-controlled chaos and may find potential applications in secret communication.

Interplay between intra- and inter-nanowires dynamic dipolar interactions in the spin wave band structure of Py/Cu/Py nanowires

We have studied both experimentally and theoretically the reprogrammable spin wave band structure in Permalloy(10 nm)/Cu(5 nm)/Permalloy(30 nm) nanowire arrays of width w = 280 nm and inter-wire separation in the range from 80 to 280 nm. We found that, depending on the inter-wire separation, the anti-parallel configuration, where the magnetizations of the two Permalloy layers point in opposite directions, is stabilized over specific magnetic field ranges thus enabling us to directly compare the band structure with that of the parallel alignment. We show that collective spin waves of the Bloch type propagate through the arrays with different magnonic bandwidths as a consequence of the interplay between the intra- and inter-nanowire dynamic dipolar interactions. A detailed understanding, e.g. whether they have a stationary or propagating character, is achieved by considering the phase relation (in-phase or out-of-phase) between the dynamic magnetizations in the two ferromagnetic layers and their average value. This work opens the path to magnetic field-controlled reconfigurable layered magnonic crystals that can be used for future nanoscale magnon spintronic devices.

Spin wave dispersion and intensity correlation in width-modulated nanowire arrays: A Brillouin light scattering study

Using Brillouin light scattering spectroscopy and dynamical matrix method calculations, we study collective spin waves in dense arrays of periodically double-side width-modulated Permalloy nanowires. Width modulation is achieved by creating a sequence of triangular notches on the two parallel nanowire sides, with a periodicity of p = 1000 nm and a tunable relative displacement (Δ) of the notch sequence on the two lateral sides. Both symmetric (Δ = 0) and asymmetric (Δ = 250 and 500 nm) width-modulated nanowires were investigated. We have found that the detected modes have Bloch-type character and belong to a doublet derived from the splitting of the mode characteristics of the nanowire with the homogeneous width. Interestingly, the amplitude of the magnonic band, the frequency difference of the doublet, and their relative scattering intensity can be efficiently controlled by increasing Δ rather than having single- or symmetric (Δ = 0) double-side width-modulation.

Hybrid Quantum System with Nitrogen-Vacancy Centers in Diamond Coupled to Surface-Phonon Polaritons in Piezomagnetic Superlattices

We investigate a hybrid quantum system where an ensemble of nitrogen-vacancy (NV) centers in diamond is interfaced with a piezomagnetic superlattice that supports surface phonon polaritons (SPhPs). We show that the strong magnetic coupling between the collective spin waves in the NV spin ensemble and the quantized SPhPs can be realized, thanks to the subwavelength nature of the SPhPs and relatively long spin coherence times. The magnon-polariton coupling allows different modes of the SPhPs to be mapped and orthogonally stored in different spatial modes of excitation in the solid medium. Because of its easy implementation and high tunability, the proposed hybrid structure with NV spins and piezoactive superlattices could be used for quantum memory and quantum computation.

Robust Deterministic Controlled Phase-Flip Gate and Controlled-Not Gate Based on Atomic Ensembles Embedded in Double-Sided Optical Cavities

We first propose a scheme for controlled phase-flip gate between a flying photon qubit and the collective spin wave (magnon) of an atomic ensemble assisted by double-sided cavity quantum systems. Then we propose a deterministic controlled-not gate on magnon qubits with parity-check building blocks. Both the gates can be accomplished with 100% success probability in principle. Atomic ensemble is employed so that light-matter coupling is remarkably improved by collective enhancement. We assess the performance of the gates and the results show that they can be faithfully constituted with current experimental techniques.

Collective spin waves in arrays of permalloy nanowires with single-side periodically modulated width

We have experimentally and numerically investigated the dispersion of collective spin waves propagating through arrays of longitudinally magnetized nanowires (NWs) with a periodically modulated width. Two nanowire arrays with single-side modulation and different periodicities of modulation were studied and compared to the nanowires with a homogeneous width. The spin-wave dispersion, measured up to the third Brillouin zone of the reciprocal space, revealed the presence of two dispersive modes for the width-modulated NWs, whose amplitude of the magnonic band depends on the modulation periodicity, and a set of nondispersive modes at higher frequency. These findings are different from those observed in homogeneous width NWs where only the lowest mode exhibits sizeable dispersion. The measured spin-wave dispersion has been satisfactorily reproduced by means of the dynamical matrix method. The results presented in this work are important in view of the possible realization of tunable frequency magnonic devices.

Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves.

We report a demonstration of two-dimensional (2D) terahertz (THz) magnetic resonance spectroscopy using the magnetic fields of two time-delayed THz pulses. We apply the methodology to directly reveal the nonlinear responses of collective spin waves (magnons) in a canted antiferromagnetic crystal. The 2D THz spectra show all of the third-order nonlinear magnon signals including magnon spin echoes, and 2-quantum signals that reveal pairwise correlations between magnons at the Brillouin zone center. We also observe second-order nonlinear magnon signals showing resonance-enhanced second-harmonic and difference-frequency generation. Numerical simulations of the spin dynamics reproduce all of the spectral features in excellent agreement with the experimental 2D THz spectra.

Universal quantum gates for hybrid system assisted by atomic ensembles embedded in double-sided optical cavities

We propose deterministic schemes for controlled-NOT (CNOT), Toffoli, and Fredkin gates between flying photon qubits and the collective spin wave (magnon) of an atomic ensemble inside double-sided optical microcavities. All the gates can be accomplished with 100% success probability in principle and no additional qubit is required. Atomic ensemble is employed so that light-matter coupling is remarkably improved by collective enhancement. We qualified the performance of the gates and the results show that they can be faithfully constituted with current experimental techniques.