Collective Spin-wave Modes Research Articles

Theory of Collective Excitations in the Quadruple-Q Magnetic Hedgehog Lattices.

Hedgehog and antihedgehog spin textures in magnets behave as emergent monopoles and antimonopoles, which give rise to astonishing transport and electromagnetic phenomena. Using the Kondo-lattice model in three dimensions, we theoretically study collective spin-wave excitation modes of magnetic hedgehog lattices which have recently been discovered in itinerant magnets such as MnSi_{1-x}Ge_{x} and SrFeO_{3}. It is revealed that the spin-wave modes, which appear in the subterahertz regime, have dominant amplitudes localized at Dirac strings connecting hedgehog-antihedgehog pairs and are characterized by their translational oscillations. It is found that their spectral features sensitively depend on the number and configuration of the Dirac strings and, thus, can be exploited for identifying the topological phase transitions associated with the monopole-antimonopole pair annihilations.

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

Observation and control of collective spin-wave mode hybridization in chevron arrays and in square, staircase, and brickwork artificial spin ices

Dipolar magnon-magnon coupling has long been predicted in nanopatterned artificial spin systems. However, observation of such phenomena and related collective spin-wave signatures have until recently proved elusive or been limited to low-power edge modes which are difficult to measure experimentally. Here we describe the requisite conditions for dipolar mode-hybridization, how it may be controlled, why it was not observed earlier, and how strong coupling may occur between nanomagnet bulk modes. We experimentally investigate four nanopatterned artificial spin system geometries: chevron arrays, square, staircase, and brickwork artificial spin ices. We observe significant dynamic dipolar-coupling in all systems with relative coupling strengths and avoided-crossing gaps supported by micromagnetic-simulation results. We demonstrate reconfigurable mode-hybridization regimes in each system via microstate control, and in doing so elucidate the underlying dynamics governing dynamic dipolar-coupling with implications across reconfigurable magnonics. We demonstrate that confinement of the bulk modes via edge effects plays a critical role in dipolar hybridized modes, and treating each nanoisland as a coherently precessing macro-spin or a standing spin-wave is insufficient to capture experimentally observed coupling phenomena. Finally, we present a parameter-space search detailing how coupling strength may be tuned via nanofabrication dimensions and material properties.

Spin waves in doped graphene: A time-dependent spin density functional approach to collective excitations in paramagnetic two-dimensional Dirac fermion gases

In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We consider here spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin density functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sj\"olander approximations. We obtain spin-wave dispersions and spin stiffnesses as a function of doping and spin polarization, and we discuss the prospects for their experimental observation.

Collective and localized modes in 3D magnonic crystals

Numerical results of spin-wave resonance excitations and spin-wave propagation in the meander-type YIG waveguide are presented. By the variation of the in-plane magnetization angle, we show that ferromagnetic resonance spectra essentially depend on the total height of the meander in the case of different magnetic field orientation with respect to meander segments. We demonstrate that the gradients of inhomogeneous static magnetic fields can lead to the effective generation of short-wavelength dipole-exchange waves having non-resonant spatial distribution. We show that the collective and localized spin-wave modes can be simultaneously excited in 3D magnonic crystals. We believe that obtained results will provide the basis for the development of 3D-elements for reconfigurable magnonic and spintronic devices with extended frequency tunability.

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.

Exact Formulation of the Transverse Dynamic Spin Susceptibility as an Initial-Value Problem

The transverse dynamic spin susceptibility is a correlation function that yields exact information about spin excitations in systems with a collinear magnetic ground state, including collective spin-wave modes. In an ab initio context, it may be calculated within many-body perturbation theory or time-dependent density-functional theory, but the quantitative accuracy is currently limited by the available functionals for exchange and correlation in dynamically evolving systems. To circumvent this limitation, the spin susceptibility is here alternatively formulated as the solution of an initial-value problem. In this way, the challenge of accurately describing exchange and correlation in many-electron systems is shifted to the stationary initial state, which is much better understood. The proposed scheme further requires the choice of an auxiliary basis set, which determines the speed of convergence but always allows systematic convergence in practical implementations.

ChemInform Abstract: Magnetic Nanoparticles: a Subject for Both Fundamental Research and Applications

AbstractReview: 167 refs.

Bias-free spin-wave phase shifter for magnonic logic

A design of a magnonic phase shifter operating without an external bias magnetic field is proposed. The phase shifter uses a localized collective spin wave mode propagating along a domain wall “waveguide” in a dipolarly-coupled magnetic dot array with a chessboard antiferromagnetic (CAFM) ground state. It is demonstrated numerically that the remagnetization of a single magnetic dot adjacent to the domain wall waveguide introduces a controllable phase shift in the propagating spin wave mode without significant change to the mode amplitude. It is also demonstrated that a logic XOR gate can be realized in the same system.

