Confined Spin Waves Research Articles

Confined spin waves in magnetochiral nanotubes with axial and circumferential magnetization

We report experimental studies of spin-wave excitations in individual 22-nm-thick ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ nanotubes with diameters of about 150 nm. We apply Brillouin light-scattering spectroscopy under microwave irradiation, and we resolve sets of discrete resonances in the center of nanotubes ranging from 2.5 to 12.5 GHz. Comparing to a recent theoretical work and micromagnetic simulations, we identify different characteristic eigenmodes depending on the axial, mixed, or vortex configuration. The mixed and vortex states give rise to modes with helical phase profiles substantiating an unusual nature of confined modes attributed to nonreciprocal spin waves. Our findings provide microscopic insight into realistic tubular spin-wave nanocavities and magnetochiral effects for three-dimensional nanomagnonics.

Brillouin light scattering from quantized spin waves in nanowires with antisymmetric exchange interactions

Antisymmetric exchange interactions lead to non-reciprocal spin-wave propagation. As a result, spin waves confined in a nanostructure are not standing waves; they have a time-dependent phase, because counter-propagating waves of the same frequency have different wavelengths. We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong Dzyaloshinskii-Moriya interactions (DMI). Spin-wave quantization in narrow ($\lesssim 200$ nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines associated with the scattering of light incident transverse to the nanowires. In contrast, the BLS frequency shift associated with the scattering of spin waves propagating along the nanowire length is independent of nanowire width. A model that considers the chiral nature of modes captures this physics and predicts a dramatic reduction in frequency shift of light scattered from higher energy spin waves in narrow wires, which is confirmed by our experiments.

Generation of Microwaves With Tuneable Frequencies in Ultracompact “Magnon Microwave Antenna” via Phonon-Magnon-Photon Coupling

Here, we report a “magnon microwave antenna” (MMA) for the generation of microwaves with tuneable frequencies, based on modulation of confined spin waves (SWs) in the patterned array of magnetostrictive nanomagnets/piezoelectric heterostructures caused by the surface acoustic waves (SAWs). A SAW launched on a piezoelectric substrate produces a periodic strain within the nanomagnets patterned on it, which, in turn, stimulates magnetization precession resulting in different magneto-dynamical resonance modes in the array of nanomagnets with a rich SW texture. The generated SWs (magnons) further interact with the EM radiation (photons) at the SAW frequency. The phonon-magnon-photon coupling in the patterned array of nanowires (NWs) generates a 0.56 GHz microwave frequency with a 13.9 MHz linewidth and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factor of 40, while that in a matrix of nanodots (having same overall area) provides tuneable frequencies leading up to 30 GHz with a linewidth of 59.1 MHz and an enhanced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factor of 439; having nonvolatile spin textures in both the cases. The generated nonvolatile spin textures of the NWs/nanodots can also be useful in energy-efficient logic and low-power computing applications.

Shaping the spin wave spectra of planar 1D magnonic crystals by the geometrical constraints

We present experimental and numerical studies demonstrating the influence of geometrical parameters on the fundamental spin-wave mode in planar 1D magnonic crystals. The investigated magnonic crystals consist of flat stripes separated by air gaps. The adjustment of geometrical parameters allows tailoring of the spin-wave frequencies. The width of stripes and the width of gaps between them affect spin-wave frequencies in two ways. First, directly by geometrical constraints confining the spin waves inside the stripes. Second, indirectly by spin-wave pinning, freeing the spin waves to a different extent on the edges of stripes. Experimentally, the fundamental spin-wave mode frequencies are measured using an all-optical pump-probe time-resolved magneto-optical Kerr-effect setup. Our studies address the problem of spin-wave confinement and spin-wave dipolar pinning in an array of coupled stripes. We show that the frequency of fundamental mode can be tuned to a large extent by adjusting the width of the stripes and the width of gaps between them.

Optimization of Y3Fe5O12 based layered structures for quasi-optic spin wave elements

We present theoretical and experimental results on the losses and confinement of spin waves (SW) in a Ferromagnetic/Normal Metal/Air/Ferrite multilayer structure. The above structure can be used for the creation of a desired topology of static magnetic field in a thin ferrite film, used as SW waveguide. It is shown that a screening Normal Metal (NMe) layer, inserted between SW waveguide and ferromagnetic (FM) layer, significantly decreases the SW losses caused by a lossy FM. It is also shown that the SW amplitude increases within the air gap (d) between a Ferrite film and NMe layer, when the gap satisfies the relation kd = 1, where k is SW wavenumber. The power flow density at Ferrite/Air interface is maximal when d is equal to a quarter wavelength of SW.

