Spin-wave Modes Research Articles

Micromagnetic study of the dynamics of toron chains

This work analyzes the nucleation and stabilization of torons in cylindrical nanopillars with bulk DMI and easy-plane anisotropy. A micromagnetic study reveals the dependence of toron chains on the nanopillar length and the different behaviors when nucleating an even or odd number of torons in a magnetic nanopillar. Spin wave resonant modes in these systems are explored, evidencing differences according to the number of torons. The interplay between torons, chiral bobbers, and their associated spin wave modes is analyzed, which is relevant for applications demanding dynamical modes in the range of gigahertz.

Spin-wave mode coupling in the presence of the demagnetizing field in cobalt-permalloy magnonic crystals

We present the results of studies on the non-uniform frequency shift of spin wave spectrum in a two-dimensional magnonic crystal of cobalt/permalloy under the influence of external magnetic field changes. We investigate the phenomenon of coupling of modes and, as a consequence, their hybridization. By taking advantage of the fact that compressing the crystal structure along the direction of the external magnetic field leads to an enhancement of the demagnetizing field, we analyse its effect on the frequency shift of individual modes depending on their concentration in Co. We show that the consequence of this enhancement is a shift in the coupling of modes towards higher magnetic fields. This provides a potential opportunity to design which pairs of modes and in what range of fields hybridization will occur.

Magnetization States and Coupled Spin-Wave Modes in Concentric Double Nanorings.

Concentric multiple nanorings have previously been fabricated and investigated mainly for their different static magnetization states. Here, we present a theoretical analysis for the magnetization dynamics in double nanorings arranged concentrically, where there is coupling across a nonmagnetic spacer due to the long-range dipole-dipole interactions. We employ a microscopic, or Hamiltonian-based, formalism to study the discrete spin waves that exist in the magnetic states where the individual rings may be in either a vortex or an onion state. Numerical results are shown for the frequencies and the spatial amplitudes (with relative phase included) of the spin-wave modes. Cases are considered in which the magnetic materials of the rings are the same (taken to be permalloy) or two different materials such as permalloy and cobalt. The dependence of these properties on the mean radial position of the spacer were studied, showing, in most cases, the existence of two distinct transition fields. The special cases, where the radial spacer width becomes very small (less than 1 nm) were analyzed to study direct interfaces between dissimilar materials and/or effects of interfacial exchange interactions such as Ruderman-Kittel-Kasuya-Yoshida coupling. These spin-wave properties may be of importance for magnetic switching devices and sensors.

Meron-Mediated Phase Transitions in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy: Successive Transformation of the Hexagonal Skyrmion Lattice into the Square Lattice and into the Tilted FM State.

I revisit the well-known structural transition between hexagonal and square skyrmion lattices and subsequent first-order phase transition into the tilted ferromagnetic state as induced by the increasing easy-plane anisotropy in quasi-two-dimensional chiral magnets. I show that the hexagonal skyrmion order first transforms into a rhombic skyrmion lattice, which, adjusts into a perfect square arrangement of skyrmions ("a square meron-antimeron crystal") within a narrow range of anisotropy values. These transitions are mediated by merons and anti-merons emerging in the boundaries between skyrmion cells; energetically unfavorable anti-merons annihilate, whereas pairs of neighboring merons merge. The tilted ferromagnetic state sets in via mutual annihilation of oppositely charged merons; as an outcome, it contains bimeron clusters (chains) with the attracting inter-soliton potential. Additionally, I demonstrate that domain-wall merons are actively involved in the dynamic response of the square skyrmion lattices. As an example, I theoretically study spin-wave modes and their excitations by AC magnetic fields. Two found resonance peaks are the result of the complex dynamics of the domain-wall merons; whereas in the high-frequency mode the merons rotate counterclockwise, as one might expect, in the low-frequency mode merons are instead created and annihilated consistently with the rotational motion of the domain boundaries.

Dipolar induced nonreciprocal magnon hybridization in FeNi/YIG bilayers

We investigated the magnon hybridization behavior in FeNi films, which were deposited on the yttrium-iron garnet (YIG) films by using Brillouin light scattering. Nonreciprocal magnon hybridizations have been detected not only on the mode densities but also the dispersion relations. The perpendicular standing spin wave mode confined in the thickness direction hybridized with the top surface magnetostatic surface spin wave at smaller wave vectors range while hybridized with the bottom surface mode at larger wave vectors range. The dipolar interaction between the FeNi layer and the YIG layer should be the main reason for the nonreciprocal hybridization of the two modes in the FeNi layer. The nonreciprocal hybridization characteristics of FeNi/YIG double-layer magnetic films enrich the nonreciprocal magnon hybridization system and might have potential application in constructing spin wave-based devices.