Dynamical current-induced ferromagnetic and antiferromagnetic resonances

We demonstrate that ferromagnetic and antiferromagnetic excitations can be triggered by the dynamical spin accumulations induced by the bulk and surface contributions of the spin Hall effect. Due to the spin-orbit interaction, a time-dependent spin density is generated by an oscillatory electric field applied parallel to the atomic planes of Fe/W(110) multilayers. For symmetric trilayers of Fe/W/Fe in which the Fe layers are ferromagnetically coupled, we demonstrate that only the collective out-of-phase precession mode is excited, while the uniform (in-phase) mode remains silent. When they are antiferromagnetically coupled, the oscillatory electric field sets the Fe magnetizations into elliptical precession motions with opposite angular velocities. The manipulation of different collective spin-wave dynamical modes through the engineering of the multilayers and their thicknesses may be used to develop ultrafast spintronics devices. Our work provides a general framework that probes the realistic responses of materials in the time or frequency domain.

Collective spin excitation in finite size array of patterned magnonic crystals

We explore further details of the collectively excited spin wave mode in finite arrays of elliptically shaped ferromagnetic nanoelements as two-dimensional magnonic crystals by means of micromagnetic simulations. Under a pulsed magnetic driving field, collective spin wave modes were intensively investigated with variation of nanoelement dimensions and interelement separation as structural parameters of the magnonic crystal as well as changing the applied bias magnetic field. Via observing and analyzing the dynamic behavior of collective spin wave modes, we have found that the dynamic behavior strongly depends on the bias magnetic field with a quasi-linear dependency. The quasi-linear dependency of spin wave frequency transition can be achieved to a high sensitivity of the pT/Hz level. By modulating the magnonic crystal lattice structures and the bias magnetic field, the spin wave dynamic behavior is tunable which might be a promising property for a future magnonic crystal application and multifunctional sensors.

Influence of the properties of soft collective spin wave modes on the magnetization reversal in finite arrays of dipolarly coupled magnetic dots

Magnetization reversal in finite chains and square arrays of closely packed cylindrical magnetic dots, having vortex ground state in the absence of the external bias field, has been studied experimentally by measuring static hysteresis loops, and also analyzed theoretically. It has been shown that the field Bn of a vortex nucleation in a dot as a function of the finite number N of dots in the array's side may exhibit a monotonic or an oscillatory behavior depending on the array geometry and the direction of the external bias magnetic field. The oscillations in the dependence Bn(N) are shown to be caused by the quantization of the collective soft spin wave mode, which corresponds to the vortex nucleation in a finite array of dots. These oscillations are directly related to the form and symmetry of the dispersion law of the soft SW mode: the oscillation could appear only if the minimum of the soft mode spectrum is not located at any of the symmetric points inside the first Brillouin zone of the array's lattice. Thus, the purely static measurements of the hysteresis loops in finite arrays of coupled magnetic dots can yield important information about the properties of the collective spin wave excitations in these arrays.

Multiplets of Collective Spin-Wave Modes During Magnetization Reversal in a One-Dimensional Magnonic Crystal Consisting of Alternating-Width Nano-Stripes

We have studied the field evolution of spin waves frequency in a dense array of dipolarly interacting magnetic stripes of alternating widths during the magnetization reversal process by Brillouin light scattering technique. This represents a model system of a one-dimensional magnonic crystal which can sustain collective spin excitations. Their frequencies have been accounted for by a simple analytical approach when all the stripes are in the coaligned magnetization state. Each excitation of the array observed in the magnetically saturated state splits into either a doublet or a triplet in the field range where the inversion of the stripe magnetization takes place. This has been interpreted as due to the simultaneous presence, within the probed region, of clusters of adjacent stripes with either parallel or antiparallel magnetization.

Universal spin dynamics in two-dimensional Fermi gases

Experiments with ultracold atomic gases can provide insight into more general phenomena, such as spin transport. A study of spin diffusion in a two-dimensional Fermi gas measured the lowest spin diffusion constant so far, approaching its quantum-limited value. Harnessing spins as information carriers has emerged as an elegant extension to the transport of electrical charges1. The coherence of such spin transport in spintronic circuits is determined by the lifetime of spin excitations and by spin diffusion. Fermionic quantum gases allow the study of spin transport from first principles because interactions can be precisely tailored and the dynamics is on directly observable timescales2,3,4,5,6,7,8,9,10,11,12. In particular, at unitarity, spin transport is dictated by diffusion and the spin diffusivity is expected to reach a universal, quantum-limited value on the order of the reduced Planck constant ħ divided by the mass m. Here, we study a two-dimensional Fermi gas after a quench into a metastable, transversely polarized state. Using the spin-echo technique13, for strong interactions, we measure the lowest transverse spin diffusion constant14,15 so far 6.3 (8) × 10-3 ħ/m. For weak interactions, we observe a collective transverse spin-wave mode that exhibits mode softening when approaching the strongly interacting regime.