Edge spin wave transmission through a vertex domain wall in triangular dots

Spin waves (SWs), being usually reflected by domain walls (DWs), could also be channeled along them. Edge SWs yield the interesting, and potentially applicable to real devices property of broadband spin wave confinement to the edges of the structure. Here, we investigate through numerical simulations the propagation of quasi one-dimensional spin waves in triangle-shaped amorphous YIG (Y3Fe5O12) micron sized ferromagnets as a function of the angle aperture. The edge spin waves (ESWs) have been propagated over the corner in triangles of 2 microns side with a fixed thickness of 85 nm. Parameters such as superior vertex angle (in the range of 40^circ –75^circ ) and applied magnetic field have been optimized in order to obtain a higher transmission coefficient of the ESWs over the triangle vertex. We observed that for a certain aperture angle for which dominated ESW frequency coincides with one of the localized DW modes, the transmission is maximized near one and the phase shift drops to pi /2 indicating resonant transmission of ESWs through the upper corner. We compare the obtained results with existing theoretical models. These results could contribute to the development of novel basic elements for spin wave computing.

Merging of spin-wave modes in obliquely magnetized circular nanodots

Magnetic nanoelements attract great interest due to their prospects for data storage and signal processing. Spin-wave confinement in these elements implies wave-number quantization, discrete frequency spectra and thus complex resonance patterns, strongly dependent on the elements' geometry and static magnetic configuration. Here we report experimental observation of unconventional single-frequency resonance response of flat circular Permalloy nanodots, which is achieved via the application of a magnetic field at a certain critical angle ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\theta}}}_{B}$ with respect to the dot normal. This observation is explained as the merging of spin-wave eigenmodes under the transition of the spin-wave dispersion from the forward-volume to the backward-volume type, as elucidated by micromagnetic simulations in conjunction with an analytical theory. Our results offer a way for the creation of spin-wave systems with spectrally narrow magnetic noise.

Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu$_2$OSeO$_3$ by means of introducing asymmetry on their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy we observe confined spin waves up to eleventh order in bulk Cu$_2$OSeO$_3$ in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to (47.2 $\pm$ 0.05) nm attributed to the exchange interaction modulation. Our results suggest DMI to be effective to create exchange spin waves in a bulk sample without the challenging nanofabrication and thereby to explore their scattering with noncollinear spin textures.

Electrical characterisation of higher order spin wave modes in vortex-based magnetic tunnel junctions

NiFe-based vortex spin-torque nano-oscillators (STNO) have been shown to be rich dynamic systems which can operate as efficient frequency generators and detectors, but with a limitation in frequency determined by the gyrotropic frequency, typically sub-GHz. In this report, we present a detailed analysis of the nature of the higher order spin wave modes which exist in the Super High Frequency range (3–30 GHz). This is achieved via micromagnetic simulations and electrical characterisation in magnetic tunnel junctions, both directly via the spin-diode effect and indirectly via the measurement of the coupling with the gyrotropic critical current. The excitation mechanism and spatial profile of the modes are shown to have a complex dependence on the vortex core position. Additionally, the inter-mode coupling between the fundamental gyrotropic mode and the higher order modes is shown to reduce or enhance the effective damping depending upon the sense of propagation of the confined spin wave.

Confined magnetoelastic waves in thin waveguides

The characteristics of confined magnetoelastic waves in nanoscale ferromagnetic magnetostrictive waveguides have been investigated by a combination of analytical and numerical calculations. The presence of both magnetostriction and inverse magnetostriction leads to the coupling between confined spin waves and elastic Lamb waves. Numerical simulations of the coupled system have been used to extract the dispersion relations of the magnetoelastic waves as well as their mode profiles.

Graded index confined spin waves in a mixed Bloch-Néel domain wall

We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle $\ensuremath{\alpha}$ $(0&lt;\ensuremath{\alpha}&lt;\ensuremath{\pi}/2 \mathrm{radians})$ between domains. The model is obtained from the linearized Bloch equations of motion and under reasonable assumptions that can apply to the scenario of a thick (80 nm) magnetic patch, which simplifies the calculations without a high impact on the model accuracy. The model shows that there is a clear dependence of the local wave number of the confined spin wave on the local angle of domain magnetization with respect to the wall and on the excitation magnetic field frequency. From this model, we can define a local mode index in the wall as a function of such angle and excitation frequency. Therefore, the model can be applied to 1D propagating modes, although it also has physical implications for 2D scenarios where a domain wall merges with a saturated magnetic region. Micromagnetic simulations are in good agreement with the predictions of the model. Our model can also give insight on the effects that curved edge structures may have on the propagating characteristics of spin waves bounded in domain walls.