Reconfigurable spin-wave properties in two-dimensional magnonic crystals formed of diamond and triangular shaped nanomagnets

Two-dimensional ferromagnetic nanodot structures exhibit intriguing magnetization dynamics and hold promise for future magnonic devices. In this study, we present a comparative experimental investigation into the reconfigurable magnetization dynamics of non-ellipsoidal diamond and triangular-shaped nanodot structures, employing broadband ferromagnetic resonance spectroscopy. Our findings reveal substantial variations in the spin wave (SW) spectra of these structures under different bias field strengths (H) and angles (φ). Notably, the diamond nanodot structure exhibits a variation from nearly symmetric W-shaped dispersion to a skewed dispersion and subsequent transition to a discontinuous dispersion with subtle variation in bias field angle. On the other hand, in the triangular nanodot array a SW mode anti-crossing appears at φ = 15° which is starkly modified with the increase in φ to 30°. By analyzing the static magnetic configurations, we unveil the nature of the SW spectra in these two shapes. We reinforce our observations with simulated spatial power and phase maps. This study underscores the critical impact of dot shape and inversion symmetry on SW dynamical response, highlighting the significance of selecting appropriate structures and bias field strength and orientation for required functionalities. The remarkable tunability demonstrated by the magnonic crystals underscores their potential suitability for future magnonic devices.

Stability and Spin Waves of Skyrmion Tubes in Curved FeGe Nanowires.

In this work, we investigate the influence of curvature on the dynamic susceptibility in FeGe nanowires, both curved and straight, hosting a skyrmionic tube texture under the action of an external bias field, using micromagnetic simulations. Our results demonstrate that both the resonance frequencies and the number of resonant peaks are highly dependent on the curvature of the system. To further understand the nature of the spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases, describing the differences among resonance modes observed. The ability to control the dynamic properties and frequencies of these nanostructures underscores their potential application in frequency-selective magnetic devices.

Manipulation of Magnonic Activity by Electric Currents in Ferromagnetic Nanocylinders

Electric currents passing through ferromagnets can impact the magnetization dynamics via the so-called spin-transfer torque (STT) effect. In this paper, we present a theoretical study on the current influence on magnonic activity, a recently reported spin wave (SW) chiral effect in ferromagnetic nanotubes. By micromagnetic simulations, we show that an electric current can cause a significant change in the rotatory power of the SW modes propagating in a longitudinally magnetized nanotube. This result is well explained by using the Fresnel model in optics assuming a SW circular birefringence. An analytical method is developed to solve the first-order mode, yielding perfect agreements with the numerical results. Our results provide a new approach to manipulate the SW propagating properties in ferromagnetic nanocylinders.

Bright and Dark ILSM in a bilinear and biquadratic antiferromagnetic spin lattice

In the semiclassical limit, we investigate the intrinsic localized spin-wave modes (ILSM) in an antiferromagnetic spin system with bilinear, biquadratic and D-M interactions. Derivation of the nonlinear Schrödinger equation for the coherent-state amplitude involves the introduction of the multiple scale approximation paired with a quasi discreteness approximation. Consequently, we discover that the oscillatory frequency of the Bright–Dark stationary type ILSM’s can appear below the linear spin wave spectrum and the Bright–Dark type kink lies below the upper of the linear spin-wave spectrum. The effect of the interaction parameters in the system is also examined.