Theory of ground-state switching in an array of magnetic nanodots by application of a short external magnetic field pulse

A theory of a ground-state switching in an array of axially magnetized cylindrical magnetic dots arranged in a square lattice is developed. An array can be switched into a quasiregular chessboard-antiferromagnetic state by the application of a short pulse of external in-plane magnetic field having a sufficiently long trailing front. The statistical properties of an array magnetization in its final (after switching) state are determined at the linear stage of growth of unstable collective spin-wave modes of the array under the action of a time-dependent magnetic field, and depend critically on the rate of the field decrease: the slower this decrease, the more regular is the final magnetization state. An analytical procedure is presented that allows one to relate the statistical properties of the final demagnetized state of the array and the linewidth of the array's microwave absorption to the parameters of the external switching pulse. The comparison of the developed analytic theory with the results of numerical simulations is presented and demonstrates good agreement between analytical and numerical results.

Magnetic Nanoparticles: A Subject for Both Fundamental Research and Applications

Single domain magnetic nanoparticles (MNPs) have been a vivid subject of intense research for the last fifty years. Preparation of magnetic nanoparticles and nanostructures has been achieved by both bottom‐up and top‐down approaches. Single domain MNPs show Néel‐Brown‐like relaxation. The Stoner‐Wohlfarth model describes the angular dependence of the switching of the magnetization of a single domain particle in applied magnetic fields. By varying the spacing between the particles, the inter‐particle interactions can be tuned. This leads to various supermagnetic states such as superparamagnetism, superspin glass, and superferromagnetism. Recently, the study of the magnetization dynamics of such single domain MNPs has attracted particular attention, and observations of various collective spin wave modes in patterned nanomagnet arrays have opened new avenues for on‐chip microwave communications. MNPs have the potential for various other applications such as future recording media and in medicine. We will discuss the various aspects involved in the research on MNPs.

Magnetic hysteresis of dynamic response of one-dimensional magnonic crystals consisting of homogenous and alternating width nanowires observed with broadband ferromagnetic resonance

We systematically probed the dynamic behavior of homogenous and alternating width (AW) Ni${}_{80}$Fe${}_{20}$ nanowire (NW) arrays using broadband ferromagnetic resonance (FMR) spectroscopy as a function of geometrical parameters such as wire width and interwire spacing. For homogenous width NWs, the FMR responses are markedly sensitive to wire widths and interwire spacing due to spatially varying demagnetizing field. The collective spin-wave mode profile for ferromagneticly and antiferromagneticly ordered ground state has been investigated by controlling the relative alignment of magnetization of neighboring NWs. We show that magnetic ground states of coupled AW NW arrays can be controlled by applying different magnetic field histories, and the collective spin-wave mode is very sensitive to the difference in the widths of wires constituting AW wire arrays. We have also mapped the ferromagnetic and antiferromagnetic ground states magnetic configurations using magnetic force microscopy. Our experimental results are in good agreements with a simple analytical theory we suggest for phenomenological description of the collective oscillations.

Magnonic Crystal as a Medium with Tunable Disorder on a Periodical Lattice

We show that periodic magnetic nanostructures represent a perfect system for studying excitations on disordered periodical lattices because of the possibility of controlled variation of the degree of disorder by varying the applied magnetic field. Magnetic force microscopy images and ferromagnetic resonance (FMR) data collected inside minor hysteresis loops for a periodic array of Permalloy nanowires were used to demonstrate correlation between the type of FMR response and the degree of disorder of the magnetic ground state.

Linear and nonlinear collective modes in magnetic microstructures formed by coupled disks

We have experimentally studied the collective spin-wave modes in microscopic magnetic structures formed by Permalloy disks, connected to each other by nanobridges. By using Brillouin light-scattering spectroscopy, we were able clearly to identify in-phase and out-of-phase modes and investigate their characteristics over wide intervals of the static magnetic field and the strength of the excitation signal. Our results show that the main characteristics of the modes are practically independent of the static field and the geometry of bridges, but are significantly affected by the nonlinearity.

Dipolar spin waves of lateral magnetic superlattices

We investigate the high-frequency dynamics of dysprosium and cobalt gratings fabricated at the surface of a $\text{GaAs}/{\text{Al}}_{0.33}{\text{Ga}}_{0.67}\text{As}$ heterojunction. We detect the collective and localized spin-wave modes of the grating by measuring the photovoltage and the photoresistance induced in the two-dimensional electron gas (2DEG). The magnetic excitations couple to the 2DEG through their stray magnetic field. We perform a spectroscopy of dipolar-exchange spin waves as a function of microwave power, temperature, the tilt angle of the applied magnetic field, and by varying the structural and material parameters to change the strength of dipolar interactions. The data reveal two types of spin waves. Dipolar magnetization waves propagate across the grating through the magnetostatic interaction between the stripes. We derive an analytical expression of their dispersion curve and obtain a good fit of the ferromagnetic resonance broadening from first principles. The second type is dipolar edge spin waves which manifest through a series of sharp resonances at lower magnetic field. These waves are confined near the pole surfaces and interact very little with neighboring stripes. We calculate the eigenfrequencies of the quantized modes and obtain a qualitative explanation of the low-field resonances. The fit yields a value of the exchange stiffness constant of dysprosium, $A=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{J}\text{ }{\text{m}}^{\ensuremath{-}1}$. Our experiments show that photovoltage measurements in hybrid semiconductor-ferromagnetic structures provide a sensitive and noninvasive tool for probing the spin waves of small magnets (10--500 nm).