Hippopede curves for modeling radial spin waves in an azimuthally graded magnonic landscape

We propose a mathematical model for describing radially propagating spin waves emitted from the core region in a magnetic patch with n vertices in a magnetic vortex state. The azimuthal anisotropic propagation of surface spin waves (SSW) into the domain, and confined spin waves (or Winter's Magnons, WM) in domain walls increases the complexity of the magnonic landscape. In order to understand the spin wave propagation in these systems, we first use an approach based on geometrical curves called 'hippopedes', however it provides no insight into the underlying physics. Analytical models rely on generalized expressions from the dispersion relation of SSW with an arbitrary angle between magnetization M and wavenumber k. The derived algebraic expression for the azimuthal dispersion is found to be equivalent to that of the 'hippopede' curves. The fitting curves from the model yield a spin wave wavelength for any given azimuthal direction, number of patch vertices and excitation frequency, showing a connection with fundamental physics of exchange dominated surface spin waves. Analytical results show good agreement with micromagnetic simulations and can be easily extrapolated to any n-corner patch geometry.

Localized spin waves at low temperatures in a cobalt carbide nanocomposite

We study magnetic, transport, and thermal properties of Co2C and Co3C nanocomposites mixed in a 1:1 ratio. The nanocomposite has clusters with an average diameter of 40 ± 15 nm. We show that the behavior of the nanocomposite is completely different from that of only Co3C or Co2C. We observed that with decreasing temperature, the saturation magnetization MS(T) increases, with a steep rise seen below 100 K. A detailed analysis shows that the increase in MS(T) down to 100 K is explained via a surface spin freezing model. However, below 100 K, the steep increase in MS(T) is explained by a finite size effect related to the confinement of spin waves within nanoparticles. Heat capacity measurements show a broad peak at 100 K along with a low temperature anomaly at 43 K (=Tex). Resistance measurements of the nanocomposite show metallic behavior at high T with an anomalous feature appearing at Tex, which is near the T regime, where MS(T) begins to increase steeply. A measurement of the temperature gradients across the sample thickness indicates an abrupt change in thermal conductivity at Tex. Our results suggest a transformation from a magnetically coupled state with a continuous spectrum of spin waves into a magnetically decoupled state below 100 K with confined spin waves.

Brillouin-Mandelstam spectroscopy of stress-modulated spatially confined spin waves in Ni thin films on piezoelectric substrates

We report the results of micro-Brillouin-Mandelstam light scattering spectroscopy of thermal magnons in the two-phase synthetic multiferroic structure consisting of a piezoelectric [Pb(Mg1/3Nb2/3)O3](1−x)–[PbTiO3]x (PMN-PT) substrate and a Ni thin film. The experimental data reveal the first two modes of the perpendicular standing spin waves (PSSW) spatially confined across the Ni thin film. A theoretical analysis of the frequency dependence of the PSSW peaks on the external magnetic field reveals the asymmetric boundary condition, i.e. pinning, for variable magnetization at different surfaces of the Ni thin film. The strain field induced by applying DC voltage to PMN-PT substrate leads to a downshift of PSSW mode frequency owing to the magneto-elastic effect in Ni, and corresponding changes in the spin-wave resonance conditions. The observed non-monotonic dependence of the PSSW frequency on DC voltage is related to an abrupt change of the pinning parameter at certain values of the voltage. The obtained results are important for understanding the thermal magnon spectrum in ferromagnetic films and the development of the low-power spin-wave devices and quantum sensors.

Spin-wave confinement and coupling in organic-based magnetic nanostructures

Vanadium tetracyanoethylene (V[TCNE]x) is an organic-based ferrimagnet that exhibits robust magnetic ordering (TC of over 600 K), high quality-factor (high-Q) microwave resonance (Q up to 3500), and compatibility with a wide variety of substrates and encapsulation technologies. Here, we substantially expand the potential scope and impact of this emerging material by demonstrating the ability to produce engineered nanostructures with tailored magnetic anisotropy that serve as a platform for the exploration of cavity magnonics, revealing strongly coupled quantum confined standing wave modes that can be tuned into and out of resonance with an applied magnetic field. Specifically, time-domain micromagnetic simulations of these nanostructures faithfully reproduce the experimentally measured spectra, including the quasiuniform mode and higher-order spin-wave (magnon) modes. Finally, when the two dominant magnon modes present in the spectra are brought into resonance by varying the orientation of the in-plane magnetic field, we observe anticrossing behavior, indicating strong coherent coupling between these two magnon modes at room temperature. These results position V[TCNE]x as a leading candidate for the development of coherent magnonics, with potential applications ranging from microwave electronics to quantum information.