Magnetic irreversibility and magnetization processes in Ni5Al3/NiO core/shell nanoparticle system

This work brings out many interesting facets of magnetism in the Ni5Al3/NiO core/shell nanoparticle system. Theweakandstrongmagnetic irreversibility lines (TWI(H)andTSI(H)) reproduce the previously reportedH - Tphase diagram at fieldsH⩽30 Oe, but strong departures occur forH > 30 Oe. Comparison with the theoretically predictedH - Tphase diagram allows us to identifyTWIwithTCG+SG, where the paramagnetic (PM)-chiral glass (CG) and PM-spin glass (SG) phase transitions occursimultaneously, andTSIwithTSG, the temperature at which transition to the replica symmetry breakingSGstate takes place. TheTSI(H)transition line abruptly ends at the point (H≃30 Oe,T≃90K). AsHexceeds 30 Oe, a new transition appears which gets completely suppressed at fieldsH>1 kOewhere the magnetic irreversibility ceases to exist. Nointrinsiclong-range ferromagnetic ordering exists but fields as low as 3 kOe suffice to induce long-range ferromagnetic order. At fixed temperatures, the magnetocrystalline anisotropy fluctuations essentially govern the 'approach-to-saturation' in magnetization for fields in the range 3 - 70 kOe. The present nanocrystalline system behaves as an isotropic system with random easy axis in which the magnetization reversal occurs through the coherent rotation of the magnetizations of weakly-interacting single-domain Ni5Al3particles. Saturation magnetization, likeM(T) atH⩾2 kOe, exhibits an anomalous upturn at temperatures below ≈ 30 K. This upturn is associated with the anomalous softening of spin-wave modes which results in the thermal excitation of a large number of non-equilibrium (finite lifetime) magnons. At sub-Kelvin temperatures, these magnons undergo Bose-Einstein condensation.

Spin waves in antiferromagnetically coupled bilayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

In this paper we analyse quantized spin waves (also referred to as magnons) in bilayers of two-dimensional van der Waals materials, like Vanadium-based dichalcogenides, VX2 (X = S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzyaloshinskii–Moriya interaction and in-plane easy-axis magnetic anisotropy due to symmetry breaking induced externally (e.g. by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc.). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation. Accordingly, the description takes into account quantum antiferromagnetic fluctuations. However, it is limited to linear spinwave modes. The Dzyaloshinskii–Moriya interaction is shown to modify the spin wave spectrum of the bilayers, making its low energy part qualitatively similar to the electronic spectrum of the Rashba spin–orbit model.

The importance of long range Fe–Fe interactions in magnetically ordered 2D Fe0.2Ni0.8/Ni(001) and Fe0.3Ni0.7/Ni(001) alloy systems

We develop a theoretical approach to study the magnonic properties of the 2D ordered surface Fe–Ni alloys with 20% and 30% Fe on a face-centered cubic Ni(001) surface substrate. The surface alloy nanostructures in stable equilibrium are determined by computing the lowest energy configurations of constitutive supercells of the ordered alloys. The magnetic exchange constants of the ground state of the stable systems are calculated to define their Heisenberg Hamiltonians using the DFT Spin-Polarized Relativistic Korringa–Kohn–Rostoker (SPRKKR) method and considering Fe–Fe interactions up to third nearest neighbors. To determine the propagating exchange spin-wave modes, evanescent modes, and the consequent magnonic properties, the spin dynamics of the magnetic surface alloy nanostructures are solved using the phase field matching theory (PFMT). Our results indicate that the Fe–Fe exchange interactions up to third nearest neighbors are vital for accurately describing their magnonics. In particular, the exchange interactions influence the form of dispersion branches for the high-energy spin-wave modes of the Fe–Ni surface alloys considered. Appropriate Green’s functions are also derived from the PFMT method to compute the local densities of states (LDOS) for the atomic sites at the surface boundary. For the case of 20% Fe surface alloy, the Fe–Fe exchange interactions shift the Fe LDOS peaks to lower frequency intervals. We also distinguish the emergence of remarkable LDOS peaks for the he case of the 30% Fe surface alloy at specific Ni sites. These peaks change positions under second and third nearest neighbor Fe–Fe interactions, heralding new accessible spin-wave channels. Our results contribute to establishing a systematic understanding of the magnonics of the magnetic surface alloys of transition metal (TM) materials. This new knowledge will enable the study of the quantum transport of spin waves at interfacial alloy nanojunctions composed of such materials. The present DFT-PFMT theoretical approach is general and can be applied to other surface TM alloy magnetic nanostructures.