Theory for the spin dynamics in ultrathin disordered binary magnetic alloy films: Application to cobalt-gadolinium

Abstract We present the theory of a dynamic variant of the non-local coherent potential approximation (DNLCPA) to investigate the spin dynamics in ultrathin magnetic cobalt-gadolinium random alloy films Co 1 - c Gd c n , n atomic monolayers being their thickness. This novel theoretical approach in the classical spin wave representation introduces the idea for the scattering potential of a defect as an operator built up from the phase matching of the spin dynamics on the defect site with the spin dynamics in an otherwise virtual crystal. The scattering potentials are then used to establish a dynamic formulation of the CPA employing the Dyson’s formalism. A mathematical approach is rigorously developed to solve analytically the Dyson T-matrix equation, and determine the unique physical solution for the configurationally averaged Green’s function propagator of the disordered system. The DNLCPA numerical calculations for the Co 1 - c Gd c n systems yield the characteristic eigenmodes and energy dispersion curves of the confined spin wave excitations and their corresponding lifetimes, for arbitrary alloy concentration and diverse film thickness. Our theoretical results for the lifetimes of spin waves depend strongly on their wave vectors, and are in general agreement with recent experimental data. The developed DNLCPA theoretical method is general and can be applied to compute the spin dynamics for any magnetic random binary alloy nanostructure.

Selective Excitation of Localized Spin-Wave Modes by Optically Pumped Surface Acoustic Waves

We explore the feasibility of exciting localized spin-wave modes in ferromagnetic nanostructures using surface acoustic waves. The time-resolved Faraday effect is used to probe the magnetization dynamics of an array of nickel nanowires. The optical-pump pulse excites both spin-wave modes of the nanowires and acoustic modes of the substrate and we observe that, when the frequencies of these modes coincide, the amplitude of magnetization dynamics is substantially enhanced due to magnetoelastic coupling between the two. Notably, by tuning the magnitude of an externally applied magnetic field, optically excited surface acoustic waves can selectively excite either the upper or lower branches of a splitting in the nanowire’s spin-wave spectrum, which micromagnetic simulations indicate is caused by localization of spin waves in different parts of the nanowire. Thus, our results indicate the feasibility of using acoustic waves to selectively excite spatially confined spin waves, an approach that may find utility in future magnonic devices where coherent structural deformations could be used as coherent sources of propagating spin waves.

Incoherent Nuclear Resonant Scattering from a Standing Spin Wave

We introduce a method to study the spatial profiles of standing spin waves in ferromagnetic microstructures. The method relies on Nuclear Resonant Scattering of 57Fe using a microfocused beam of synchrotron radiation, the transverse coherence length of which is smaller than the length scale of lateral variations in the magnetization dynamics. Using this experimental method, the nuclear resonant scattering signal due to a confined spin wave is determined on the basis of an incoherent superposition model. From the fits of the Nuclear Resonant Scattering time spectra, the precessional amplitude profile across the stripe predicted by an analytical model is reconstructed. Our results pave the way for studying non-homogeneous dynamic spin configurations in microstructured magnetic systems using nuclear resonant scattering of synchrotron light.

Eavesdropping on spin waves inside the domain-wall nanochannel via three-magnon processes

One recent breakthrough in the field of magnonics is the experimental realization of reconfigurable spin-wave nanochannels formed by magnetic domain wall with a width of $10-100$ nm [Wagner \emph{et al}., Nat. Nano. \textbf{11}, 432 (2016)]. This remarkable progress enables an energy-efficient spin-wave propagation with a well-defined wave vector along its propagating path inside the wall. In the mentioned experiment, a micro-focus Brillouin light scattering spectroscopy was taken in a line-scans manner to measure the frequency of the bounded spin wave. Due to their localization nature, the confined spin waves can hardly be detected from outside the wall channel, which guarantees the information security to some extent. In this work, we theoretically propose a scheme to detect/eavesdrop on the spin waves inside the domain-wall nanochannel via nonlinear three-magnon processes. We send a spin wave in one magnetic domain to interact with the bounded mode in the wall. Two kinds of three-magnon processes, i.e., confluence and splitting, are expected to occur. The confluence process is conventional. We predict a stimulated three-magnon splitting (or "magnon laser") effect: the presence of a bound magnon propagating along the domain wall channel assists the splitting of the incident wave into two modes, one of which is identical to the bound mode in the channel. Micromagnetic simulations confirm our theoretical analysis. These results demonstrate that one is able to uniquely infer the spectrum of the spin-wave in the domain-wall nanochannel once we know both the injection and the transmitted waves.

Voltage-Controlled Reconfigurable Spin-Wave Nanochannels and Logic Devices

Though confinement of spin waves (SWs) through nanochannels (NCs) is essential for the development of magnonic logic hardware, voltage-controlled reconfigurable SW nanochannels and logic devices have remained elusive. Here numerical micromagnetic simulations show that NCs of arbitrary shape and size, down to a few tens of nanometers, can be easily configured to transmit SWs with variable wave vectors as needed, even in the absence of a magnetic field. Operation of reconfigurable logic devices using the NCs is also demonstrated. This study is expected to have a large impact on the development of all-voltage-controlled low-power nanoscale magnonic devices.