Spin–wave dynamics in perpendicularly magnetized antidot multilayers

Using all-optical time-resolved magneto-optical Kerr effect measurements we demonstrate an efficient modulation of the spin–wave (SW) dynamics via the bias magnetic field orientation around nanoscale diamond shaped antidots that are arranged on a square lattice within a [Co(0.75 nm)/Pd(0.9 nm)]8 multilayer with perpendicular magnetic anisotropy (PMA). Micromagnetic modeling of the experimental results reveals that the SW modes in the lower frequency regime are related to narrow shell regions around the antidots, where in-plane (IP) domain structures are formed due to the reduced PMA, caused by Ga+ ion irradiation during the focused ion beam milling process of antidot fabrication. The IP direction of the shell magnetization undergoes a striking change with magnetic field orientation, leading to the sharp variation of the edge localized (shell) SW modes. Nevertheless, the coupling between such edge localized and bulk SWs for different orientations of bias field in PMA systems gives rise to interesting Physics and attests to new prospects for developing energy efficient and hybrid-system-based next-generation nanoscale magnonic devices.

Waveguide modes of exchange spin waves in epitaxial YIG films

It has been shown that exchange spin wave (ESW) waveguide modes can be excited in epitaxial ferrite films. This is facilitated by the presence of a thin transition layer at the interface between the ferrite film and the non-magnetic substrate. A method for calculating the dispersion and energy characteristics of ESW waveguide modes is proposed. It is shown that the propagation of ESW modes is accompanied by the transfer of exchange power in the plane of the film. As the wave numbers increase indefinitely, the dispersion of the ESW modes asymptotically approaches the quadratic dispersion law. At zero wave numbers, the frequencies of the ESW modes coincide with the frequencies of uniform spin wave resonances. The possibility of crossing the dispersion branches of different ESW modes is demonstrated, which indicates the possibility of intermodal magnon-magnon hybridization.

Investigation of phonons and magnons in [Ni80Fe20/Au/Co/Au] N multilayers

The interaction between phonons and magnons is a rapidly developing area of research, particularly in the field of acoustic spintronics. To discuss this interaction, it is necessary to observe two different waves (acoustic and spin waves) with the same frequency and wavelength. In the Ni80Fe20/Au/Co/Au system deposited on a silicon substrate, we observe the interaction between spin waves and surface acoustic waves using Brillouin light scattering spectroscopy. As a result, we can selectively control (activate or deactivate) the magnetoelastic interaction between the fundamental spin wave mode and surface acoustic waves. This is achieved by adjusting the magnetostrictive layer thickness in the multilayer. We demonstrate that by adjusting the number of layers in a multilayer structure, it is possible to precisely control the dispersion of surface acoustic waves while having minimal impact on the fundamental spin wave mode.

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.

Asymmetric Magnon Frequency Comb.

We theoretically show the asymmetric spin wave transmission in a coupled waveguide-skyrmion structure, where the skyrmion acts as an effective nanocavity allowing the whispering gallery modes for magnons. The asymmetry originates from the chiral spin wave mode localized in the circular skyrmion wall. By inputting two-tone excitations and mixing them in the skyrmion wall, we observe a unidirectional output magnon frequency comb propagating in the waveguide with a record number of teeth (>50). This coupled waveguide-cavity structure turns out to be a universal paradigm for generating asymmetric magnon frequency combs, where the cavity can be generalized to other magnetic structures that support the whispering gallery mode of magnons. Our results advance the understanding of the nonlinear interaction between magnons and magnetic textures and open a new pathway to exploring the asymmetric spin wave transmission and to steering the magnon frequency comb.

The role of non-uniform magnetization texture for magnon–magnon coupling in an antidot lattice

We numerically study the spin-wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show a different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon–magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk–rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon–magnon coupling, highlighting the significant role of exchange interactions in the hybridization.

A spin-wave frequency demultiplexer based on YIG nanowaveguides intersecting at a small angle

We experimentally demonstrate a simple design for a spin-wave frequency demultiplexer based on submicrometer-width yttrium iron garnet waveguides intersecting at an angle of 30°. We show that, depending on the frequency, spin waves excited in the input arm of the device are predominantly directed to one of the two output arms. This spin-wave routing is characterized by a large extinction ratio of about 10. The frequency response of the demultiplexer can be efficiently controlled by changing the static magnetic field and the geometry of the device. Due to the small intersection angle and symmetry of the device, its operation does not require conversion between different types of spin-wave modes. This results in a high efficiency of the device and allows its facile integration into magnonic networks for complex signal processing and computing with spin waves.

Generation of localized, half-frequency spin waves in micron sized ferromagnetic stripes: Experiments and simulations

Generation of localized, half-frequency spin waves in micron sized ferromagnetic stripes: Experiments and simulations